Drinking Water Treatment Sludge Production and Dewaterability

DRINKING WATER TREATMENT SLUDGE PRODUCTION AND DEWATERABILITY

David Ignatius Verrelli BA, BE(Chemical) Hons. (Monash)

Submitted in total fulfilment of the requirements of the degree of Doctor of Philosophy November 2008

Particulate Fluids Processing Centre Department of Chemical & Biomolecular Engineering The University of Melbourne

Drinking Water Treatment Sludge Production and Dewaterability

David Ignatius Verrelli

D. I. Verrelli Melbourne

National Library of Australia Cataloguing-in-Publication entry Author:

Verrelli, David Ignatius, 1977-

Title:

Drinking water treatment sludge production and dewaterability [electronic resource] / David Ignatius Verrelli.

ISBN:

9780980629729 (pdf.)

Notes:

Bibliography.

Subjects:

Drinking water--Purification. Water--Purification. Water treatment plant residuals. Water treatment plants--Waste disposal. Water treatment plant residuals--Management.

Dewey Number:

628.162

ISBN 978-0-9806297-0-5

(hard bound in 2 volumes)

ISBN 978-0-9806297-1-2

(soft bound in 2 volumes)

ISBN 978-0-9806297-2-9

(PDF, single file)

© D. I. Verrelli November 2008, March 2009, April 2009 Copying and printing are permitted for personal and approved uses. The author’s moral rights are asserted.

SUMMARY

The provision of clean d r i n k i n g w a t e r typically involves t r e a t m e n t processes to remove contaminants.

The conventional process involves coagulation with hydrolysing

metal salts, typically of aluminium (‘alum’) or trivalent iron (‘ferric’).

Along with the

product water this also produces a waste by-product, or s l u d g e . The fact of increasing sludge p r o d u c t i o n — due to higher levels of treatment and greater volume of water supply — conflicts with modern demands for environmental best practice, leading to higher financial costs. A further issue is the significant quantity of water that is held up in the sludge, and wasted.

One means of dealing with these problems is to dewater the sludge further. This reduces the volume of waste to be disposed of. The consistency is also improved (e.g. for the purpose of landfilling).

And a significant amount of water can be recovered.

The efficiency, and

efficacy, of this process depends on the d e w a t e r a b i l i t y of the sludge. In fact, good dewaterability is vital to the operation of conventional drinking water treatment plants (WTP’s). The usual process of separating the particulates, formed from a blend of contaminants and coagulated precipitate, relies on ‘clarification’ and ‘thickening’, which are essentially settling operations of solid–liquid separation. WTP operators — and researchers — do attempt to measure sludge dewaterability, but usually rely on empirical characterisation techniques that do not tell the full story and can even mislead. Understanding of the physical and chemical nature of the sludge is also surprisingly rudimentary, considering the long history of these processes.

The present work begins by reviewing the current state of knowledge on raw water and sludge composition, with special focus on solid aluminium and iron phases and on fractal aggregate structure.

Next the theory of dewatering is examined, with the adopted

phenomenological theory contrasted with empirical techniques and other theories.

i

D. I. VERRELLI

The foundation for subsequent analyses is laid by experimental work which establishes the solid phase density of WTP sludges.

Additionally, alum sludges are found to contain

pseudoböhmite, while 2-line ferrihydrite and goethite are identified in ferric sludges.

A key hypothesis is that dewaterability is partly determined by the treatment conditions. To investigate this, numerous WTP sludges were studied that had been generated under diverse conditions: some plant samples were obtained, and the remainder were generated in the laboratory (results were consistent). Dewaterability was characterised for each sludge in concentration ranges relevant to settling, centrifugation and filtration using models developed by LANDMAN and WHITE inter alia; it is expressed in terms of both equilibrium and kinetic parameters, py(φ) and R(φ) respectively. This work confirmed that dewaterability is significantly influenced by treatment conditions. The strongest correlations were observed when varying coagulation pH and coagulant dose. At high doses precipitated coagulant controls the sludge behaviour, and dewaterability is poor. Dewaterability deteriorates as pH is increased for high-dose alum sludges; other sludges are less sensitive to pH. These findings can be linked to the faster coagulation dynamics prevailing at high coagulant and alkali dose. Alum and ferric sludges in general had comparable dewaterabilities, and the characteristics of a magnesium sludge were similar too. Small effects on dewaterability were observed in response to variations in raw water organic content and shearing. Polymer flocculation and conditioning appeared mainly to affect dewaterability at low sludge concentrations.

Ageing did not produce clear changes in

dewaterability. Dense, compact particles are known to dewater better than ‘fluffy’ aggregates or flocs usually encountered in drinking water treatment. This explains the superior dewaterability of a sludge containing powdered activated carbon (PAC). Even greater improvements were observed following a cycle of sludge freezing and thawing for a wide range of WTP sludges.

Further aspects considered in the present work include deviations from simplifying assumptions that are usually made. Specifically: investigation of long-time dewatering behaviour, wall effects, non-isotropic stresses, and reversibility of dewatering (or ‘elasticity’).

ii


Several other results and conclusions, of both theoretical and experimental nature, are presented on topics of subsidiary or peripheral interest that are nonetheless important for establishing a reliable basis for research in this area.

This work has proposed links between industrial drinking water coagulation conditions, sludge dewaterability from settling to filtration, and the microstructure of the aggregates making up that sludge. This information can be used when considering the operation or design of a WTP in order to optimise sludge dewaterability, within the constraints of producing drinking water of acceptable quality.

Keywords ageing;

aggregates;

aluminium sulfate;

centrifugation;

coagulation;

creep;

delayed

settling; dewatering; elasticity; ferric chloride; filtration; flocculation; flocs; fractal dimension; freeze–thaw conditioning; long-time behaviour; magnesium sulfate; natural organic matter; polymer; powdered activated carbon; reversibility; settling; sludge; shear; wall effects; water.

Indicative translations of title Trinkwasseraufbereitung: Erzeugung und Entwässerungsfähigkeit des Schlammes Trattamento delle acque potabili: La generazione e la facilità di disidratazione del fango Tratamiento de aguas potables: La generación y la facilidad de deshidratación de fangos Traitement de l'eau potable: La formation et la facilité de déshydratation des boues (schlamms) Обработка питьевой воды — формирование и легкость обезвоживание осадков (шламов) 饮用水处理中污泥的产生及其脱水特性飲料水の処理 — 沈積物の生成とその脱水 Behandling af Drikkevand, Slam Produktion og Evne Til at Afvande [cf. Drikkevand Behandling, Slam Produktion og Afvanding] Pengolahan Air Minum — Pembentukan Endapan, Produksi Endapan Lumpur, dan Kemudahan Pemisahan Air dari Lumpur

iii

DECLARATION

This is to certify that:

1.

the thesis comprises only my original work towards the Ph.D., except where indicated in the Preface & Acknowledgements;

2.

due acknowledgement has been made in the text to all other material used; and

3.

the thesis is approximately 130000 words in length, exclusive of tables, maps, bibliographies and appendices.

David Ignatius Verrelli

v

PREFACE

This work was initiated as part of a project carried out as a collaboration between The University of Melbourne, United Utilities (U.K.), and Yorkshire Water (U.K.).

I entered this course of study with the dual aims of furthering my own knowledge and skills, and arriving at research outcomes that have real application. The topic of drinking water treatment sludge dewatering does indeed have a direct relevance to industry, and thus indirectly affects the community. I have learned a great deal in my research, and hope that my findings will fall on receptive ears.

It has traditionally been the duty of academics and Ph.D. candidates to challenge accepted wisdom. Various pressures combine to discourage these enquiries. Too frequent and too great is the temptation to take the expedient path of accepting, without question, the established doctrine of the day. Examples include use of A400nm to estimate true colour, the derivation(s) of TERZAGHI’s hydraulic diffusion equation, omission of CORIOLIS forces, use of nominal ρS values, description of alum and ferric precipitates as Al(OH)3 and Fe(OH)3, the irreversibility of dewatering, description of dewaterability with only D (φ), conflation of Df with internal aggregate structure, and belief that smaller Df guarantees smaller ρagg (all elucidated herein). I have been fortunate to have had the implicit support of my supervisors to correct these fundamental errors. I would particularly like to thank Peter Scales for his patience.

vii

ACKNOWLEDGEMENTS

This work was carried out under the supervision of Prof. Peter J. Scales & Dr. David R. Dixon. They have added considerable expertise and experience to the project. This work would not have been possible without the assistance of postdoctoral research fellows Dr. Shane P. Usher & Dr. Ross G. de Kretser. It is rare to find a technical problem they are unable to resolve. I would also like to acknowledge the fellowship of the other members of the Scales research group, past and present. While it is not possible to list them all individually, it would be remiss not to mention Rachael C. Wall, Rudolf Spehar, Hemadri K. Saha and Ainul A. b. A. Aziz. Numerous other members of the Department of Chemical and Biomolecular Engineering, the Particulate Fluids Processing Centre, the School of Engineering, and the university as a whole have supported this work, either directly or indirectly.

This includes students,

general staff, and academics. Particular mention should be made of: the workshop staff — Kevin Smeaton and team; the analytical facility — Ernest H. Gutsa; the SEM imaging facility — Roger C. A. Curtain; the administrative staff; and the library staff. Access to equipment was facilitated by G. W. Stevens (spectrophotometer) and M. Ashokkumar (TOC). S. E. Kentish and her group generously gave up laboratory space to accommodate my work.

Discussions with L. R. White, T. W. Healy, R. J. Eldridge, G. V. Franks, P. Liovic, P. S. Grassia, E. K. Hill, F. Grieser, W. A. Ducker, and B. Jefferson are appreciated, as are correspondence with V. J. Blue, J. Bellwood, E. M. Furst, R. Simard & P. L’Ecuyer, R. M. L. Evans, J.-P. Jolivet, W. R. Knocke, and J. H. Kwon. Assistance from Ina Ritsner with a Russian text is also gratefully acknowledged. Thanks to James Tardio for helping to validate TOC results. I also recognise Peter Jarvis’s generosity in providing access to his collection of articles from the literature. Thanks to Nathan Matteson for typography tips.

ix

D. I. VERRELLI

United Utilities and Yorkshire Water provided project sponsorship, with particular support from Dr. Martin Tillotson and Dr. Peter Hillis. The Australian Research Council and The University of Melbourne provided funds for a postgraduate scholarship. Melbourne Water (C. Barber et alii), the Cooperative Research Centre for Water Quality and Treatment (G. Newcombe et alia), United Utilities Australia (L. Choy † et alii), and United Water (D. Becker et alii), and Ciba Specialty Chemicals (J. Bellwood) are acknowledged for assistance in obtaining samples.

Research does not always run smoothly, and I want to make especial acknowledgement of Alicia for her companionship. Even when research does run smoothly, it is good to be able to take a break now and again, and spend time with friends. The path I have taken through the education system has formed the foundation upon which these studies have been built, and I trust reflects favourably upon Waverley Meadows P.S., Wheelers Hill S.C., and Monash University (Clayton) — aside from my current institution. Finally, my parents, Vince & Virginia, instilled in me an appreciation for knowledge and learning, and supported me continuously throughout my education, as well as at home, for which I am grateful. Along with my supervisors, they also assisted by proofreading the text.

x

OVERVIEW OF CONTENTS 1.

INTRODUCTION ...................................................................... 1

2.

BACKGROUND ....................................................................... 57

3.

EXPERIMENTAL METHODS ................................................... 157

4.

SOLID PHASE ASSAYS AND DENSITIES ............................... 253

5.

EFFECT OF COAGULANT TYPE, DOSE, AND pH .................... 301

6.

EFFECT OF RAW WATER QUALITY........................................ 359

7.

EFFECT OF SHEAR AND POLYMER ADDITION ..................... 375

8.

EFFECT OF UNUSUAL TREATMENTS .................................... 433

9.

UNUSUAL MATERIAL BEHAVIOUR ....................................... 469

10.

OUTCOMES ........................................................................... 543

11.

BIBLIOGRAPHY .................................................................... 559

APPENDICES ................................................................................ 619

REVIEW ........................................................................................ 621

SUPPORTING MATERIAL ............................................................. 825 xi

D. I. VERRELLI

xii


DETAILED CONTENTS

SUMMARY ....................................................................................... i Keywords.......................................................................................................................... iii Indicative translations of title ........................................................................................ iii

DECLARATION ................................................................................ v

PREFACE....................................................................................... vii

ACKNOWLEDGEMENTS .................................................................. ix

FIGURES ..................................................................................... xxix

TABLES ...................................................................................... xxxix

NOMENCLATURE ....................................................................... xliii Symbols ................................................................................................. xliii Latin symbols ............................................................................................................................xliii Greek symbols.........................................................................................................................xlviii Cyrillic symbols ............................................................................................................................. l Mathematical operators and other symbols ............................................................................. li Superscripts................................................................................................................................... li Subscripts...................................................................................................................................... lii Abbreviations .......................................................................................... liii Terminology ............................................................................................. lv

xiii

D. I. VERRELLI

1.

INTRODUCTION ...................................................................... 1 1▪1

Drinking water production processes ................................................. 1

1▪2

Sludge production .............................................................................. 7

1▪3

Sludge transportation ........................................................................ 9

1▪4

Sludge dewatering ........................................................................... 11

1▪4▪1

Clarification and thickening.......................................................................................13

1▪4▪2

Natural dewatering .....................................................................................................15

1▪4▪3

Centrifugation ..............................................................................................................18

1▪4▪4

Filtration........................................................................................................................20

1▪5

1▪4▪4▪1

Filter presses.........................................................................................................20

1▪4▪4▪2

Belt filter presses ..................................................................................................22

1▪4▪4▪3

Vacuum drum filters ...........................................................................................23

1▪4▪4▪4

Other filters...........................................................................................................24

Sludge disposal ................................................................................ 24

1▪5▪1

Overview of disposal routes ......................................................................................26

1▪5▪2

Discharge to a natural water body............................................................................28

1▪5▪3

Discharge to sewer ......................................................................................................31

1▪5▪4

Discharge to lagoons ...................................................................................................34

1▪5▪5

Waste landfill ...............................................................................................................36

1▪5▪6

Engineering fill.............................................................................................................40

1▪5▪7

Land application, including agricultural uses.........................................................41

1▪5▪7▪1

Regulatory issues.................................................................................................45

1▪5▪8

Chemical reuse.............................................................................................................47

1▪5▪9

Other beneficial uses ...................................................................................................49

1▪6

The nexus between sludge generation, sludge dewatering, and sludge disposal ................................................................................ 51

1▪7

xiv

Aim of this work .............................................................................. 52


2.

BACKGROUND ....................................................................... 57 2▪1

Introduction to dewatering .............................................................. 58

2▪1▪1

Solidosity ......................................................................................................................59

2▪1▪2

Dewatering regimes ....................................................................................................60

2▪1▪3

The dewatering ‘spectrum’ ........................................................................................62

2▪1▪4

Driving ‘forces’ and resistances to dewatering .......................................................64

2▪1▪5

Packing..........................................................................................................................67

2▪2

Slow particle motion ........................................................................ 68

2▪3

Flow through porous media ............................................................. 71

2▪3▪1

DARCY’s law .................................................................................................................71

2▪3▪2

Extensions and alternatives to DARCY’s law............................................................75

2▪4

Dewatering analysis ......................................................................... 76

2▪4▪1

Empirical methods ......................................................................................................78

2▪4▪1▪1

Compressibility....................................................................................................82 Isothermal compressibility..............................................................................................82 Extension to particulate systems ....................................................................................82 Coefficient of volume compressibility...........................................................................84 Reciprocal ‘confined elastic modulus’...........................................................................85 Compressibility coefficients............................................................................................86

2▪4▪1▪2

Zone settling rate .................................................................................................86

2▪4▪1▪2(a)

Definition of zone settling.............................................................................86

2▪4▪1▪2(b)

Measurement ..................................................................................................87

2▪4▪1▪3

Capillary suction time (CST) and derivatives .................................................88

2▪4▪1▪4

Specific resistance to filtration (SRF).................................................................90

2▪4▪1▪4(a) 2▪4▪1▪5

Adjusted SRF ..................................................................................................91

Other ad hoc methods ..........................................................................................92

2▪4▪2

Early dewatering theory.............................................................................................93

2▪4▪3

Kinematical batch settling theory of KYNCH ...........................................................93

2▪4▪3▪1

Shock thickness ....................................................................................................95

2▪4▪3▪2

Polydisperse suspensions and instability ........................................................96

2▪4▪3▪3

Influence of BROWNian motion..........................................................................99 xv

D. I. VERRELLI

2▪4▪4

Permeation theories of settling and filtration ........................................................100

2▪4▪5

Phenomenological dewatering theory of LANDMAN, WHITE et alia ...................104

2▪4▪5▪1

Model parameters..............................................................................................105

2▪4▪5▪1(a)

Compressive yield stress.............................................................................106

System anisotropy and osmosis ..................................................................................107 Empirical and model functional forms of py(φ) ........................................................109 Creep effects at low stresses.........................................................................................109 Elastic behaviour ...........................................................................................................111 2▪4▪5▪1(b)

‘Hindered settling’ parameters ..................................................................111

Empirical and model functional forms of R(φ) .........................................................113 2▪4▪5▪1(c)

Dynamic compressibility ............................................................................113

2▪4▪5▪1(d) Solids diffusivity...........................................................................................116 2▪4▪5▪2

General equations..............................................................................................117

2▪4▪5▪3

Batch settling ......................................................................................................119

2▪4▪5▪3(a)

Early time ......................................................................................................119

2▪4▪5▪3(b)

General equation ..........................................................................................121

2▪4▪5▪3(c)

Practical solution ..........................................................................................122

2▪4▪5▪3(d) Settling in real systems ................................................................................126 2▪4▪5▪3(e)

Ideal settling..................................................................................................128

2▪4▪5▪3(f)

Multiple-test theory .....................................................................................129

2▪4▪5▪3(g)

Long-time behaviour ...................................................................................132

2▪4▪5▪4

2▪4▪5▪4(a)

Comprehensive analysis .............................................................................134

2▪4▪5▪4(b)

Simplified one-dimensional analysis.........................................................140

2▪4▪5▪5

Permeation..........................................................................................................143

2▪4▪5▪6

Filtration..............................................................................................................144

2▪4▪6

Other continuum models .........................................................................................151

2▪4▪7

Fundamental mechanistic theory ............................................................................151

2▪4▪7▪1 2▪4▪8

xvi

Batch centrifugation ..........................................................................................133

Micromechanical dependence of yield stress on d0 ......................................152

Stochastic analysis .....................................................................................................155


3.

EXPERIMENTAL METHODS ................................................... 157 3▪1

Treatment parameters .................................................................... 157

3▪2

Experimental materials .................................................................. 161

3▪2▪1

Purified water.............................................................................................................161

3▪2▪2

Raw water...................................................................................................................161

3▪2▪3

Coagulants..................................................................................................................164

3▪2▪3▪1 3▪2▪4

Magnesium .........................................................................................................164

Alkali ...........................................................................................................................166

3▪2▪4▪1

Hydrolysis ratio .................................................................................................166

3▪2▪5

Polymers .....................................................................................................................168

3▪2▪6

Plant and pilot plant sludges ...................................................................................168

3▪3

3▪2▪6▪1

Winneke ..............................................................................................................168

3▪2▪6▪2

Macarthur ...........................................................................................................169

3▪2▪6▪3

Happy Valley .....................................................................................................171

Sludge generation .......................................................................... 172

3▪3▪1

Industrial practice......................................................................................................172

3▪3▪2

Scaling by velocity gradient .....................................................................................173

3▪3▪2▪1 3▪3▪3

‘Standard’ tank configuration ..........................................................................174

Jar test rig (optimal dose selection).........................................................................178

3▪3▪3▪1

Mechanical construction and operation .........................................................178

3▪3▪3▪2

Identifying the optimum ..................................................................................180

3▪3▪4

Tank .............................................................................................................................181

3▪3▪5

Reproducibility ..........................................................................................................185

3▪3▪6

pH ................................................................................................................................185

3▪4

Treatment characterisation ............................................................. 186

3▪4▪1

Absorbance .................................................................................................................186

3▪4▪1▪1

Procedure............................................................................................................187

3▪4▪1▪2

Spectra .................................................................................................................188

3▪4▪1▪3

Single wavelengths............................................................................................188

3▪4▪2

True colour .................................................................................................................190

xvii

D. I. VERRELLI

3▪4▪2▪1

Spectrophotometric determination .................................................................191

3▪4▪2▪1(a) 3▪4▪3

Estimation from single-wavelength absorbance......................................193

Turbidity .....................................................................................................................194

3▪4▪3▪1

Measurement......................................................................................................194

3▪4▪3▪2

Experimental ......................................................................................................195

3▪4▪4

Dissolved organic carbon (DOC) ............................................................................196

3▪4▪5

Total solids and dissolved solids.............................................................................200

3▪4▪6

Conductivity...............................................................................................................200

3▪5

Sludge characterisation — compressional rheology ........................ 202

3▪5▪1

Batch settling ..............................................................................................................202

3▪5▪1▪1

Temporal data (single test)...............................................................................203

3▪5▪1▪1(a)

Reproducibility .............................................................................................203

3▪5▪1▪2

Equilibrium data (multiple test) ......................................................................205

3▪5▪1▪3

Accuracy .............................................................................................................206

3▪5▪2

Batch centrifugation ..................................................................................................207

3▪5▪2▪1

Pre-thickening ....................................................................................................208

3▪5▪2▪2

Accelerated settling ...........................................................................................208

3▪5▪2▪2(a)

Results............................................................................................................211

Reproducibility ..............................................................................................................220 3▪5▪2▪2(b) 3▪5▪3

Dead-end filtration ....................................................................................................222

3▪5▪3▪1

Stepped pressure analysis ................................................................................223

3▪5▪3▪1(a)

Reproducibility .............................................................................................224

3▪5▪3▪2

Permeation..........................................................................................................228

3▪5▪3▪3

Improvements made to methodology ............................................................230

3▪5▪3▪3(a)

Rig design and operation ............................................................................230

3▪5▪3▪3(b)

Data processing and analysis .....................................................................233

3▪5▪3▪4

Key interferences ...............................................................................................233

3▪5▪3▪4(a)

Temperature..................................................................................................233

3▪5▪3▪4(b)

Violation of one-dimensional dewatering assumption ..........................235

3▪5▪4 xviii

Implications...................................................................................................221

Reproducibility ..........................................................................................................239


3▪6

Sludge characterisation — shear yield stress .................................. 243

3▪6▪1

Conventional subaerial slump tests........................................................................245

3▪6▪2

Proposed subaqueous slump test............................................................................246

3▪7

Modelling of unit operations .......................................................... 249

3▪7▪1

Gravity settling and centrifugation.........................................................................249

3▪7▪2

Filtration......................................................................................................................249

4.

SOLID PHASE ASSAYS AND DENSITIES ............................... 253 4▪1

Published data ............................................................................... 255

4▪1▪1

Mass balance of sludge generation .........................................................................255

4▪1▪2

Pure component densities ........................................................................................259

4▪1▪3

WTP sludge densities................................................................................................263

4▪2

4▪1▪3▪1

Bulk densities .....................................................................................................263

4▪1▪3▪2

Solid phase densities .........................................................................................264

Experimental determination of composition ................................... 267

4▪2▪1

Method ........................................................................................................................268

4▪2▪1▪1

Energy-dispersive spectrometry (EDS) ..........................................................268

4▪2▪1▪1(a) 4▪2▪1▪2

Samples..........................................................................................................268

X-ray diffraction (XRD).....................................................................................269

4▪2▪1▪2(a)

Theory ............................................................................................................269

4▪2▪1▪2(b)

Reference data...............................................................................................270

4▪2▪1▪2(c)

Equipment .....................................................................................................272

4▪2▪1▪2(d) Samples..........................................................................................................272 4▪2▪2

Results .........................................................................................................................275

4▪2▪2▪1

Energy-dispersive spectrometry (EDS) ..........................................................275

4▪2▪2▪2

X-ray diffraction (XRD).....................................................................................280

4▪2▪2▪2(a)

Aluminium ....................................................................................................280

4▪2▪2▪2(b)

Iron .................................................................................................................282

4▪2▪3

Discussion...................................................................................................................285

4▪2▪4

Conclusions ................................................................................................................286

xix

D. I. VERRELLI

4▪3

Experimental density determination ............................................... 287

4▪3▪1

Method ........................................................................................................................287

4▪3▪1▪1 4▪3▪2

Equipment ..........................................................................................................289

Results .........................................................................................................................290

4▪3▪2▪1

Liquid phase.......................................................................................................290

4▪3▪2▪2

Solid phase..........................................................................................................291

4▪3▪3

Model curves..............................................................................................................295

4▪3▪4

Discussion...................................................................................................................296

4▪3▪5

Conclusions ................................................................................................................299

5.

EFFECT OF COAGULANT TYPE, DOSE, AND pH .................... 301 5▪1

Published observations .................................................................. 301

5▪1▪1

Effect of dose ..............................................................................................................301

5▪1▪2

Effect of pH and hydrolysis ratio ............................................................................302

5▪1▪2▪1

Aluminium .........................................................................................................303

5▪1▪2▪2

Iron.......................................................................................................................305

5▪1▪2▪3

Magnesium .........................................................................................................306

5▪1▪3

Effect of coagulant .....................................................................................................306

5▪2

Materials and methods ................................................................... 308

5▪3

Alum sludges: variation of dose .................................................... 311

5▪3▪1

5▪3▪1▪1

Intermediate pH (6) ...........................................................................................311

5▪3▪1▪2

High (8½) and low (5) pH ................................................................................314

5▪3▪2 5▪4

Results and discussion..............................................................................................311

Conclusions ................................................................................................................316

Alum sludges: variation of pH ...................................................... 317

5▪4▪1


5▪4▪2

Conclusions ................................................................................................................321

5▪5

Alum sludges: combined dose–pH effects ...................................... 321

5▪6

Alum sludges: comparison with plant and pilot plant data ........... 330

5▪6▪1 xx

Winneke WTP ............................................................................................................330


5▪6▪2

Happy Valley pilot plant ..........................................................................................330

5▪6▪3

Other plants................................................................................................................334

5▪7

Ferric sludges: variation of dose and pH ....................................... 335

5▪7▪1

Experimental ..............................................................................................................335

5▪7▪2


5▪7▪3

Conclusions ................................................................................................................340

5▪8

Ferric sludges: comparison with plant data ................................... 341

5▪8▪1

Macarthur WFP..........................................................................................................341

5▪8▪2

Other plants................................................................................................................342

5▪9

Comparison of alum and ferric sludges .......................................... 343

5▪9▪1

Compressive yield stress and hindered settling function ...................................343

5▪9▪2

DARCY’s law permeability, KD .................................................................................345

5▪9▪3

Solids diffusivity........................................................................................................346

5▪10 Industrial implications ................................................................... 351 5▪11 Magnesium sludge ......................................................................... 352 5▪11▪1

Experimental ..............................................................................................................353

5▪11▪2

Results .........................................................................................................................354

5▪11▪3

Discussion...................................................................................................................356

5▪11▪4

Conclusions ................................................................................................................357

6.

EFFECT OF RAW WATER QUALITY........................................ 359 6▪1

Published observations .................................................................. 359

6▪1▪1

NOM is beneficial ......................................................................................................360

6▪1▪2

NOM has no significant effect .................................................................................360

6▪1▪3

NOM is detrimental ..................................................................................................360

6▪1▪4

NOM has a mixed effect ...........................................................................................362

6▪2

Experimental .................................................................................. 363

6▪2▪1

Dialysed MIEX eluate (“dMIEX”)...........................................................................363

6▪2▪2

Sludges ........................................................................................................................365

xxi

D. I. VERRELLI

6▪3

Results ........................................................................................... 367

6▪4

Discussion...................................................................................... 371

6▪5

Conclusions ................................................................................... 373

7.

EFFECT OF SHEAR AND POLYMER ADDITION ..................... 375 7▪1

Previous investigations and experience .......................................... 376

7▪1▪1

Polymer addition .......................................................................................................376

7▪1▪2

Shear ............................................................................................................................378

7▪2

7▪1▪2▪1

During formation...............................................................................................378

7▪1▪2▪2

After formation, before settling .......................................................................383

7▪1▪2▪3

After formation and settling ............................................................................385

Shear during coagulation ............................................................... 387

7▪2▪1

Materials and methods .............................................................................................388

7▪2▪2

Results .........................................................................................................................389

7▪2▪3

Discussion and conclusions .....................................................................................391

7▪3

Flocculation ................................................................................... 392

7▪3▪1

Materials and methods .............................................................................................392

7▪3▪2

Results .........................................................................................................................394

7▪3▪3


7▪4

After settling: shear and polymer conditioning ............................. 397

7▪4▪1

xxii

Methodology ..............................................................................................................398

7▪4▪1▪1

Materials .............................................................................................................398

7▪4▪1▪2

Dose setting by capillary suction time (CST).................................................400

7▪4▪1▪3

Shear and mixing rig .........................................................................................401

7▪4▪1▪4

Characterisation .................................................................................................407

7▪4▪2

Polymer dose selection .............................................................................................408

7▪4▪3

Preliminary findings .................................................................................................410

7▪4▪4

Optimisation, error/sensitivity analysis, and calibration and validation ..........414

7▪4▪4▪1

Optimisation.......................................................................................................414

7▪4▪4▪2

Error/sensitivity analysis ..................................................................................415


7▪4▪4▪2(a)

Sub-set selection ...........................................................................................415

7▪4▪4▪2(b)

Experimental and fitting errors ..................................................................417

7▪4▪4▪3

Calibration and validation ...............................................................................420

7▪4▪4▪3(a)

Approach .......................................................................................................420

7▪4▪4▪3(b)

Moderate-pH sludges ..................................................................................421

7▪4▪4▪3(c)

High-pH sludges ..........................................................................................424

7▪4▪5

Principal results .........................................................................................................425

7▪4▪6

Discussion...................................................................................................................429

7▪4▪7

Conclusions ................................................................................................................431

8.

EFFECT OF UNUSUAL TREATMENTS .................................... 433 8▪1

Ageing ........................................................................................... 433

8▪1▪1

Reported effects .........................................................................................................433

8▪1▪2

Experimental methods..............................................................................................435

8▪1▪3

Results .........................................................................................................................438

8▪1▪4

Discussion...................................................................................................................443

8▪1▪5

Conclusions ................................................................................................................445

8▪2

Freeze–thaw conditioning .............................................................. 445

8▪2▪1

Background ................................................................................................................445

8▪2▪1▪1

Mechanism..........................................................................................................446

8▪2▪1▪2

Operational parameters ....................................................................................449

8▪2▪1▪3

Improvements to dewaterability .....................................................................454

8▪2▪1▪4

Industrial application........................................................................................455

8▪2▪2

Experimental methods..............................................................................................456

8▪2▪3

Experimental results .................................................................................................457

8▪2▪4


8▪3

Powdered activated carbon (PAC) .................................................. 462

8▪3▪1

Reported effects .........................................................................................................462

8▪3▪2

Equipment ..................................................................................................................463

8▪3▪3

Materials .....................................................................................................................463

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D. I. VERRELLI

8▪3▪4

Experimental results .................................................................................................464

8▪3▪5


9.

UNUSUAL MATERIAL BEHAVIOUR ....................................... 469 9▪1

Induction time ............................................................................... 469

9▪1▪1

Published observations and theories ......................................................................469

9▪1▪1▪1

Delayed settling .................................................................................................470

9▪1▪1▪1(a)

Delay due to channelling ............................................................................471

9▪1▪1▪1(b)

Delay due to densification ..........................................................................476

9▪1▪1▪1(c)

Delay due to wall effects .............................................................................479

9▪1▪1▪2

Deterministic chaos: self-organised criticality and periodicity..................480

9▪1▪2

Practical relevance and analysis ..............................................................................482

9▪1▪3

Experimental findings...............................................................................................483

9▪2

Wall effects .................................................................................... 486

9▪2▪1

Cylinder diameter......................................................................................................486

9▪2▪1▪1

Previous recommendations..............................................................................487

9▪2▪1▪1(a) 9▪2▪1▪2

Settling ...........................................................................................................490

9▪2▪1▪2(b)

Filtration ........................................................................................................492

Cylinder surface properties......................................................................................493

9▪2▪2▪1

Experimental ......................................................................................................493

9▪2▪2▪2

Results and discussion ......................................................................................494

9▪2▪3

Conclusions ................................................................................................................496

Long-time dewatering behaviour ................................................... 497

9▪3▪1

xxiv

Present findings .................................................................................................490

9▪2▪1▪2(a)

9▪2▪2

9▪3

Torpid matter................................................................................................488

Ageing and biological activity during experiment...............................................498

9▪3▪1▪1

Observed biological activity.............................................................................498

9▪3▪1▪2

Development of large-scale morphology .......................................................499

9▪3▪1▪3

Exposure to light................................................................................................501

9▪3▪1▪4

Conclusions ........................................................................................................502


9▪3▪2

Creep and long-time metastability..........................................................................503

9▪3▪2▪1

Postulated behaviour ........................................................................................503

9▪3▪2▪2

Settling.................................................................................................................504

9▪3▪2▪3

Filtration..............................................................................................................511

9▪3▪2▪4

Discussion...........................................................................................................515

9▪3▪2▪4(a)

Bulk viscosity theory....................................................................................517

9▪3▪2▪4(b)

Thermally-activated barrier hopping theory ...........................................518

9▪3▪2▪5 9▪3▪3 9▪4

10.

Non-diffusive processes ...................................................................................519

Conclusions ................................................................................................................519

Reversibility: Elastic cake re-expansion ........................................ 521

9▪4▪1

Literature reports.......................................................................................................523

9▪4▪2

Elasticity theory .........................................................................................................529

9▪4▪3

Methodology ..............................................................................................................537

9▪4▪4

Results .........................................................................................................................538

9▪4▪5


OUTCOMES ........................................................................... 543

10▪1 Catalogue of outcomes and conclusions ......................................... 543 10▪1▪1

Theoretical ..................................................................................................................543

10▪1▪2

Experimental ..............................................................................................................546

10▪2 Industrial implications ................................................................... 552 10▪3 Further work .................................................................................. 553 10▪3▪1

Experimental ..............................................................................................................553

10▪3▪2

Theoretical development ..........................................................................................555

10▪4 Closing remarks ............................................................................. 557

11.

BIBLIOGRAPHY .................................................................... 559

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D. I. VERRELLI

APPENDICES ................................................................................ 619

REVIEW ........................................................................................ 621

R1.

CONDITIONS AFFECTING THE NATURE OF THE SLUDGE MATERIAL FORMED ............................................................. 627

R1▪1 Important constituents of raw water — natural organic matter (NOM) ........................................................................................... 627 R1▪2 Coagulation ................................................................................... 640 R1▪3 Flocculation ................................................................................... 704 R1▪4 Mixing ........................................................................................... 715 R1▪5 Aggregate structure and fractal dimension ..................................... 735

R2.

BEHAVIOUR OF SLUDGE-LIKE MATTER ............................... 791

R2▪1 Endogenous synæresis ................................................................... 791 R2▪2 Geomechanics and creep ................................................................ 799 R2▪3 Macrorheological models ............................................................... 814

xxvi


SUPPORTING MATERIAL ............................................................. 825

S1.

EARLY DEWATERING THEORY ............................................. 831

S2.

GENERAL PRINCIPLES OF KINEMATIC WAVES .................... 834

S3.

EXPERIMENTAL OBSERVATIONS OF LONG-TIME SETTLING ............................................................................. 836

S4.

DOUBLE-EXPONENTIAL VERSION OF LONG-TIME FILTRATION ASYMPTOTE .................................................... 840

S5.

STOCHASTIC SETTLING ANALYSIS ..................................... 841

S6.

JAR TESTING PRACTICE ....................................................... 843

S7.

LIGHT ABSORBANCE ............................................................ 848

S8.

COLOUR MEASUREMENT ..................................................... 856

S9.

EVALUATION AND SELECTION OF SYRINGE FILTERS ......... 867

S10. MULTIPLE BATCH SETTLING ANALYSIS .............................. 874

S11. SLUMP TEST RESULTS .......................................................... 892

S12. CONTOUR SENSITIVITY ANALYSIS ..................................... 895

S13. FILTER PRESS MODELLING .................................................. 898

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D. I. VERRELLI

S14. POLYMER CONDITIONER MIXING RECOMMENDATION OF WRc ................................................................................. 908

S15. BOOTSTRAP AND JACKKNIFE STATISTICS .......................... 913

S16. SILANISATION ..................................................................... 925

S17. BULK VISCOSITY .................................................................. 928

S18. BARRIER HOPPING THEORY ................................................ 941

S19. FILTRATION RIG FRAME EXPANSION .................................. 943

S20. ESTIMATION OF THE BULK MODULUS OF COMPRESSIBILITY, BS, THROUGH CENTRIFUGATION ......... 945

S21. METAL COMPLEXATION BY ‘FOREIGN’ ANIONS ................. 947

S22. PSEUDOBÖHMITE STRUCTURE AND COMPOSITION ........... 954

S23. OCCURRENCE OF IRON(II) ................................................... 956

S24. RELATIVE STABILITY OF HÆMATITE AND GOETHITE ........ 957

S25. CORRELATIONS OF dmax ....................................................... 960

S26. ESTIMATION OF G FOR INDUSTRIAL SCENARIOS............... 964

The Review and Supporting Material appendices each begin with a d e t a i l e d listing of their contents.

xxviii


FIGURES

Figure 1-1: Distribution of raw water sources and treatments in England and Wales circa 1997, by water volume [315].............................................................................................................................. 2 Figure 1-2: Indicative flowchart of conventional water treatment process with gravity settling, including sludge processing operations. ............................................................................................... 5 Figure 1-3: U.K. landfill tax rates since inception [53, 70, 72, 315].............................................................. 38 Figure 2-1: Simplified schematic of hypothetical equilibrium particle packing resulting from sequential application of axial and lateral stresses. ......................................................................... 108 Figure 2-2: Typical flux plot [cf. 205], showing key features of the settling flux function, qS∗ (φ), and illustrating the range of solidosities for which R(φ) can be analytically evaluated for a given initial solidosity of φ0 or φ0′: the range is the same, as material loaded at φ0 jumps directly to φ0′ [cf. 652]. Not to scale.................................................................................................... 123 Figure 2-3: Schematic representation of typical batch settling behaviour with φ0 < φg......................... 128 Figure 2-4: Schematic representation of typical batch settling behaviour with φ0 > φg [495]. .............. 128 Figure 2-5: Schematic of centrifuge system, looking down on plane of rotation. Gravity is assumed to act in the –z direction....................................................................................................... 135 Figure 2-6: Interface settling rates of c en tri fug ed samples. (The two alternatives given for each sludge type refer to the local form of h(t) assumed in numerically estimating the derivative.) ............................................................................................................................................. 138 Figure 3-1: Range of alum sludges characterised. ...................................................................................... 158 Figure 3-2: Range of ferric sludges characterised. ...................................................................................... 159 Figure 3-3: Location of alum and ferric sludge generation conditions with respect to the aluminium and iron(III) solubility curves. “Plant Al” includes the pilot plant sludges............ 160 Figure 3-4: Experimental hydrolysis ratios for alum coagulation, [OH–]added / [Al]. The solubility envelope is indicated by the dashed lines. ........................................................................................ 167 Figure 3-5: Schematic of HOLLAND & CHAPMAN’s [485] ‘standard’ tank configuration. ...................... 176 Figure 3-6: Large (53.5L) mixing vessel based on ‘standard’ tank configuration................................... 182 Figure 3-7: Large-scale coagulation equipment. ......................................................................................... 183 Figure 3-8: Transient pH profiles for five consecutive ferric treatments at 80mg(Fe)/L carried out on Winneke raw water collected 2004-09-15. ............................................................................. 186 Figure 3-9: Compressive yield stress curves computed from seven batch settling tests. Centrifugation and filtration data also shown.................................................................................. 204 Figure 3-10: Hindered settling function curves computed from seven batch settling tests. Filtration data also shown. .................................................................................................................. 204 Figure 3-11: Compressive yield stress determined first without centrifugation data, and then with centrifugation data, for a laboratory and a plant alum sludge.............................................. 212

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D. I. VERRELLI

Figure 3-12: Compressive yield stress determined first without centrifugation data, and then with centrifugation data, for a laboratory and a plant ferric sludge. ............................................ 213 Figure 3-13: Hindered settling function computed with and without centrifugation data for a laboratory and a plant alum sludge. .................................................................................................. 215 Figure 3-14: Hindered settling function computed with and without centrifugation data. Revised fits using centrifugation data were obtained only by adjusting py(φ) as in Figure 3-11.......................................................................................................................................................... 216 Figure 3-15: Predicted centrifugation h(t) profiles. The prediction for the py(φ) and R(φ) curves obtained without centrifugation data is for comparison only. The first ‘improved’ fit was obtained using the adjusted py(φ) curve from Figure 3-11, and this was optimised to yield the second ‘improved’ prediction by iteratively adjusting R(φ) to yield the curve shown in Figure 3-13. ........................................................................................................................................ 219 Figure 3-16: Predicted gravity settling h(t) profiles. The first prediction uses py(φ) and R(φ) curves obtained without centrifugation data. The second prediction was obtained using the adjusted py(φ) curve from Figure 3-11. The final prediction was obtained by iteratively adjusting R(φ) (see Figure 3-13) to optimise the predicted centrifugation h(t) profile (see Figure 3-15)........................................................................................................................ 220 Figure 3-17: Schematic of laboratory filtration rig. ..................................................................................... 222 Figure 3-18: Duplicate compressive yield stress measurements from stepped-pressure filtration. .... 226 Figure 3-19: Hindered settling function estimates from duplicate stepped-pressure permeability runs, based on a verag e of py(φ) measurements............................................................................. 227 Figure 3-20: (a) The period from 500 to 1700 seconds shows the close control of sample pressure attainable using automatic control when the rate of dewatering is not too high. (b) the period from 340 to 370 seconds shows the level of control achievable using ‘manual’ control when the rate of dewatering is high..................................................................... 229 Figure 3-21: Thermal cycling in filtration. 160mg(Fe)/L sludge filtered on newer ‘aluminiumframed’ rig. ............................................................................................................................................ 234 Figure 3-22: Schematic of cake unloaded from filtration rig showing crevice in top surface and non-straight side profile. These features were present in a minority of cases............................. 239 Figure 3-23: Compressive yield stress data for replicate alum sludge samples. .................................... 242 Figure 3-24: Hindered settling function data for replicate alum sludge samples. Asterisked samples are taken as representative in subsequent charts. ............................................................. 243 Figure 4-1: Effect of solid phase density, ρS, on the compressive yield stress of a sludge with typical dewatering properties. The envelope defined by the broken lines illustrates the range of behaviours encountered for drinking water sludges (with ρS = 2500kg/m3)................. 254 Figure 4-2: Effect of solid phase density, ρS, on the hindered settling function of a sludge with typical dewatering properties. The envelope defined by the broken lines illustrates the range of behaviours encountered for drinking water sludges (with ρS = 2500kg/m3)................. 255 Figure 4-3: Raw and smoothed XRD scans for the Macarthur WFP ferric sludge generated 2005-03-23 and heated at 80°C. ........................................................................................................... 275 Figure 4-4: SEM image of air-dried laboratory ferric sludge (9 days old): one EDS measurement averaged over approximately 0.01mm2 (centred on largest horizontal face). The concentric circles formed upon drying. ............................................................................................. 277 Figure 4-5: SEM image of grains of calcite in a plant ferric sludge (aged sample)................................. 280

xxx


Figure 4-6: Powder x-ray diffractograms for air-dried aged laboratory alum sludges. ........................ 280 Figure 4-7: Powder x-ray diffractograms for an air-dried plant alum sludge, original and freeze–thaw conditioned. Influence of blank shown dotted.......................................................... 281 Figure 4-8: X-ray powder diffractograms for a selection of fresh and aged ferric sludges. The aged plant sample is offset by +50 units for clarity. Ages in months............................................ 283 Figure 4-9: X-ray powder diffractograms for a selection of ferric sludges with and without heating. The plant samples are offset by +100 units for clarity...................................................... 284 Figure 4-10: X-ray powder diffractograms for a selection of ferric sludges. The curves are progressively offset by +50 units for clarity. ..................................................................................... 284 Figure 4-11: Solid phase densities for various drinking water sludges as a function of φ. Data obtained using volumetric flasks shown with dotted error bars. .................................................. 292 Figure 4-12: Solid phase densities for various drinking water sludges as a function of coagulant dose. Data obtained using volumetric flasks shown with dotted error bars............................... 293 Figure 5-1: Effect of coagulant dose on py(φ) for a range of alum sludges at pH 6.0±0.2. ..................... 312 Figure 5-2: Effect of coagulant dose on R(φ) for a range of alum sludges at pH 6.0±0.2....................... 313 Figure 5-3: Effect of coagulant dose on py(φ) for a range of alum sludges at pH 8.5±0.1 and pH 4.9±0.1. .................................................................................................................................................... 315 Figure 5-4: Effect of coagulant dose on R(φ) for a range of alum sludges at pH 8.5±0.1 and pH 4.9±0.1. .................................................................................................................................................... 316 Figure 5-5: Effect of coagulation pH on py(φ) for a range of alum sludges at 80mg(Al)/L dose. ......... 317 Figure 5-6: Effect of coagulation pH on R(φ) for a range of alum sludges at 80mg(Al)/L dose. .......... 318 Figure 5-7: Effect of coagulation pH on py(φ) for a range of alum sludges at 5mg(Al)/L dose. ........... 319 Figure 5-8: Effect of coagulation pH on R(φ) for a range of alum sludges at 5mg(Al)/L dose. ............ 320 Figure 5-9: Contour plot of estimated gel point, φg, (i.e. at py → 0+) for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. ............................................. 323 Figure 5-10: Contour plot of solidosity, φ, at py = 50kPa for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. ...................................................................... 325 Figure 5-11: Contour plot of solidosity, φ, at R = 5×1010Pa.s/m2 for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH......................................................... 326 Figure 5-12: Contour plot of solidosity, φ, at R = 1×1014Pa.s/m2 for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH......................................................... 327 Figure 5-13: Contour plot of hindered settling function, R, [1013 Pa.s/m2] at py = 50kPa for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. ....... 328 Figure 5-14: Variation in compressive yield stress with coagulant dose for various Happy Valley alum pilot plant sludges. ......................................................................................................... 332 Figure 5-15: Variation in hindered settling function with coagulant dose for various Happy Valley alum pilot plant sludges. ......................................................................................................... 333 Figure 5-16: Compressive yield stress for laboratory-generated and plant ferric sludges. The leftmost curve is for the 80mg(Fe)/L pH 5.6 sample. ....................................................................... 337 Figure 5-17: Hindered settling function for laboratory-generated and plant ferric sludges. ............... 338

xxxi

D. I. VERRELLI

Figure 5-18: Comparison of compressive yield stress for alum and ferric sludges. The numbers shown in the legend are the coagulant dose and coagulation pH. ................................................ 344 Figure 5-19: Comparison of hindered settling function for alum and ferric sludges. The numbers shown in the legend are the coagulant dose and coagulation pH................................. 345 Figure 5-20: Comparison of KD / ηL for alum and ferric sludges. Data of Figure 5-19. ......................... 346 Figure 5-21: Comparison of solids diffusivity for alum and ferric sludges — full curves on log– log scale. The numbers shown in the legend are the coagulant dose and coagulation pH. ...... 347 Figure 5-22: Comparison of solids diffusivity for alum and ferric sludges — filtration data only on log–linear scale. The numbers shown in the legend are the coagulant dose and coagulation pH...................................................................................................................................... 348 Figure 5-23: Compressive yield stress of a magnesium sludge (nominal conditions quoted — see discussion in text) compared to the range of typical laboratory alum sludge behaviour. .............................................................................................................................................. 355 Figure 5-24: Hindered settling function of a magnesium sludge (nominal conditions quoted — see discussion in text) compared to the range of typical laboratory alum sludge behaviour. .............................................................................................................................................. 356 Figure 6-1: Compressive yield stress for laboratory alum sludges generated from spiked (dMIEX) and non-spiked (Lab.) raw water. ...................................................................................... 368 Figure 6-2: Hindered settling function for laboratory alum sludges generated from spiked (dMIEX) and non-spiked (Lab.) raw water. ...................................................................................... 369 Figure 7-1: Compressive yield stress for two pairs of sludges subjected to different shear intensities in the slow-mix phase (given as G).................................................................................. 389 Figure 7-2: Hindered settling function for two pairs of sludges subjected to different shear intensities in the slow-mix phase (given as G).................................................................................. 390 Figure 7-3: Compressive yield stress for two pairs of sludges where flocculants were added to promote aggregation, compared to ‘controls’ with no flocculant. ................................................. 395 Figure 7-4: Hindered settling function for two pairs of sludges where flocculants were added to promote aggregation, compared to ‘controls’ with no flocculant. ................................................. 396 Figure 7-5: Schematic of the sludge shearing and conditioning rig. ........................................................ 401 Figure 7-6: CST values for an 80mg(Al)/L pH 5.9 laboratory sludge at φ0 ≈ 0.0026 conditioned with Magnafloc 338 and Zetag 7623 at various doses........................................................................ 409 Figure 7-7: CST values for an 80mg(Al)/L pH 8.9 laboratory sludge at φ0 ≈ 0.0016 conditioned with Zetag 7623 at various doses. Symbols and labels as in Figure 7-6. ....................................... 409 Figure 7-8: Hindered settling function estimates by various methods for an 80mg(Al)/L pH 5.9 laboratory sludge conditioned with 40mg/L Zetag 7623, listed chronologically. “preSS” denotes material collected before the conditioning operation had reached steady state. .......... 412 Figure 7-9: Hindered settling function estimates by various methods for an 80mg(Al)/L pH 8.9 laboratory sludge conditioned with 40mg/L Zetag 7623. “Jack” denotes jackknife results (iterative removal of individual raw data points and re-estimation). ........................................... 413 Figure 7-10: Sensitivity of parameter estimates to sub-set specification. ................................................ 416 Figure 7-11: Error estimates (95% confidence intervals) on the equilibrium solids diffusivity and R2 statistic for fitting parameter E3...................................................................................................... 418

xxxii


Figure 7-12: Comparison of D (φ∞) data determined from stepped pressure ‘permeability’ run analysis (by two methods) and from the extrapolation method (φ∞ estimation) for zirconia at pH 7.0 [reproduced from 606].......................................................................................... 420 Figure 7-13: Comparison of estimates of R for an 80mg(Al)/L, pH 5.9 laboratory sludge.................... 423 Figure 7-14: As in Figure 7-13, except after conditioning the sludge with 90mg/L Magnafloc 338. ..... 423 Figure 7-15: Compressive yield stress curves for high-alum-dose WTP sludges at moderate and high pH — coagulated only, sheared, and conditioned cases........................................................ 427 Figure 7-16: Hindered settling function curves for high-alum-dose WTP sludges at moderate and high pH — coagulated only, sheared, and conditioned cases. High-pH curves have been appropriately shifted (see text), and are not directly comparable with results presented elsewhere. ............................................................................................................................ 428 Figure 7-17: Schematic of the macroscopic structural differences between conditioned and coagulated materials as loaded into a filtration cell......................................................................... 430 Figure 8-1: Compressive yield stresses for three pairs of fresh and aged laboratory alum sludges.................................................................................................................................................... 439 Figure 8-2: Hindered settling function for one pair of fresh and aged laboratory alum sludges. ....... 440 Figure 8-3: Compressive yield stresses for a pair of fresh and aged laboratory alum sludges prepared from raw water spiked with dMIEX. ................................................................................ 441 Figure 8-4: Compressive yield stresses for two sets of fresh and aged ferric sludges. .......................... 442 Figure 8-5: Hindered settling function for two sets of fresh and aged ferric sludges. .......................... 443 Figure 8-6: Schematic of the progressive exclusion of particulates by a moving freeze front.............. 458 Figure 8-7: Compressive yield stress of sludges subjected to freeze–thaw conditioning. The thinner curves at left illustrate behaviour of the unconditioned sludges. .................................... 459 Figure 8-8: Hindered settling function of sludges subjected to freeze–thaw conditioning. The thinner curves at top and left illustrate behaviour of the unconditioned sludges....................... 460 Figure 8-9: Compressive yield stress for alum pilot plant sludges of varying coagulant dose compared to a pilot plant sludge of intermediate coagulant dose but containing some algæ and a high PAC load (pH assumed to be comparable). ......................................................... 465 Figure 8-10: Hindered settling function for alum pilot plant sludges of varying coagulant dose compared to a pilot plant sludge of intermediate coagulant dose but containing some algæ and a high PAC load (pH assumed to be comparable). ......................................................... 466 Figure 9-1: Gravity batch settling of alum sludge (80mg(Al)/L, pH 5.9) conditioned with Zetag 7623. ........................................................................................................................................................ 484 Figure 9-2: Gravity batch settling of alum sludge (80mg(Al)/L, pH 8.9) conditioned with Zetag 7623. ........................................................................................................................................................ 484 Figure 9-3: Gravity batch settling of an alum sludge in cylinders of varying capacity and diameter (as indicated in the legend)................................................................................................. 491 Figure 9-4: Comparison of settling of plant alum sludge with silylated glass walls against settling in an unmodified glass cylinder............................................................................................ 495 Figure 9-5: Meniscus of untreated surface (left) and of surface treated with CTMS (right). ................ 496

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Figure 9-6: Strands of vegetation adhering to cylinder wall for laboratory alum sludge [Winneke raw water 2004-05-11 coagulated with 1.5mg(Al)/L at pH 6.0 (2004-08-19)] (left), and plant alum sludge [Winneke WTP sludge 2005-04-05 (on 2005-06-17)] (right). ......... 499 Figure 9-7: Macarthur WFP plant ferric sludge 2005-09-21 (on 2007-02-02). Images of ‘synæresed’ sludge and ‘biomembrane’ under tension between liquid meniscus and ‘crown’ of shrunken sludge bed. ........................................................................................................ 499 Figure 9-8: Central depression, vegetation, and material rolled against (or down) the walls, in sludge from Winneke raw water 2004-07-05 with dMIEX, 5mg(Al)/L, pH 6.0 (2005-01-07). Large-scale features of the interface are shown schematically at right in cross-section. ............ 500 Figure 9-9: Batch settling of Macarthur WFP ferric sludge 2005-03-23. Photograph (taken 2005-06-17) and schematic cross-section. At long times extensive stratification developed: the lower (charcoal-coloured) layer underwent synæresis, and supports a ‘plug’ of wellpacked white material, with ‘fluffy’ rust-coloured flocs on top — some flocs from the top layer have fallen past the ‘plug’ into the gap created by the shrinkage. Several cracks are also apparent. ........................................................................................................................................ 501 Figure 9-10: Continuation of settling after asymptote appeared to have been reached. The sample was laboratory ferric sludge at 160mg(Fe)/L and pH ≈ 5.1 (see Table 5-4)...................... 505 Figure 9-11: Batch settling of plant ferric sludge [Macarthur WFP, 2005-03-23 (see Table 5-4)]. Arrows indicate the end of a height ‘plateau’................................................................................... 505 Figure 9-12(a): Batch settling of a ferric sludge, 80mg(Fe)/L and pH ≈ 6.1, showing tendencies toward logarithmic-type primary creep at long times in two regions. ......................................... 507 Figure 9-13: End-point prediction for a laboratory alum sludge at 80mg(Al)/L and pH ≈ 4.8 (see Table 5-1(b)). The crosses labelled “Predicted h∞ (exp. fit)” represent the prediction based on applying the exponential fit over seven data points up to that time; here “R2” represents the coefficient of determination. ...................................................................................... 509 Figure 9-14: Curves fitted to batch settling data for a dMIEX alum sludge at 5mg(Al)/L and pH ≈ 6.0 (see Table 6-2). Only the linear fit over the first section has a clear theoretical basis. ....................................................................................................................................................... 510 Figure 9-15: Linear regression on dt/dV 2 for three pressures in a stepped-pressure compressibility run. The dashed curve is the 40-point prior moving average of dt/dV 2 typically considered (default output of Press-o-matic software); the points are obtained from a 2-point central moving average (that is, local Δt/ΔV 2) and are better estimates, albeit noisier........................................................................................................................................... 512 Figure 9-16: Standard linear regressions of t against ln(E3 – V ) for long and short sets of data optimising R2, and alternative fits optimising the fit of V 2 and its slope against t...................... 513 Figure 9-17: Long-time fits to V 2 and dt/dV 2 over the last 141 points using equation 2-125b with standard (LW) and modified (LW') parameter estimation, and using an assumption of linear behaviour in dt/dV 2 (DIV). ...................................................................................................... 514 Figure 9-18: Long-time fits to V 2 and dt/dV 2 over the last 41 points using equation 2-125b with standard (LW) and modified (LW') parameter estimation, and using an assumption of linear behaviour in dt/dV 2 (DIV). ...................................................................................................... 515 Figure 9-19: Preliminary indications of elastic cake re-expansion in batch centrifugation. Arrows indicate data points of interest, where h increased after leaving the sample to stand. ...................................................................................................................................................... 522

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Figure 9-20: Compressive loading and unloading curves for a PAC-dosed alum WTP sludge; data of KOS & ADRIAN [598]. Solid phase density taken as 2050kg/m3 (cf. Figure 9-21)............. 527 Figure 9-21: Hindered settling function estimated for a PAC-dosed alum WTP sludge; data of KOS & ADRIAN [598]. Solid phase densities as indicated................................................................ 527 Figure 9-22: Compressive loading and unloading curves for three WTP sludges; data of WANG et alia [1098]. ........................................................................................................................................... 528 Figure 9-23(a): Expansion of a WTP sludge sample upon partial relief of the applied pressure. The initial height of material, h0, was 0.1079m.................................................................................. 538 Figure R1-1: Solubility curves for Al and Fe(III) from various references [90, 155, 219, 326, 533] at various ionic strengths. Temperature is assumed to be 25°C in all cases. ............................... 648 Figure R1-2: Solubility of magnesium in equilibrium with Mg(OH)2, and indicative speciation........ 649 Figure R1-3: Prediction of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals as a function of pH according to the partial charge model [466, 675] referenced to [H9O4]+, H2O, and [H7O4]− at pH 0, 7 and 14 respectively (see §S21) [538]. ........... 652 Figure R1-4: Prediction of partial charge on the metal, M, in various series of aqueous complexes as a function of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals according to the partial charge model [466, 675]......................................... 653 Figure R1-5: Schematic of anion complexation, ‘hydrolysis’ and ionic dissociation [466, 677]............ 654 Figure R1-6: Plot of critical pH against the mean electronegativity of the q-protonated anion, HqX(n−q)− for various values of q and illustrated by a selection of real ions. ................................... 655 Figure R1-7: Formation of Al(OH)3 species from Al3+ ions........................................................................ 680 Figure R1-8: Summary of the formation of more stable phases upon the precipitation of iron from solution under environmental conditions. .............................................................................. 693 Figure R1-9: Schematic of polymer flocculation dynamics; extended version of GREGORY’s [428] diagramme............................................................................................................................................. 706 Figure R1-10: Theoretical relationship between relative aggregate sizes, ч, to obtain the same solidosity with various combinations of fractal dimension, Df. The structure prefactor is assumed constant for the thicker, solid lines; for the thinner, dashed lines the correlation of GMACHOWSKI [405] is used; for the feint, dotted lines the correlation of SORENSEN & ROBERTS [956] is used............................................................................................................................ 746 Figure R1-11: Theoretical relationship between aggregate solidosity, aggregate and cluster size, and aggregate and cluster fractal dimension (Df,i ~ βi)..................................................................... 747 Figure R1-12: Possible structures to illustrate low-solidosity networks in two dimensions. ............... 776 Figure R2-1: Illustration of typical creep progression, showing key parameters that describe creep failure life [361]. .......................................................................................................................... 805 Figure R2-2: Strain behaviour as a function of material parameter m, the exponent in equation R2-16a for the arbitrary specification ε 1 = 1 / t1 . Alternative profiles for the solution to equation R2-16b are shown by the lighter, red curves. The thicker curves are for the typical limits on m................................................................................................................................. 808 Figure R2-3: The fractional consolidation, Uc, as a function of time, t, for a spring and a KELVIN–VOIGT element in series using the parameter values given in the text. .......................... 817 Figure R2-4: Behaviour of viscoelastic fibre bundles with GLS and uniformly distributed breaking strains for a range of dimensionless stresses, Σ. .............................................................. 821

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Figure S7-1: Absorbance spectra and components thereof for a raw water and the supernatant resulting from coagulation of the raw water with ferric chloride at 80mg(Fe)/L, pH ≈ 7.3........ 853 Figure S7-2: Absorbance spectra and components thereof for a raw water and the supernatant resulting from coagulation of the raw water with aluminium sulfate at 79mg(Al)/L, pH ≈ 6.3................................................................................................................................................... 854 Figure S8-1: Absorbances for raw and coagulated water, and for platinum–cobalt colour standards, all normalised such that A400nm is plotted as unity. ....................................................... 859 Figure S8-2: Absorbance of platinum–cobalt colour standards. ............................................................... 861 Figure S9-1: Ultraviolet light absorbances of progressive filtrate portions............................................. 870 Figure S9-2: Visible light absorbances of progressive filtrate portions.................................................... 870 Figure S9-3: The effect of different filters on absorbance (first 25mL of filtrate discarded).................. 871 Figure S10-1: Curve fits of data from four batch settling experiments on the same material at different dilutions. ................................................................................................................................ 875 Figure S10-2: Variation in solidosity at the bottom of the bed as a function of bed depth from curve fits of data from four batch settling experiments on the same material at different dilutions. ................................................................................................................................................ 876 Figure S10-3: Variation in particle pressure as a function of solidosity, both at the bottom of the bed, from curve fits of data from four batch settling experiments on the same material at different dilutions. ................................................................................................................................ 877 Figure S10-4: Compressive yield stress computed using B-SAMS for individual settling tests A, B, C and D compared to a multiple-test analysis. The multiple-test analysis is presented as a composite curve, with exponential (E) and linear (L) interpolation alternatives................. 879 Figure S10-5: Hindered settling function computed using B-SAMS for individual settling tests A, B, C and D compared to the results of manually adjusting R to match settling curve C using either compressive yield stress curve Cd (default B-SAMS) or cE (multiple-test analysis) of Figure S10-4. ..................................................................................................................... 880 Figure S10-6: Solids diffusivity computed using B-SAMS for individual settling tests A, B, C and D compared to the results of manually adjusting R to match settling curve C using either compressive yield stress curve Cd (default B-SAMS) or cE (multiple-test analysis) of Figure S10-4....................................................................................................................................... 881 Figure S10-7: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — tes t A . Suspension heights (first in legend) and isoconcentration curves for φg (second in legend) are shown for each scenario.......................... 886 Figure S10-8: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — tes t B. Both suspension heights (first in legend) and isoconcentration curves for φg (second in legend) are shown for each scenario. ................. 887 Figure S10-9: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — tes t C. The solid lines are suspension heights, the isoconcentration curves for φg are shown as broken lines........................................................ 888 Figure S10-10: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — te s t D. Both (falling) suspension heights and (initially rising) isoconcentration curves for φg are shown for each scenario....................... 889

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Figure S10-11: Estimated range of solidosities occurring in tests A to D (based upon compressive yield stress from multiple-test analysis); the corresponding gel point is shown as a divider................................................................................................................................ 890 Figure S11-1: Subaerial slump tests. Final height ≈ 13mm  Slump ≈ 12mm. Minor leakage in first image is not significant for the purposes of this experiment. ................................................. 892 Figure S11-2: Subaqueous slump tests. Final height ≈ 26mm  Slump ≈ –1mm (INVALID). Note: sample lifted up with cylinder until water surface reached (see centre image). .............. 892 Figure S11-3: Subaerial slump tests. Final height ~ 2.5mm  Slump ~ 22.2mm (INVALID). ........... 893 Figure S11-4: Subaqueous slump tests. Final height ~ 13mm  Slump ~ 12mm. Note: final height taken as lowest point of top surface of slumped column.................................................... 893 Figure S11-5: Subaerial slump tests. Final height ~ 2.5mm  Slump ~ 22.5mm (INVALID). Note: glass surface was on a slight incline in this test. ................................................................... 894 Figure S11-6: Subaqueous slump tests. Final height ≈ N/A  Slump ≈ N/A (Not applicable). Final image shows dispersion after about one minute of standing. .............................................. 894 Figure S12-1: Effect of removing the low-dose, low-pH data point on the contour plot of φ at R = 5×1010Pa.s/m2 for laboratory alum sludges as a function of dose and pH. ............................. 896 Figure S12-2: Effect of removing the 10mg(Al)/L, pH 6 data point on the contour plot of φ at R = 5×1010Pa.s/m2 for laboratory alum sludges as a function of dose and pH. ............................. 897 Figure S13-1: Solids throughput as a function of final average cake solidosity for various alum doses. ...................................................................................................................................................... 900 Figure S13-2: Solids throughput as a function of final average cake solidosity for alum sludges coagulated at various pH values. ....................................................................................................... 902 Figure S13-3: Solids throughput as a function of final average cake solidosity for a selection of alum sludges coagulated under various conditions. (Compilation from Figure S13-1 and Figure S13-2.) ......................................................................................................................................... 903 Figure S13-4: Solids throughput as a function of final average cake solidosity for a selection of ferric sludges coagulated under various conditions. ....................................................................... 904 Figure S13-5: Influence of membrane resistance on filter throughput predictions for alum sludges of good and of poor dewaterability. .................................................................................... 905 Figure S15-1: Illustration of the effect of assuming a fitting parameter to be constant when evaluating uncertainties of the fit. ...................................................................................................... 914 Figure S15-2: Illustration of the bias arising as parameters are bootstrapped. Estimation of area by numerical integration of observed data points. It is assumed the intercepts are fixed. Values are indicative only. .................................................................................................................. 917 Figure S17-1: Compressive yield stress as a function of solidosity (left) as per Figure 5-18, and the corresponding local power-law exponent (right). ..................................................................... 935 Figure S17-2: Estimates of the characteristic relaxation time (trelax), bulk viscosity (ηbulk), and compressive yield stress (σy), based on the interaction potential (–Umin) as a function of particle size (d0) for several scenarios................................................................................................. 936 Figure S19-1: Correlation for frame expansion correction......................................................................... 943 Figure S20-1: Hypothetical centrifugation unloading results. .................................................................. 945

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Figure S21-1: pH–electronegativity diagrammes for complexation of Al3+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively.......................... 949 Figure S21-2: pH–electronegativity diagrammes for complexation of Al3+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H5O2]+ and H2O at pH 0 and 7 respectively. ............................................... 950 Figure S21-3: pH–electronegativity diagrammes for complexation of Mg2+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively.......................... 951 Figure S21-4: pH–electronegativity diagrammes for complexation of Zr4+ (co-ordination number = 8 or 6) by multiple ‘foreign’ bidentate anions of various types. The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively............................................................... 952 Figure S21-5: Prediction of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals as a function of pH according to the partial charge model referenced to [H5O2]+ and H2O at pH 0 and 7 respectively [466, 675].................................................................... 953 Figure S22-1: Variation in physically- and chemically-bound water with pseudoböhmite crystallite size. (Data of BAKER & PEARSON [121].) .......................................................................... 955 Figure S24-1: Influence of particle size on the relative stability of hæmatite (Hm) and goethite (Gt) in the (hypothetical [280]) reaction 2Gt → Hm + H2O at 298K [cf. 633, 634]......................... 958 Figure S26-1: Representative profiles for key variables (taken as dimensionless in the plot) related to the shear imposed on fluid elements in lami nar pipe flow........................................ 966

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TABLES

Table 1-1: I nd ica ti ve dry solids contents [%m]a for feed and output from various dewatering processes and other operations handling WTP coagulation sludges. ............................................. 12 Table 1-2: Number of facilities practising various dewatering operations recorded circa 1991 from a survey of 438 utilities and 347 WTP’s in the U.S.A. [880]. .................................................... 13 Table 1-3: Popularity of various disposal routes, as percentages, for sludge generated at WTP’s in New Zealand (122 plantsa, August 1996) [161, 797], the U.K. (circa 1999) [827], and the U.S.A. (circa 2000) [282]. Major routes in bold. .................................................................................. 27 Table 1-4: Classification of key parameters influencing sludge properties............................................... 54 Table 2-1: Conventional empirical methods.................................................................................................. 79 Table 2-2: Important ‘compressibility’ parameters of TERZAGHI, PECK & MESRI [see 1014]. .................. 84 Table 3-1: Water quality variables for Winneke raw water as sampled or as received. Statistics are weighted by the actual number of sludges characterised for the given raw water. ............. 162 Table 3-2: Analysis of Winneke raw water. Outstanding values in bold type. ..................................... 163 Table 3-3: Preliminary ‘jar testing’ coagulation experiments with various magnesium formulations. ......................................................................................................................................... 165 Table 3-4: Specifications for HOLLAND & CHAPMAN’s [485] ‘standard’ tank configuration. ................ 175 Table 3-5: Scale-up of vessel mixing parameters. All used a RUSHTON turbine impeller..................... 184 Table 3-6: Typical values of A254nm [289]. ...................................................................................................... 190 Table 3-7: Options for instrumental colour measurement according to the U.S. Standard Methods [334]. ....................................................................................................................................... 192 Table 3-8: Single test and multiple test batch settling estimates of φg. .................................................... 206 Table 3-9: Considerations in specifying centrifugation speed. ................................................................. 210 Table 3-10: Generation conditions for sludge samples used in batch centrifugation. ........................... 211 Table 3-11: Typical Press-o-matic stepped pressure filtration run settings for compressibility (py) and permeability (R)............................................................................................................................. 232 Table 3-12: Default linearity criterion parameters for Press-o-matic stepped-pressure permeability runs.................................................................................................................................. 232 Table 3-13: Radial variation in solidosity for a filter cake consolidated at ~450kPa. ............................. 238 Table 3-14: (a) Generation conditions for ‘replicate’ laboratory sludge samples. ................................. 240 Table 4-1: Theoretical composition of WTP sludges produced under various conditions [879].......... 256 Table 4-2: (a) Predicted composition of alum sludges derived from typical Winneke raw water at various doses..................................................................................................................................... 259 Table 4-3: Selected solid aluminium (oxy)hydroxide phases and their densities [223, 504, 870]......... 260

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Table 4-4: Key chemical and physical data of selected iron (oxy)hydroxides [279, 280, 397, 520]....... 261 Table 4-5: Other solid phases arising from drinking water treatment [662]. .......................................... 262 Table 4-6: Key chemical and physical data of naturally appearing phases............................................. 262 Table 4-7: Solid phase densities, ρS [kg/m3], for alum and ferric sludges according to a range of publications. .......................................................................................................................................... 265 Table 4-8: Ferric sludge samples characterised by EDS. ............................................................................ 268 Table 4-9: XRD peaks for pseudoböhmite [499, 500, 584, 748, 1099, 1150]. ............................................. 271 Table 4-10: Generation conditions for alum sludge samples characterised by powder XRD............... 273 Table 4-11: Generation conditions for ferric sludge samples characterised by powder XRD. ............. 274 Table 4-12: Molar percentages for the incidence of detections corresponding to lumped Kα (peak) radiation of the elements listed, and ratio of Fe to O (or Cl) in laboratory ferric sludges of different ages and ferric chloride reagent. The averaging area is illustrated in Figure 4-4. .............................................................................................................................................. 276 Table 4-13: Molar percentages for the incidence of detections corresponding to lumped Kα (peak) radiation of the elements listed, and ratio of Fe to O in plant ferric sludges of different ages. Key values are in boldface. ....................................................................................... 278 Table 4-14: Liquid phase densities for a range of drinking water sludges.............................................. 290 Table 5-1: (a) Generation conditions for alum sludge samples with coagulation pH ≈ 6. Samples for which replicate data was presented in §3▪5▪4 are marked with a hash symbol, #. .............................................................................................................................................................. 309 Table 5-2: Schematic of key trends and features identified in Figure 5-10 (py = 50kPa). Note, symbol ↓ denotes decreasing and symbol ↑ denotes increasing.................................................... 324 Table 5-3: Generation conditions for Happy Valley pilot plant sludge samples.................................... 331 Table 5-4: Generation conditions for ferric sludge samples. ..................................................................... 336 Table 5-5: Generation conditions for sludge samples used in batch centrifugation. ............................. 354 Table 6-1: Change in MIEX eluate properties upon dialysis, and change in ‘raw’ water properties upon spiking with dialysed MIEX eluate to approximately 1.25%V. Values for undialysed MIEX eluate have an uncertainty of around ±20%. ..................................................... 364 Table 6-2: ‘Raw water’ quality and coagulation conditions for dMIEX sludges and non-spiked sludges (the latter in parentheses, where different). Dashes indicate that no measurement was made. .............................................................................................................................................. 366 Table 6-3: Summary of significant changes in behaviour associated with spiking of dMIEX.............. 370 Table 7-1: Generation conditions for alum sludge samples used to investigate the effect of shear........................................................................................................................................................ 388 Table 7-2: Generation conditions for alum sludge samples used to investigate flocculation............... 393 Table 7-3: Generation conditions and estimated gel points for alum sludge samples used to investigate the effect of polymer conditioning. Parameters for the sheared sludges are identical to those of the unsheared (unconditioned) sludges......................................................... 399 Table 7-4: Solidosities at which the samples were sheared or conditioned. ........................................... 399 Table 7-5: Tubing details for the sludge shearing and conditioning rig (see Figure 7-5). ..................... 402

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Table 7-6: Approximate pressure drop, in metres of water, downstream of the T-junction in Figure 7-5. Key values in bold............................................................................................................ 403 Table 7-7: Estimated shear schedule, for both unconditioned and conditioned sludges (η = 6mPa.s)............................................................................................................................................ 405 Table 7-8: Shear schedule for limiting alternative effective viscosities.................................................... 405 Table 8-1: (a) Experimental conditions for fresh and aged laboratory sludge samples. ...................... 436 Table 8-2: Overview of freeze–thaw conditioned sludges......................................................................... 457 Table 8-3: Size distribution of suspended solids in Happy Valley PAC sludge..................................... 464 Table 9-1: Long-time batch settling data curve fits (h and h∞ in mm, t in days). .................................... 508 Table 9-2: Pressure differentials employed in a ‘reversible compressibility’ test [kPa]. ....................... 537 Table 9-3: Changes in cake height in response to increases and decreases in applied pressure. ......... 539 Table R1-1: Various NOM classification schemes based on hydrophilicity–hydrophobicity and charge. The hierarchy presented is intended to indicate approximate synonyms and hyponyms. ............................................................................................................................................. 629 Table R1-2: Typical observed NOM configurations and conformations under a variety of conditions [1024]. .................................................................................................................................. 633 Table R1-3: Typical organic matter contents in common soil types [1066]. ............................................ 637 Table R1-4: Classes of hydrolysed species arising in sequence [466, 677]............................................... 651 Table R1-5: Influence of humic acid upon aluminium (oxy)hydroxide formation from 1.1mM AlCl3 (30mg(AL)/L) after 80 days ageing in the mother liquor at ~25°C [940]. ............................ 677 Table R1-6: Influence of fulvic acid upon aluminium (oxy)hydroxide formation from 0.9mM AlCl3 (24mg(AL)/L) after 70 days ageing in the mother liquor at 30°C [584]. .............................. 678 Table R1-7: Characteristics of raw waters containing various levels of magnesium [156]. .................. 699 Table R1-8: Processes following from polymer addition according to polymer properties and addition point (or purpose). ................................................................................................................ 711 Table R1-9: Optimal polyelectrolyte sizes for assorted dewatering operations [505]............................ 715 Table R1-10: Typical agitator tip speeds [484, 485]..................................................................................... 723 Table R1-11: Typical values of G, t and G.t for coagulation–flocculation operations on full-scale WTP’s ahead of clarifiers. .................................................................................................................... 734 Table R1-12: Schematic of the ‘fractal’ size correlations of several regular aggregates......................... 740 Table R1-13: Limiting choices in formulating models of aggregation. Most common choices/assumptions are listed first. The column at far right gives the limiting assumption yielding the larger (apparent) value of Df.................................................................... 756 Table R1-14: Plausible scenarios for ‘simple’ cluster–cluster aggregation based on transport mode and rate-limiting step. ............................................................................................................... 760 Table S6-1: Key specifications implemented or recommended for jar testing in the literature............ 844 Table S6-2: Tapered mixing protocol suggested by KAWAMURA [557]. ................................................... 845 Table S6-3: Tapered mixing protocol suggested by HUDSON & WAGNER [503]. .................................... 845 Table S6-4: Examples of treatment objectives in jar testing [229]. ............................................................ 846

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Table S7-1: Ultraviolet absorbance curve-fit parameters (used in equation S7-10)................................ 852 Table S8-1: Concentrations of standard platinum–cobalt colour solutions............................................. 856 Table S8-2: A ppr o xi mate equivalencies and related terms for colour space parameters [173, 260, 334, cf. 1134]................................................................................................................................... 864 Table S8-3: Typical values of colourimetric parameters. Sample ‘A’ is Winneke raw water (collected 2004-07-05); sample ‘B’ is sample A plus 1.25% dMIEX; sample ‘C’ is sample B treated with 80mg(Al)/L at pH ≈ 6.4. The illuminant is D65.......................................................... 865 Table S10-1: Individual settling tests. ........................................................................................................... 874 Table S10-2: Fitting parameters for multiple batch settling experiment analysis. ................................. 874 Table S10-3: Error in h∞ using equation 2-102 only, or 2-102 and 2-103 depending on φ0. ................... 878 Table S10-4: Gel points estimated by B-SAMS based on each settling test taken individually, and by multiple-test analysis. ............................................................................................................. 878 Table S10-5: Overview of input parameters for h(t) predictions from various sources. Predicted (output) equilibrium heights, ĥ∞, are included here for convenient comparison with observed h∞. ........................................................................................................................................... 883 Table S10-6: Effect of the interpolation (or extrapolation) of the compressive yield stress at intermediate solidosity on the predicted equilibrium height for test A. The final observed height was 0.1681m............................................................................................................................... 885 Table S13-1: Key flexible-membrane filter press model parameters. ....................................................... 899 Table S14-1: Mixing of polymer conditioner into settled sludge using an orifice plate according to the specifications of DILLON [315] (shown in bold)...................................................................... 910 Table S17-1: Values of parameters used to estimate ηbulk, σy, and trelax. Baseline values are presented, along with values used in the alternative scenarios (where relevant). ...................... 935 Table S17-2: Indicative viscosities (in the zero-shear-rate limit) of several materials usually classed as ‘solids’, “mostly at room temperature” [127].................................................................. 937 Table S25-1: Floc breakage correlations of MÜHLE and colleagues [763, 776]......................................... 961

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NOMENCLATURE

Symbols Symbols, units, and terminology used generally follow recognised standards, guidelines, or convention (e.g. BIPM [61], IUPAC [275, 349, 689, 725, 747], ISO, ASTM, AS, et cetera). A notable exception is the coefficient of determination (R2), which is treated as a ligature and printed in roman type to avoid confusion with the hindered settling function (R). The base units listed can, of course, be substituted with compatible alternatives. Some trivial symbols, whose definition is provided in the text where the symbol is used, have been omitted.

Latin symbols a

[–]

acceleration constant in a bootstrap method

av c

[Pa‒1]

coefficient of compressibility

A

[m2]

area

AH

[J]

(‘effective’) HAMAKER constant

Aλ

[10/m]

absorbance at wavelength λ (100mm path length)

A

[–]

absolute (fractional) absorbance

B

[Pa]

bulk modulus

BS

[Pa]

‘drained’ bulk modulus of compressibility for the particulate network in a confined geometry (assuming isotropic stress)

B

[m‒2]

number of bonds per m2

c

[m/s]

wave velocity

cv c

[m2/s]

coefficient of consolidation

C

[M]

molar concentration

C

[mg/L Pt units] true colour

Cc

[–]

primary compression index

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D. I. VERRELLI

Ce

[kg2/s.m4]

coefficient of primary consolidation

Cα

[–]

secondary compression index

d

[m]

crystallite size

[m]

diameter or size of general particulate

d0

[m]

primary particle diameter

dagg

[m]

aggregate diameter

dclus

[m]

cluster diameter

dhkl

[m]

interplanar spacing (for crystals)

dKolmogorov [m]

KOLMOGOROV turbulence microscale

D

[m]

‘external’ diameter or lengthscale of system

Da

[m]

agitator diameter

Df

[–]

fractal dimension (in 3-dimensional EUCLIDean space, unless otherwise stated)

Dl

[–]

fractal dimension of the (load-bearing) chains

Ds

[–]

surface fractal dimension

DT

[m]

tank internal diameter

D

[m2/s]

solids diffusivity

D ij

[m2/s]

diffusivity tensor (intermingling of particle species i and j)

e e

base of natural logarithms [m]

absolute surface roughness

[–]

void ratio

ei

[s‒1]

parameters in long-time filtration equation (i = 1, 2, 3, ...)

e

[–]

relative surface roughness

E

[Pa]

YOUNG’s modulus; spring constant

[V]

electrochemical potential

Ei

[s], [m]

parameters in asymptotic long-time dewatering formulæ (i = 1, 2, 3, 4)

Ek

[–]

EKMAN number

fi

[–]

parameters in long-time settling and filtration equations

fFanning [–]

FANNING friction factor

F

[N]

force

Fr

[–]

FROUDE number

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g

[m/s2]

acceleration due to gravity

g

[–]

pair correlation function — cf. Appendix S18

G

[1/s]

characteristic (or root-mean-square) velocity gradient

ΔfG°T [J/mol]

standard GIBBS energy of formation at temperature T

h

height, especially relating to the interface height of a settling bed of

[m]

sludge [–]

extent of ‘hydrolysis’

H

[–]

probability density function: empirical distribution

ΔH°T

[J/mol]

standard enthalpy of reaction (i.e. change in enthalpy) at temperature T

Hloss

[m]

frictional head loss

i

[–]

index

I

[M]

ionic strength

[W/m2]

intensity of illumination

[–]

instability parameter for polydisperse settling

j

[–]

number of particles per aggregate

k

[–]

structure ‘prefactor’

[varies]

arbitrary quantity per unit distance

kˆ

[–]

unit vector in +z direction

k0

[–]

curvature of interparticle pair potential

kB

[J/K]

BOLTZMANN constant (= R / NA ≈ 1.3807×10−23J/K [752])

K

[–]

head loss factor for fitting

[varies]

equilibrium constant of reaction (theoretically dimensionless)

[m2]

permeability

KD

KD 1856 [m/s]

DARCY’s original permeability coefficient

Ki

ratio of the local energy dissipation rate in the impeller discharge zone

[–]

to the mean for the entire volume

Kb

[–]

curvature of interparticle potential curve barrier

Kw

[–]

curvature of interparticle potential curve well

l

[m]

length

L

[m]

length

xlv

D. I. VERRELLI

m

[kg]

mass

[–]

number of ‘foreign’ ions complexed per metal

[–]

index of bootstrap number

[–]

material parameter in creep equations

mv c

[1/Pa]

coefficient of volume compressibility

mV c

[1/Pa]

coefficient of vertical compression

M

[–]

number of bootstrap samples

Mc

[N.m]

critical bending moment

n

[–]

solvent refractive index

[–]

index of data point number

n1

[–]

number of active chains per junction

N

[s‒1]

stirring rate (revolutions)

[–]

co-ordination number

[–]

number of data points

[–]

number of jackknife samples

[–]

standard normal (i.e. GAUSSian) distribution

o

[–]

porosity

p

[Pa]

pressure (i.e. isotropic compressive stress)

py

[Pa]

compressive yield stress

P

[W]

power

[–]

particle form factor

[–]

cumulative density function (probability)

Pé

[–]

PÉCLET number

Pésett

[–]

PÉCLET number for settling

Po

[–]

power number

p

[Pa]

excess pore-water pressure, (≡ p + ρL g z ‒ ρL g h = P ‒ ρL g h)

P

[Pa]

modified pressure, (≡ p + ρL g z)

q

[–]

degree of protonation (of anion)

[m‒1]

wavenumber

[varies]

arbitrary quantity per unit time

[m/s]

flux of solid volume; solid flux–density function

qS

xlvi


qS∗

[m/s]

flux of solid volume if there were no network stress, i.e. ‘unsupported’ solid-phase flux; solid flux–density function

Q

[m/s]

volume flux of material (solid and liquid) entering or exiting; throughput

r

rcake

[–]

hindered settling factor

[m]

radius (e.g. from centrifuge rotor axis)

[m‒1]

hydraulic resistance of filter cake

rmembrane [m‒1]

hydraulic resistance of filter membrane

R2

[–]

coefficient of determination (i.e. fraction of variance explained)

R

[Pa.s/m2]

hindered settling function

R

[J/mol.K]

ideal gas constant (molar)

Re

[–]

REYNOLDS number

Ro

[–]

ROSSBY number

S

[–]

interparticle structure factor

t

[s]

time

T

[K]

temperature

Ta

[–]

(modified) TAYLOR number

T

[–]

transmittance

u

[m/s]

particle velocity (or volumetric flux)

u°

[m/s]

STOKES settling velocity

u

[m/s]

settling velocity of a single particle in an infinite, quiescent medium

u∗

[m/s]

settling velocity in the absence of solid phase stress

U

[J]

interparticle potential

Uc

[–]

dimensionless change in height (or normalised strain)

v

[m/s]

fluid velocity (or volumetric flux)

V

[m3]

volume

V

[m]

specific filtrate volume (volume per unit superficial cross-sectional flow area)

w

[m/s]

local mean velocity of the mixture relative to the container

We

[–]

WEBER number

x

[–]

mass fraction of (suspended) solids

xlvii

D. I. VERRELLI

y

[–]

mass fraction of (total) solids

z

[–]

ordinate in EUCLIDean space, typically perpendicular to phase motion

[–]

charge (e.g. on the unhydrolysed cation), oxidation number

[–]

co-ordination number

zα

[–]

100αth percentile point of the standard normal distribution

Z

[m]

networked-sample height

Greek symbols α

[–]

statistical significance level

[–]

structure ‘prefactor’

[–]

denticity

αh

[m‒2]

cake specific resistance, based upon cake height

αm

[m/kg]

cake specific resistance, based upon mass of solids in cake (per unit area)

αSRF

[m/kg]

specific resistance to filtration

αV

[m‒2]

cake specific resistance, based upon equivalent height of pure solids in cake

β

[–]

empirical exponent ~ Df

β∗

[Pa‒1]

‘compressibility’ for particulate systems (for plastic deformation)

[–]

cumulative equilibrium-formation constants

βT

[Pa‒1]

isothermal compressibility

βVS

[Pa‒1]

‘compressibility’ for particulate systems (general, analogous to βT)

γ

[–]

fibre bundle model parameter

[varies]

empirical parameters in long-time settling correlations

γ

[s‒1]

shear strain rate

Γ

[–]

aspect ratio, L / d0

δ

[m]

interparticle (surface) separation

[–]

loss tangent (viscoelastic phase lag: ratio of loss and storage moduli)

Δ

[varies]

ad hoc parameter or constant

ε

[W/kg]

(time-average) energy dissipation rate per unit mass

[–]

linear strain

[V]

refers to electrokinetic potential in the term ζ-potential

∗

βn

ζ

xlviii


η

[Pa.s]

viscosity

ηbulk

[Pa.s]

‘bulk viscosity’: solid-phase creep-like response to (low) stress

θ

[radian]

(half) scattering angle

[varies]

general parameter of interest

[–]

ratio of strains (FBM)

Θ

[NTU]

turbidity

ι

[–]

ratio of compressive yield stress to total weight of solid phase per area

κ

[(Pa.s)‒1]

dynamic compressibility

[m‒1]

inverse of DEBYE length

[m]

wavelength (e.g. for light)

[kg/s]

drag coefficient

1/λ

[m‒1]

mean wavenumber

Λ

[–]

power function (≡ Po / Fry )

μ

[–]

friction coefficient of AMONTONS and COULOMB

[varies]

mean

[J/mol]

chemical potential

μσ

[Pa.s]

viscosity parameter in macrorheological model

ν

[–]

POISSON’s ratio

ξ

[varies]

empirical constants

[m]

characteristic lengthscale

Ξ

[varies]


π

[–]

ratio of circle circumference to diameter

π

[Pa]

empirical constant

Π

[Pa]

osmotic pressure

ρ

[kg/m3]

density

σ

[Pa]

(normal) stress

[N/m]

surface tension

[varies]

standard deviation

Σ

[–]

ratio of stresses (FBM)

τ

[Pa]

shear stress (i.e. tangential stress)

τy

[Pa]

shear yield stress

λ

xlix

D. I. VERRELLI

υ

[–]

volume-prefactor

Υ

[M–1 m–1]

molar absorptivity

φ

[–]

solidosity (i.e. volume fraction of the solid phase) of the system

φagg

[–]

solidosity of the aggregates

φg

[–]

solidosity of the system at the gel point

φ

[–]

volume fraction of aggregates or flocs in the system, equal to φ/φagg

Φ

[–]

probability density function of standard normal distribution

[m]

parameter in long-time filtration and settling equations

χ

[–]

electronegativity (ALLRED–ROCHOW electronegativity scale)

ψ

[–]

fraction of the overall equilibrium consolidation due to ‘creep’

Ψ

[Pa‒1]

concrete “creep rate” parameter

ω

[s‒1]

rotation rate (radians); angular velocity

ωtotal

[m]

total volume of solids per unit (superficial) area

Cyrillic symbols Б

[varies]


г

[–]

parameter relating n1 to φ

Ж

[–]

SCHERRER constant

И

[–]

number of calls to random number generator

м

[varies]

parameter related to aggregate strength

н

[–]

ratio of lateral to axial stresses (virgin compression, laterally constrained)

ч

[–]

relative aggregate size, dagg/d0

чx

[–]

relative aggregate size, dagg/d0, with Df = x

ш

[–]

parameter related to sensitivity of aggregate to shear (G)

э

[–]

relative density difference

я

[–]

correction factor: ratio of STOKES settling velocity to actual velocity,

я ≡ u°/u

l


Mathematical operators and other symbols O(·)

of order ....

C·D

(ensemble) average

ˆ 

(point) estimator — used above pronumeral

˙

time derivative — used above pronumeral

%m

percent (mass basis)

%V

percent (volume basis)

=

equal

≈

approximately equal

~

roughly equal

bias-corrected (point) estimator — used above pronumeral

has the distribution (probability density function) ∝

proportional to

 ∝

approximately proportional to

δ

small change

Δ

change (final minus initial) or difference (solid minus liquid; sample minus ambient)

p

negative decimal logarithm

′

derivative — for functions

Superscripts ′

alternative or modified — for constants

∗

addition of a protonated ligand with elimination of the proton — used as a prefix (note that the mark used for footnotes is ‘ * ’)

∗, •, 

alternative or modified

0

at infinite dilution

B

bootstrap estimator — used as a prefix

J

jackknife estimator — used as a prefix

li

D. I. VERRELLI

Subscripts 0

initial (except as above)

2dim.

two-dimensional

50

median (i.e. 50th percentile)

a

agitator

agg

aggregate

c.f.

(during) cake formation

clus

cluster

con.

confined

cp

close-packed

crit

critical

DS

dissolved solids

f

fluid final (output)

i

impeller (discharge zone)

L

liquid phase — including d i s s o l v e d solids

max

maximum

min

minimum

M

metal

p

particle

ref

reference

S

(suspended) solid phase

T

tank

vdW

VAN DER WAALS

y

yield

∞

at equilibrium (t → ∞)

lii


Abbreviations alum

aluminium sulfate

BIPM

Bureau International des Poids et Mesures

BOD

biological oxygen demand

B-SAMS

See §3▪5▪1▪1

CA

cellular automata

CIE

Commission Internationale de l'Éclairage / International Commission on Illumination / Internationale Beleuchtungskommission

CLCA

convection-limited cluster–cluster aggregation

COD

chemical oxygen demand

CSIRO

Commonwealth Science and Industrial Research Organisation

CST

capillary suction time

CTMS

chlorotrimethylsilane

DAF

dissolved air floatation

DLCA

diffusion-limited cluster–cluster aggregation

DLVO

DERJAGUIN–LANDAU – VERWEY–OVERBEEK

dMIEX

dialysed MIEX (waste brine) eluate

DML

dynamic multiple lane

DOC

dissolved organic carbon

EDS

energy-dispersive spectrometry

FBM

fibre bundle model

ferric

ferric chloride (unless otherwise indicated)

GAC

granular activated carbon

GLS

Global Load Sharing

HTCO

high-temperature catalytic oxidation

ICP

inductively-coupled plasma discharge

i.e.p.

isoelectric point

IUPAC

International Union of Pure and Applied Chemistry

lab.

laboratory

LLS

Local Load Sharing

liii

D. I. VERRELLI

MIEX

‘magnetic ion-exchange’ resin (tradename of a water treatment resin)

NDIR

non-dispersive infrared

NOM

natural organic matter

PAC

powdered activated carbon

PACl

polyaluminium chloride

PCB

poorly crystalline böhmite

POC

particulate organic carbon

RLCA

reaction-limited cluster–cluster aggregation

RMS

root-mean-square

SA(L)LS

small-angle (laser) light scattering

SBW

spectral bandwidth

SEM

scanning electron microscope

SRF

specific resistance to filtration

SRP

soluble reactive phosphorus

SUVA254nm

specific ultraviolet absorbance at λ = 254nm

TBS

See §3▪7▪1 (transient batch settling)

TCLP

toxic characteristic leaching procedure

TDS

total dissolved solids

TOC

total organic carbon

TS

total solids (conceptually, the sum of TSS and TDS [cf. 334])

TSS

total suspended solids

TTF

time-to-filter

UU

United Utilities

UV

ultraviolet

WFP

water filtration plant

WTP

water treatment plant

WWTP

wastewater treatment plant

XRD

x-ray diffraction

YW

Yorkshire Water

liv


Terminology The most recent recommendations by relevant authorities (e.g. IUPAC [349, 515, 548, 689,

725, 1120]) regarding terminology are followed as far as practical.

lv

1.

INTRODUCTION

In spite of the wealth of experience which surrounds sweep coagulation, few studies have addressed the question of what happens to the precipitate [sludge]. Where does it go? What does it do? Since many operational problems can stem from an unsatisfactory floc [or aggregate], asking such questions offers the prospect of developing more

effective

strategies

for

combating

the

problems. — BACHE et alia (1999) [113]

1▪1

Drinking water production processes

Clean drinking water is a vital resource. In the least developed countries, accessing safe drinking water can be difficult, if not impossible [cf. 54, 62]. Yet despite droughts, growing concerns over climate change [71], and a range of unsustainable practices [55, 244, 245, 311], residents of developed countries generally continue to enjoy access to high quality potable water. There are many factors that contribute to the availability of this clean drinking water, including political stability and governance, wealth and infrastructure, and education and environmental protection. From a technical point of view we are most interested in the water treatment operation.

Raw water abstracted from reservoirs, rivers, aquifers and the like may contain a wide variety of contaminants, including micro-organisms, inorganic and organic chemicals, and radionuclides [34]. These impurities may be present as dissolved species, as suspended solid particles, or as species bound to such particles.

Drinking water provision increasingly

involves (centralised) treatment to remove these contaminants.

1

D. I. VERRELLI

Drinking water treatment serves two purposes, which are to improve the quality of the water in terms of its impact on human health and its æsthetic appeal [cf. 34], although safety obviously must take precedence.

To do this the level of impurities in the water must

generally be decreased, although in some cases (e.g. fluoride; calcium and magnesium salts [cf. 34], §R1▪2▪7▪6) minimum levels are also recommended. In some cases the motivation for contaminant removal is ‘indirect’, such as for ordinarily harmless organic molecules which would subsequently react with the disinfectant to yield carcinogens, or for particulates to which heavy metals are adsorbed.

Even in developed countries the level of treatment varies according to the size of the community served [cf. 32, 34, 43, 59] and the quality of the raw water [e.g. 161, 797]. An indication of the scope of treatment processes commonly practised in developed countries is given by Figure 1-1. Clearly surface water constitutes the major source of raw water, and this is generally treated by the ‘conventional’ coagulation process described below [282, 315].

100% 80%

groundwater upland

60% 40% 20%

surface water

disinfection

(some: Fe/Mn removal)

coagulation

(high colour, low turbidity)

(+ settling/DAF) & rapid gravity filtration

lowland

(+ settling/DAF) & rapid gravity filtration

coagulation (low colour, high turbidity)

0%

slow sand filtration

Figure 1-1: Distribution of raw water sources and treatments in England and Wales circa 1997, by water volume [315].

In contrast groundwater may receive little [315] to no [161] treatment. The “relatively pure” sludges formed by oxidation of iron (or manganese) in groundwaters are claimed to be “easier to treat” than those from conventional coagulation” [315].

2

Chapter 1 : Introduction


Slow sand filtration is no longer common in many countries, such as New Zealand [797] and Australia — although it continues to be used in the U.K. for some (turbid, low-colour) lowland waters [315], and in the U.S.A. at some small water treatment plants (WTP’s) treating low-turbidity water [880]. Even where slow sand filtration is practised, the resulting “natural sludge” waste stream generated at infrequent intervals is of low volume and is readily treated [315]. Lime–softening also produces a sludge, considered to comprise predominantly calcium carbonate with magnesium hydroxide. Softening is rarely practised in the U.K. [315], New Zealand [797], or Australia [232], and the resulting sludge dewaters readily [e.g. 107]. Furthermore, lime–softening operations are anticipated to be gradually replaced by membrane technology [493]. The present work focusses on conventional coagulation based on its prevalence and the greater amount of problematic sludge it produces.

The conventional treatment process is well-established, and robust. It consists of dosing a ‘coagulant’ (chemical), which forms a precipitate in the water as it is neutralised upon addition of an alkali. In some raw waters sufficient natural ‘alkalinity’ is present to buffer the pH without alkali addition [282] [see also 430, 1141].

The most commonly used

coagulants are aluminium sulfate (“alum”) and trivalent iron salts (“ferric”) — see §R1▪2. The precipitate is aggregated with the raw water contaminants, so that these are held together in a solid phase suspended in the purified liquid water. By separating these two phases a clear supernatant stream can be taken off for possible further processing and distribution to customers. The aggregates can be formed into larger ‘flocs’ by addition of a ‘flocculant’ (polymer) to aid the solid–liquid separation. The separation may be accomplished by gravity settling (‘sedimentation’, or ‘clarification’), direct filtration (through a bed of granular media), or floatation (typically as ‘dissolved air floatation’). In the present work attention centres on sludges obtained from gravity settling, which is considered the conventional operation [e.g. 384, 557]. However this should not detract from the large reductions of ~30 to 80% in sludge production that can be obtained by operating a direct filtration process [557] (or reductions by other process modifications, such as pre-oxidation [136] or polymer-only clarification [142, 171, 289] [cf. 521, 781, 782]).

1▪1 : Drinking water production processes

3

D. I. VERRELLI

The waste stream comprises the partially ‘dewatered’ aggregates, which in thickened form is referred to as ‘ s l u d g e ’ . In general the solid components of the sludge can be considered a waste, although efforts have been made to find beneficial uses for them (§1▪5). The sludge still contains large amounts of water, due to the open or flocculent structure of the aggregates, and while this water remains associated it must also be treated as a waste. It is possible to further dewater the sludge prior to disposal, which reduces the volume of waste to be handled and transforms it from a thick fluid consistency to a firmer, more solid material (§1▪4). Sludges dewatered by mechanical means, as in the application of pressure, form ‘cakes’. This can be aided by the addition of conditioning chemicals (most commonly polymers [854]). Sludges dewatered by freeze–thaw conditioning form ‘zots’ (see §8▪2). An indicative flowchart of typical water treatment operations is presented in Figure 1-2. It is beyond the scope of the present work to discuss all of these operations; details can be found in various standard reference works [129, 142, 161, 289, 557, 653, 854].

A 1996 survey of 122 New Zealand WTP’s found the following prevalence of chemical usage [161]:

• Aluminium sulfate — 40 plants (32%) • Polyaluminium chloride (PACl) — 18 plants (15%) • Ferric chloride — 1 plant (1%) • Polymer — 55 plants (45%) • Permanganate — 1 plant (1%) • Lime — 1 plant (1%) • None — 26 plants (21%) This is roughly representative of Australian WTP operations. In the U.K., however, use of ferric coagulants is much more common [827].

Powdered activated carbon (PAC) can also be added on an ad hoc basis to adsorb taste- and odour-causing compounds (see §8▪3) [e.g. 189, 778, 949].

4



Raw water (Fluoride)

Alkali (PAC, ballast) Coagulant

(PAC)

Flocculant

Disinfectant

(Oxidant) Rapid

Slow

mix

mix

Granular media Clarifier

Conditioner

filtration

Storage

Backwash processing Distribution

Discharge to

to customer

Thickening

sewer, etc. KEY

Conditioner

Water Sludge Additive

Landfill,

Further

Supernatant, centrate,

etc.

dewatering

or filtrate processing

Figure 1-2: Indicative flowchart of conventional water treatment process with gravity settling, including sludge processing operations. Key components relevant to the present work are set in boldface. Items in parentheses are often omitted (this does not imply that all other items are essential). Recycle loops for backwash water, ballast, and supernatant/centrate/filtrate not shown.

While recycling filtrate, centrate or supernatant from sludge dewatering operations generally poses few problems for the final water on a well-managed plant, a persistent perception of hazard (e.g. acrylamide monomer, Cryptosporidium spp.) means that these streams are treated as wastes on some WTP’s [282, 315, 797, 879]. Conversely, water conservation considerations [797] and tightening discharge requirements [315] encourage recycling. Clean streams may be recycled back to the head of the plant, while slightly more contaminated streams are returned to the raw water supply (e.g. reservoir) or treated (e.g. settled, disinfected, filtered, coagulated, oxidised or adsorbed) prior to return [797], or returned to the sludge thickener 1▪1 : Drinking water production processes

5

D. I. VERRELLI

[315]. The initial portions of centrate and filtrate, and indeed spent backwash water, are usually more highly ‘contaminated’ [315].

Some jurisdictions prescribe specific recycle

provisions [282]. The water recycle loops can be significant. Indicative figures are [315]:

• from rapid gravity filters

— 1 to 8% of WTP throughput [cf. 879]

• from thickeners

— 0.2 to 5% of WTP throughput [cf. 880]

• from centrifuges

— 0.16 to 0.31% of WTP throughput

• from filter presses

— 0.04 to 0.17% of WTP throughput

Water that may not be recycled back to the drinking water stream must be disposed of, which may involve sending it to drain or allowing it to evaporate [879].

Sludge can also arise from backwashing of granular media filters if the spent backwash water is clarified before recycling [557, cf. 832], which the prevailing regulations increasingly require due to concerns regarding contaminant accumulation [e.g. 557, 797].

Developed and developing countries alike are raising standards for the protection of both human health and our natural environment. Efforts to minimise WTP waste output and water wastage are helpful endeavours towards those ends. Yet it is precisely the tightening drinking water quality guidelines that have increased the quantities of WTP sludge produced [cf. 577]. It is a greatly qualified blessing that impoverished regions without (conventional) WTP’s do not have a WTP sludge disposal problem.

For completeness it must be acknowledged that sludges constitute one of four distinct categories of ‘residuals’, or waste, generated by drinking water treatment plants [161, 281,

282, 880]:

• S l u d g e s — includes suspended solids from raw water and chemical reaction products from coagulation, filter backwashing, iron and manganese removal, and lime–softening.

• C o n c e n t r a t e s — includes brines, membrane reject water, and spent backwash from ion exchange regeneration and membrane filtration.

6



• S p e n t m e d i a — includes ion exchange resins, granular/powdered activated carbon (GAC/PAC), sand, anthracite, and diatomaceous earth.

• A i r e m i s s i o n s — includes off-gases from air-stripping, odour control and ozone destruction. As noted, the present work focusses on coagulation/flocculation sludges, and more specifically on ‘conventional’ treatment, where aggregates are separated by settling, as opposed to direct filtration or floatation.

1▪2

Sludge production

The processes described above produce a sludge by-product containing the precipitated chemical additives (coagulant and flocculant) and removed contaminants.

This is

concentrated somewhat in a clarification operation which may rely on settling, dissolved air floatation (DAF), or direct filtration (DF) through a granular medium.

WTP sludges are a component of the waste or ‘residuals’ generated in the operation of a drinking water treatment process. These sludges typically arise through the addition of aluminium or ferric salts, polymer flocculants and other treatment chemicals which drop out of solution as a precipitate in which raw water contaminants are also held. This initially constitutes a suspension of porous aggregates. A sludge can first be said to exist after the initial clarification process, in which most of the clear supernatant is decanted, and the aggregates are concentrated in the remaining phase.

Water treatment sludges typically comprise [161]:

• naturally-occurring colloidal and other particulate matter (e.g. silt, clay, algæ); • dissolved natural organic matter (NOM) (e.g. humic acids, fulvic acids); • precipitated water treatment chemicals; • oxide precipitates of inorganic species dissolved in the raw water (e.g. iron, manganese); and

• filter media flushed out during backwashing. The present work will assume that the contribution of the last two categories is negligible.

1▪2 : Sludge production

7

D. I. VERRELLI

It has been claimed that settled sludge production typically equates to 1 to 3%V of the raw water throughput [161].

The most recent AWWA publication [282] indicates settled

coagulant sludge flows typically vary between 0.1 and 3%V of WTP throughput. Based on an extensive 1996 survey of New Zealand WTP’s OGILVIE [797] emphasised the variation between plants: clarifier underflow represented 0.1 to 4.5%V of plant c a p a c i t y (median 0.6%V) with downstream (spent) filter backwash flows equating to 0.2 to 10%V or more of plant c a p a c i t y (median 1.5%V). DILLON [315] quoted typical backwash volumes as 2.1%V (ferric) to 4.2%V (alum) of production — but may vary by a factor of two depending upon local conditions. Other publications indicate spent filter backwash water flows to be around 2 to 5%V [879], or about 4%V [289], of plant flow. On average the surveyed spent filter backwash water had roughly one third the suspended solids of the clarifier underflow [797] — lower ratios have been reported, viz. 0.02 to 0.06%m versus 0.1 to 0.5%m [315]. The thickened sludges flowrate may be just 0.1%V [289] to 0.5%V [557] of the product water flowrate, depending upon its concentration.

Although industrial water treatment generally runs as a continuous process, flow of some waste streams may be sporadic, or periodic [315, 797]. A good example is the spent filter backwash stream (cf. Figure 1-2) [282], which may run at set time intervals, or be triggered by an on-line parameter measurement (typically pressure drop) [e.g. 797]. Other examples include desludging of thickeners or drawdown and emptying of sludge pits or settling– holding tanks [e.g. 797]. This can in turn affect the sludge processing and sludge properties, as solids-rich waste streams are commonly combined on site [282]. Longer-scale cycles also often apply, as demand varies on both a daily and a seasonal basis [797].

8



1▪3

Sludge transportation

Shear experienced by the sludge will be strongly influenced by site layout. CORBIN [277] describes three approaches to site layout: 1.

Linear layout (compact along the treatment flowpath).

2.

“Campus” layout (nodal).

3.

Compact layout (‘integrated’ or ‘cluster’ layout [277]).

Coagulant sludges may be piped [see 781, 782], pumped, conveyed, and trucked, depending on their firmness.

(Open) channels in which flocculated water flows under laminar conditions are recommended for inlets to sedimentation basins, in order to reduce shear damage to flocs [979]. In the predominantly older plants that rely on pipes or channels to convey water from flocculation basin to sedimentation basin, the water velocity may rise above or fall below the ideal value under various circumstances. Differences may also exist between parallel process routes [cf. 277, 557]. CORBIN [277] states that the turbulence created at water velocities above 0.90m/s tends to break up the floc at entrances, exits and bends. On the other hand, low velocities of less than 0.15m/s allow large flocs to settle out. While perforated inlet baffle walls are recommended for sedimentation basins, MONK & WILLIS [754] advise that velocities should not exceed about 0.3 to 0.45m/s * through the ports, in order to avoid floc break-up. This compares to their figure of 0.15 to 0.91m/s for the “horizontal flow velocity” through the sedimentation basin itself [754]: clearly this velocity can be higher than the port velocity without imparting excessive shear due to the much larger ‘diameter’ of the basin as compared to the individual ports.

Some streams will invariably require pumping. Due to the greater effective viscosity of WTP sludges, pipeline flow at typical plant velocities is often laminar [880].

*

This would be (approaching) turbulent flow for a port diameter of about 9cm, say.

1▪3 : Sludge transportation

9

D. I. VERRELLI

Positive-displacement pumps are usually favoured over centrifugal pumps, as they do less damage to floc structures, and also energy losses are minimised (due to the avoidance of high linear speeds) [161]. The progressive-cavity form of positive-displacement pump is now favoured over plunger-type forms, due to their smaller size and cost [557]. Although centrifugal pumps are generally avoided, specifically-designed configurations — such as screw-feed, bladeless, and torque-flow — are occasionally used [557]. These tend to have reduced efficiency compared to conventional centrifugal pumps [557]. RUSSELL & PECK [879] suggest centrifugal pumps with non-clog impellers be used for sludges of more ‘liquid’ consistency, while positive displacement pumps are used for thickened sludges (40 or 80 to 150g/L solids).

The most commonly used positive

displacement pump for this duty is the progressive cavity pump, which has a coil-shaped metal rotor in a synthetic stator chamber [879]. Abrasion of pump impellers is a problem [879], especially for thicker sludges and those derived from turbid raw waters [315]. Pneumatic ejectors may also be used [879].

Conveyor belts or screw conveyors are “commonly” used for thickened coagulant sludges (>150g/L) [879].

Sludge cake may be transported by truck or barge [879]. Trucks may be loaded with cake by [879]:

• gravity release into a parking bay beneath the dewatering unit; • conveyor feed; or • specifically-designed cake-handling pumps (e.g. a piston pump fed by a screw conveyor [879]). Trucking typically requires sludge solids concentrations of at least 20%m [557]. Vibration of the truck is often sufficient to significantly compress the solids in the sludge [879] [cf. 14,

1014, 1035].

10



1▪4

Sludge dewatering

Sludge properties vary tremendously depending upon the concentration of particles in the mixture. Industrially it is common to measure this by calculating the percentage of material m a s s remaining after drying. However, a little thinking tells us that dewatering should vary with the v o l u m e of the solid phase. For example, monodisperse spheres cannot be packed closer than π / 3 2 ≈

0.7405 [442, 636, 644] as a fraction of the total system volume (this drops to about 0.53 to 0.64 for random packing [442, 636, 644], but can deviate beyond this in polydisperse systems [853, 860]), whereas the mass fraction of the spheres could be anything at all! This volume fraction of the solid phase is the ‘ s o l i d o s i t y ’, φ, being the complement of the ‘porosity’. Note that the mass, through the solid phase density, ρS, is still important in settling and consolidation, where the driving force is self-weight. A further refinement is to ensure that dissolved species are not included as part of the ‘solid phase’ calculations. Details are presented in §2▪1▪1; see also §4▪3▪1.

Several devices are used to separate the solid and liquid phases of WTP sludges, and the majority rely on either density differences or physical retention of particles on a filter. Each device is suited to treat a specific range of sludge solidosity. Table 1-1 presents an overview of common devices and indicative input and output solid fractions.

1▪4 : Sludge dewatering

11

D. I. VERRELLI

Table 1-1: I n d ica t ive dry solids contents [%m]a for feed and output from various dewatering processes and other operations handling WTP coagulation sludges.

Material

Feed [161, 171]

Clarifier or Settler

Output [161]

0.03 to 0.2 0.2 to 1

[171]

[315]

1 to 3

[832, 879] 1 to 3

• High-rate

0.1 to 0.4

Pumping

0 to 8

0.1 to 4 2 to 5

0 to 5

0.03 to 0.2

3 to 4

• no polymer

1 to 3

2 to 3

• with polymer

5 to 10

5 to 10 2.5 to 10

3 to 4

2.5 to 4.5

• WRc thickener

5 to 20

• Superthickener

20 0.03 to 0.2 6 to 16+

6 to 15 10 to 15 7 to 15+

Belt filter press

12 to 22 10 to 20 10 to 15 15 to 22

• “high solids”

Centrifuge

25 to 30 1 to 5

12 to 19 12 to 17

10 to 20 18 to 25

• no polymer

12 to 23 15 to 30 1 to 10

~24 to 44 20 to 25

• fixed cavity

1 to 10

20 to 30

20 to 35

• diaphragm

1 to 10

25 to 40

20 to 35

Air drying beds

Blancmange

10 to 15

• with polymer

Filter-press

Porridge

1 to 3

• Gravity belt

Lagoons

[282]

1 to 2

• Upflow

Thickener

[827]

Target consistency [161, 315]

20 to 50 10 to 20 25 to 45

0.03 to 0.2 15 to 30

15 to 30

Windrows

20 to 25+ Soft clay [879] 50

Freeze–thaw

22 to 30

• & evaporation

Fudge

Stiff clay [879]

40 to 80 up to 80

[832, 880] Discharge to sewer

<1 to 8

Land application

<1 to 15

Landfill

15 to >25

Note

a

Several sources quote just “%”, and in some cases this is likely to denote 100 × mass [kg] / volume [L]. No

conversion has been attempted.

12



A discussion of the individual operations in Table 1-1 follows. A detailed examination of freeze–thaw conditioning is presented in §8▪2▪1. An indication of the prevalence of various dewatering operations is provided by Table 1-2.

Table 1-2: Number of facilities practising various dewatering operations recorded circa 1991 from a survey of 438 utilities and 347 WTP’s in the U.S.A. [880].

Method Gravity thickening

48

Gravity belt thickeners

0

Centrifuges

10

Vacuum filters

4

Filter presses a

20

Lagoons

180

Sand drying beds b

26

Freeze-assisted drying beds

33

Notes

1▪4▪1

Number of facilities

a

Includes belt filter presses.

b

Includes solar drying beds.

Clarification and thickening

C l a r i f i c a t i o n is the unit operation where the sludge stream originates (see Figure 1-2). A clarifier is essentially a continuous-flow settling tank, with the denser material taken off as underflow at the bottom as it sediments due to gravity, and clear supernatant taken off the top as overflow.

L a m e l l a r s e t t l e r s introduce a series of parallel plates (or tubes, et cetera) oriented diagonally in the top of the tank, which enhance the solid–liquid separation by the BOYCOTT effect [cf. 971, 1057]. At present their use on WTP’s is limited, and they may be preferred for smaller duties, such as the spent filter backwash stream, or in proprietary treatment systems.


13

D. I. VERRELLI

T h i c k e n i n g operations increase the solids fraction of the sludge, permitting return of the low solids “used water” to the process. Thickening can also provide a more consistent sludge stream to the downstream dewatering operation. Thickening may be carried out by gravity sedimentation, floatation [see 879], or by mechanical means — in particular gravity belt thickening (see below). Of these alternatives, gravity thickening is the most prevalent in industry [879, 880]. Generally these are carried out as continuous processes, however a few batch gravity thickening installations remain [315].

The g r a v i t y t h i c k e n e r s used in the water treatment industry are physically very similar to a clarifier. Key differences are its size (it has a lower volumetric loading), the presence of a thick sludge ‘bed’ or ‘blanket’ on the base (under ideal conditions), and associated appurtenances devised to gently stir the bulk of the volume or to push the sludge on the base towards the underflow takeoff [1139]. The units may have diameters between 1.5 and 16m, and depths up to 3m [315]. Thickened sludge is most commonly ‘raked’ toward a central hopper, but several other collection configurations exist, including the use of chain-andflights in rectangular basins, or it can be collected directly by opening a ‘blowdown’ valve or pumping from a sump [see 1123]; regular manual desludging was necessary in some old designs [107, 480, 557, 1123]. More specialised thickeners [see e.g. 274] are yet to become common on WTP’s. Polymer may be added to condition the sludge prior to gravity thickening — typical doses are 2 to 4kg per tonne of solids (dry basis) [315]. This is said to increase particle size and decrease particle carry-over in reclaimed water [879]. Mixing with clay or lime can also increase the output solids concentration [879]. The “sludge front” usually settles at about 8 to 33mm/min [797]. Settling periods of 6 to 24h are used to ensure supernatant quality and obtain a reasonable underflow concentration, without ‘wasting time’ on slow consolidation [797]. Typical loading limits are 2.5cm/min (liquid upflow) and 0.07kg/m2.min (solids) [315]. The upflow rate may be reduced by 50% for soft, coloured (upland) waters, and increased by the same amount for hard, turbid lowland waters [315].

14



The most common configuration of a g r a v i t y b e l t t h i c k e n e r sees polymer conditioner added to the dilute sludge in a chamber (e.g. at 0.5 to 1.0kg per tonne of dry solids [264]), after which it is fed to a porous, moving belt [879]. Water drains through the belt under gravity. The units are generally fitted with ploughs to guide the solids on the belt, and scrapers to remove the solids as they reach the end of the belt [879]. The ploughs turn over the thickened sludge cake on the belt, imparting shear that will enhance thickening (facilitating release) and allowing water to more readily drain through the belt (reducing resistance). Alongside the thickened sludge and filtrate streams, gravity belt thickeners also produce a third stream, which is generated as the belt is washed with water as it loops back around to the front roller. This technology has only recently begun to be applied to WTP sludges [880].

Subsequent dewatering processes can be separated into two categories: natural dewatering, and mechanical dewatering. Natural dewatering processes developed largely from wastewater treatment practice, and include natural evaporation, gravity dewatering and induced drainage [879]. Mechanical means of dewatering include various forms of filtration — presses, belts, drums — and centrifuges [879]. Most of these technologies were developed for application in the wastewater industry [161], with more or less adjustment to suit water treatment. Some newer technologies include the pellet flocculation drum type dehydrator from Japan [557] and cross-flow microfiltration devices developed in England [264].

1▪4▪2

Natural dewatering

Natural dewatering operations remove water primarily by either evaporation or drainage (‘percolation’ [879]).

Evaporation is driven by solar radiation, air humidity, and wind;

drainage occurs through the pull of gravity and capillary suction. In some cases runoff or supernatant may also be removed [879], such as when the sludge consolidates.


15

D. I. VERRELLI

Water treatment sludges dry “irreversibly” when exposed to the atmosphere, meaning that they do not revert to a sludge in wet weather (torrential rain may cause erosion, though) [161, 783]. However, a hard, dense surface layer may form that “severely restricts” further drying; after six months a “heap” of sludge cake may appear completely dry externally, but may still be at approximately its original solids concentration 75 to 100mm below the surface [161] [cf. 777]. Operation is generally improved by periodically applying sludge evenly, in thin layers, once the existing layer is relatively dry [880]. Enhancement to drying can also be achieved by breaking up the dry ‘crust’ [880].

U n l i n e d lagoons and drying beds dewater sludge by both evaporation and gravity drainage [879]. Clearly there may be some concern here from an environmental perspective about unchecked release of the permeate into groundwater systems [e.g. 315]. However the New Zealand sludge management guidebook [161] indicates that: such “popular concerns may be unsubstantiated in practice”, as “the potential for contaminants to mobilise is quite limited”, and “few environmental problems have been noted in the literature” [likewise 281].

In recent years lagoons with either synthetic or naturally impervious ‘linings’ (in New Zealand, at least) have predominated [161].

L i n e d beds may be constructed with

underdrain or vacuum systems to remove the underflow [879].

The drainage typically

consists of a slotted pipe in a bed of coarse sand and gravel [879].

In hot climates e v a p o r a t i o n a l o n e may be sufficient to achieve the desired dewatering [879]. Nevertheless, a water treatment plant in California * is reported to achieve sufficient dewatering (~20%m solids) in its on-site sludge dewatering “ponds”, prior to off-site disposal, only after approximately two years [740]! KAWAMURA [557] gives achievable alum sludge concentrations of 3 to 5%m if conditioned with (cationic) polymer and 6 to 9%m if conditioned with lime.

*

16

Using co-precipitation with ferric chloride followed by addition of a cationic flocculant [740].



A variation on this is referred to as a “solar drying bed”, where the base of the bed is constructed of (impermeable) pavement suitable for tractor traffic [879].

Although the

pavement inhibits or prevents drainage, superior dewatering performance can be obtained by mechanically mixing and aerating the sludge, which enhances evaporation, and decanting supernatant that is released [879]. Ultimately an air-dried alum sludge may reach a concentration of ~90%m solids [1147] (cf. Table 1-1).

To the other extreme, underflow may be promoted by applying a vacuum through rigid, porous media plates, or through the creation of hydrostatic suction using “wedgewire” beds [879]. V a c u u m - a s s i s t e d drying beds achieve solids concentrations to 110 to 170g/L, but must be carefully operated to ensure the plate is not irreversibly clogged [879]. According to RUSSELL & PECK [879], clogging of vacuum bed base media may be caused by conditioning with the wrong type or amount of polymer, or by insufficient mixing of the polymer through the sludge.

The operation of even ‘conventional’ drying beds varies greatly from site to site. Looking just at coagulant sludges [879]: • application depths range from 0.20 to 0.75m; • drainage times range from as little as 1.5 days (for polymer conditioned sludges) to

more than 4 days, under ‘ideal’ conditions, or even up to almost 1 year (to take advantage of natural freeze–thaw conditioning, see §8▪2▪1▪4); and • solids concentrations achieved range from 150g/L to 300g/L (typically 200 to 250g/L

[879]).

‘Lagoons’ are usually considered to be larger scale than drying beds, with depths of 1 to 6m and areas of 0.2 to 6ha, and they usually have longer storage times [879]. Typical storage times are at least 1 to 3 months, to achieve a solids concentration of around 6 to 10%; ultimately the sludge can be concentrated to 10 to 30% [161] (cf. Table 1-1). Both monitoring wells and lining, supernatant decanting or leachate collection systems are common features of modern lagoon installations [879].


17

D. I. VERRELLI

Drying beds are in common usage around the world, including in the U.S.A., the Netherlands, the U.K., and Australia [797]. A 1982 survey revealed that a l l of the surveyed Dutch WTP’s who carried out sludge dewatering (16%) did so using drying beds [797]. ANDERSON, DIXON & ELDRIDGE (1997) stated that drying beds were the most common form of sludge dewatering for small- to medium-sized Australian WTP’s (producing (100ML/d, cf. §3▪2▪2, §3▪2▪6) situated in suitable climate zones (i.e. low to moderate rainfall) on account of the limited operator attention required and low running costs [797]. Half of the U.K. WTP’s that undertook dewatering (19%) in 1977 did so using drying beds [797].

A drawback of natural dewatering processes is that they are located outside, exposed to the vagaries of the weather [e.g. 777] and consuming a great deal of land area [e.g. 107]. Drying beds in New Zealand are more commonly used for wastewater sludge dewatering, as drinking water sludges dry too slowly unless they are in thin layers (e.g. a dried thickness of 25mm may dry for 2 to 12 weeks, depending upon season) [161]. Use of air drying beds was historically quite common in the U.K., but “land and labour requirements [have become] prohibitive and few have been installed in recent years” [315].

1▪4▪3

Centrifugation

The principle type of centrifuge used for large-scale WTP sludge dewatering is the ‘solid bowl’ centrifuge — also known as ‘scroll’, ‘decanter’, ‘decanting’ and ‘conveyor’ centrifuge [282, 315, 797, 879, 880]. (Old ‘basket’ centrifuges, which run in batch mode, are now rarely used [880].)

The solid-bowl scroll centrifuge consists of two elements that rotate at different speeds: the bowl, which provides the centrifugal separation force; and the scroll, which drives (and perhaps compacts) the solids toward the cake discharge outlet [879, 880]. Each element spins in the same direction, at about 600 to 2000rpm *, with a differential of 10 to 20rpm [797, cf. 880]. *

18

Current models are capable of spinning faster than this, viz. up to ~4000rpm or ~5000g m/s2 if desired.



These centrifuges are available in co-current and counter-current configurations, according to the location of the outlet for the clear ‘centrate’ liquor [315, 879]. According to STICKLAND [976] the water industry predominantly uses counter-current designs. Typically the older counter-current devices require higher accelerations (~1500g to 4000g m/s2) [cf. 282] than newer co-current devices (~500g to 2000g m/s2) [315, 797]. Centrifuges used for municipal sludge dewatering typically apply an acceleration greater than 1500g m/s2 [879].

Output solids concentrations are markedly improved through the addition of polymer conditioner (cf. Table 1-1). Centrifuges are “rarely” operated without dosing conditioner [879]. Recommended dosage ranges are variously given as: 0.5 to 1kg per tonne of solids (up to ~2kg/t for low-turbidity raw water) [879]; 3 to 7kg per tonne of solids [161]; and 2.5 to 7.5kg per tonne of solids for hard, turbid raw waters, but up to 7.5 to 15kg per tonne of solids for soft, coloured raw waters [315].

Centrifuge performance is sensitive to variation in loading [161], i.e. from the feed rate or feed solids concentration. Overloading a centrifuge means that although a thick cake is still produced, the centrate quality deteriorates through solids carry-over [161]. Performance is also sensitive to polymer conditioner addition, with excessive doses being merely wasteful, but underdosing reducing the cake solids and solids recovery [783].

An early study by NIELSEN, CARNS & DEBOICE [783] found centrifuges performed well in dewatering sludges containing a high proportion of alum-derived precipitate (about 40%m), dewatering to up to 16%. For sludges derived from more turbid raw waters containing lower proportions of coagulant precipitate (e.g. 20 to 25%m), centrifugal dewatering to 22 to 26% solids is expected [783]. NIELSEN, CARNS & DEBOICE [783] found there was an optimum rotation speed at which a centrifuge could be run, where the cake solids was essentially maximised, but the polymer demand was not inflated. The inflation of polymer demand suggested could not be said to be conclusively proved in that study, but intuitively makes sense as excessive shear rates could be expected to cause more damage to delicate floc structures.


19

D. I. VERRELLI

NIELSEN, CARNS & DEBOICE [783] rated the solid-bowl scroll centrifuge as more robust than pressure filters, vacuum filters and basket centrifuges, describing it as able to handle the widest range of solids concentrations and also dealing best with ‘overloading’ — they ranked pressure filters second.

The solid-bowl scroll centrifuge also required little operator

surveillance [783].

Centrifuges are the most common form of mechanical dewatering equipment in New Zealand for WTP sludges [161].

1▪4▪4 1▪4▪4▪1

Filtration Filter presses

P l a t e * filter presses and d i a p h r a g m † filter presses are distinguished from the other forms of mechanical dewatering discussed here in that they can only be run as (cyclic) batch processes [414]. Each may have from about 10 to more than 100 plates mounted on rails [282, 315], forming a commensurate number of recesses to be filled with sludge. The faces of the plates are fitted with cloths through which the liquid phase can permeate when the device is pressurised. Generally the plates are (roughly) square, with sizes in the range 0.5 to 2.0m [315], although circular plates have also been used [282]. The difference between plate and diaphragm filter presses lies in the mechanism by which high pressure — which is the driving force for filtration — is achieved. In a plate unit high pressure (700 to 1600kPa [282]; typically around 1500kPa [161]) is achieved by pumping *

Also known as “fixed-volume” [797], “fixed-cavity” and “fill-only” [976] filter presses, with two s u b t y p e s : “ p l a t e - a n d - f r a m e ” and “ r e c e s s e d - p l a t e ” [see 293, 414]. As distinct from plate heat exchangers, where the ‘frame’ describes the support structure, here the ‘frames’ are picture-frame-like spacers alternately placed between flat plates [293, 414]. In principle the cake thickness can be changed by replacing the frames in plate-and-frame units [414]. In the water (and wastewater) treatment industry the newer recessed-plate configuration is more popular [e.g. 880, 976]; generally this sub-type is cheaper and produces thinner cakes (up to ~35mm) [414].

†

Also known as “variable-volume” [797], “membrane” [414], “flexible-membrane” and “fill-and-squeeze” [976] filter presses. These also have sub-types in the manner of “plate-and-frame” and “recessed-plate” designs [414] (see preceding footnote).

20



sludge in: the volume of the chamber is fixed [879]. In some cases a high-rate pump is used to fill the chamber initially, while a lower-rate pump is used to force more material in under the same pressure [282, 315]. (Positive displacement piston and progressive cavity pumps are preferred for feeding WTP sludge to filter presses as a practical compromise to avoid excessive shear [282, 315, 797].) In a diaphragm unit the high pressure is achieved by expansion of diaphragms into the chamber, reducing the volume which the sludge is able to occupy [879].

This usually

generates pressures in the range 1400 to 1700kPa [880]. These units have been used in water treatment plants since circa 1980, and are able to dewater more rapidly and to a greater extent [107, 879]. Typical chamber (or cavity) widths are 25, 32 or 37mm [161] (cf. 25, 30 or 40mm [282]). Current trends are toward thinner recesses (20 to 25mm) for plate filter presses; diaphragm filter presses tend to be wider (~40mm) — when deflated [315]. When the plates are cracked apart at the end of a cycle, the dewatered solids drop from the chamber. Cycle times vary from about 2.5 to 22h, with an average of 8h [879]. In general the fastest cycle times of 2 to 3h can only be achieved with cakes 25mm thick and high staffing levels [161]. Filter cloth can rapidly become fouled, increasing the resistance to dewatering. Cloths may be cleaned regularly in situ by high-pressure spray [879], e.g. every 5 pressings [797]. The cloths may be removed twice a year to enable the plates to be cleaned [797]. While the cloths are off, it is a good opportunity to subject them to a more rigorous cleaning: soaking for three days in hydrochloric acid was found to return their performance to ‘as-new’ [797]. Filter cloth usually lasts 12 to 18 months [879]. In some plants the filter cloths are ‘precoated’ with a ‘filter aid’ such as diatomaceous earth or fly ash [cf. 107] to inhibit fouling of the cloth itself, and assist in cake release [282, 879]. These materials are applied at approximately 300 to 500g/m2 (respectively) at the start of each cycle [282].

Sludge fed to filter presses may be conditioned with lime, ferric compounds, and polymers [879]. Increasingly polymers alone are preferred [879]. DILLON [315] quotes polymer doses of 2 to 4kg per tonne of solids, or less if conditioning for an upstream thickener has been maintained.


21

D. I. VERRELLI

Although the process is generally modelled as one-dimensional dewatering, in practice deviations will arise.

These include both lateral (quasi-radial) variation of flow and

solidosity within the filter press cavity [282, 976] and also variation in average loading from one end of the press to the other [797]. In both cases the solidosity is lower ‘upstream’, at locations closer to the feed inlet [797, 976].

Filter presses generally achieve the highest solids concentration of the mechanical processes (typically 350 to 450g/L, cf. Table 1-1), yield a high-quality filtrate, are reliable, and can handle varying influent concentrations [879]. Circa 1996 there were 20 known filter press installations at WTP’s in the U.S.A. [880].

1▪4▪4▪2

Belt filter presses

A belt filter press is an extended version of the gravity belt filter (see §1▪4▪1) which introduces an upper belt and increases belt tension. In the first portion of the unit, the sludge drains through the porous belt under gravity [879]. As the belts come together, and a low pressure is exerted on the sludge, a cake or “sandwich” is formed that “withstands the shear forces of the [later] high-pressure zone” [161, 879, 880]. The shear is a key feature, and arises due to the (local) differential between the speeds of the two belts [315]. Higher pressure is exerted as the upper and lower belts are squeezed around rollers of decreasing diameter [161, 879, 880]. Some units rely on the cake dropping from the belt of its own accord, followed by spray washing, while others use mechanical blade scrapers [879]. Filtrate and washwater may be recycled or disposed of according to relevant regulations [879].

Operation of the belt filter press is sensitive to the consistency of the feed stream [264]. Usually the sludge is conditioned by injection of polymer, or some other flocculant, prior to dewatering on a belt filter press [161, 879]. One effect of insufficient polymer addition is that the capture efficiency of the filter cloth can drop to e.g. 90% [264]. When optimised, this allows the production of cake at solids concentrations of 10 to 15%m solids [704, 879] or 15 to 20%m [557, 879] (cf. Table 1-1). Polymer doses are typically in the range 4.5 to 6.8kg/t(dry 22



solids) [557]. Whereas a pure alum sludge may be dewatered to 15% or more solids, sludge with a high proportion of entrained silt or sand will dewater more readily to a higher solids concentration [161, 880]: CLARK & ANDERSON [264] reported 30 to 32%m solids from a “high solids” belt press, and KAWAMURA [557] reported 22 to 25%m. Belt filter presses are usually solids limited; the primary operating variable is the belt speed [315].

Tower belt presses are a recent variation which apparently have similar performance to regular belt presses for WTP sludges [264]. The new “continuous high-pressure” filter press is an extension in which a gravity thickening zone progresses to a moderate pressure zone (~240kPa) and finally moves on a ‘mobile armoured belt’ to a high pressure zone (~2070kPa) [880]. WTP sludges can be dewatered to about 25 to 30%m solids in a high-solids belt press [282].

Belt presses are sometimes used in the U.S.A., but rarely in the U.K. for WTP sludges [315]. Yet CORNWELL [282] claims they are very popular in Europe.

1▪4▪4▪3

Vacuum drum filters

V a c u u m d r u m filtration comprises three zones: 1.

In the submerged zone new sludge adheres to the filter medium on the drum, aided by the vacuum [880].

2.

In the dewatering zone, the vacuum sucks liquid through the filter, leaving the solids behind on the surface.

3.

In the ‘discharge zone’ of the drum, the vacuum is shut off and a scraper removes cake that has formed on the filter medium [879].

Vacuum filtration was popular until the mid-1970’s [880].

Vacuum drum filtration is

becoming less popular, with low yields from metal hydroxide sludges, although it is still used for lime–softening wastes [557, 879]. The poor performance of rotating vacuum drum filters in dewatering coagulant sludges is attributed to the typically low solids concentrations at which the “highly compressible” sludge is fed to the unit and the resistance to water flow


23

D. I. VERRELLI

through the sludge [879]. Apparently the rotating drum vacuum filter cannot dewater at a high enough rate. The pressure differential is limited to ~100kPa. Under favourable conditions — high solids concentration in the feed sludge, polymer conditioner dosed, and possibly with a diatomaceous earth ‘pre-coat’ — dewatering to 200g/L solids is attainable [879]; 5%m is typical [704]. Practical experience with vacuum dewatering WTP coagulation sludges is overwhelmingly negative, summarised by the following descriptions:

unreliable, very sensitive, frequent

filter breakthrough [783]; “often ineffective” [315]; not successful [880]. However it has been used to dewater freeze–thaw conditioned sludges to 67 to 75% solids [315], and occasionally for lime–softening sludges [880].

1▪4▪4▪4

Other filters

C r o s s - f l o w filtration is not widely used in the water industry for dewatering sludges. The dewatered sludge must remain pumpable, and so the maximum extent of dewatering is less (10–20%m solids) than it would be for ‘dead end’ filtration (25–35%m solids) [264].

So-called ‘ p i n c h ’ presses operate at very high pressures, around 10MPa, and have been used for dewatering materials such as lime residuals, but not for alum sludges [264].

T u b u l a r filter presses, in which filtration occurs through long, thin, woven-fabric tubes, have been found capable of dewatering to sufficient extent (around 30%m), although the rate at such high solidosities may be prohibitively low [264].

1▪5

Sludge disposal Although the problem of sludge disposal from water treatment plants has existed for many years, very little has been done to solve it. — NEUBAUER (1968) [777]

24



In 1968 YOUNG [1139] recognised the adverse effects of “casual” WTP sludge disposal, including functional and æsthetic environmental degradation. He [1139] recorded cases in which sludge dewatered in lagoons was discharged to a river, and where continual application of sludge on drying beds did not cause accumulation, as “prevailing winds disperse[d] the cake”. (Later in the U.S.A., circa 1985–1990, the generation of dust from the top dry layer of landfilled WTP sludge was rather regarded as a p r o b l e m , and ameliorated through dosing of polymer at the dewatering stage and seeding of native grasses [880].) In the U.S.A., recognition of water treatment plant sludge disposal as a significant issue was catalysed by an AWWA Research Foundation conference in 1969, which concluded that engineers must account for this aspect in their designs [942] — a cause promoted by BLACK and co-workers [1021]. In 1973, in an introduction to a special sludge-themed edition of AWWA Journal, FABER & TARAS [353] wrote that the management and disposal of the “gooey solid” water treatment plant sludge was a long-standing problem, and a growing challenge in light of growing environmental awareness at the time. In 1981 BABENKOV & LIMONOVA [107] recognised that increasing volumes of high-moisturecontent sludges were accumulating due to increased demand for potable water and tighter quality requirements, and they dismissed the prevailing methods of “getting rid of” the sludge (viz. lagooning, waste landfill, and discharge to natural water) as quite obviously “obsolete” for both environmental and economic reasons.

There is increasing pressure to minimise sludge sent to waste, even in Australia, where historically there has seemed to be plenty of land to send the sludge to lagoons or landfill, or plenty of water to dilute discharges to natural water bodies. For example, it is now a requirement as part of Sydney Water’s Operating Licence that it monitor and report on production and b e n e f i c i a l r e u s e of water treatment “residuals” (including the types of sludge studied in this work), and put into place a complementary Environmental Management System [49]. In accordance with this, Sydney Water have made a commitment to ultimately reuse all of the water treatment residuals produced in water filtration plants (WFP’s) in their system, and are currently meeting this objective [47, 48, 65]. Furthermore, some plants have reported

1▪5 : Sludge disposal

25

D. I. VERRELLI

significant reductions in the quantities of residuals generated [47], despite an increase in the population served and a fairly static volume of water supplied over the 7 year period [48]. (Unfortunately the data for dry and wet residuals are generally not reported together [e.g. 65], complicating comparisons, and obscuring the importance of dewatering.) About two thirds of the residuals produced are currently reused for some beneficial purpose [48, 65].

At Macarthur WFP, sludge had been stored on site in drying beds since

commissioning in 1995 [47, 48]; in 2004–2005 all of the stored residuals were removed by Wollondilly Shire Council and used as topsoil on a sports field [48]. This is a common scenario for ‘small’ WTP’s, where it is uneconomical to continually transfer the residuals [65].

Similar situations of increasing attention to and restrictions upon WTP sludge disposal have been reported from numerous other countries around the world, including Korea [225]. DILLON [315] wrote in 1997: At the present time, waste disposal legislation appears to be in a state of almost continuous change.

1▪5▪1

Overview of disposal routes

There are a number of popular disposal routes for water treatment sludges [254, 879]: • discharge to a natural water body; • discharge to sewer; • discharge to lagoons; • waste landfill; • engineering fill; and • land application, such as for agricultural use.

A moderate amount of research has been carried out on a range of other beneficial uses of WTP sludge, or chemical reuse, but few have been adopted in industrial practice. Each route is discussed in more detail in the following sub-sections.

There is considerable variation in the predominant disposal routes from country to country, alongside trends over a period of decades.

26



In the U.K. in 1977 the WRc reported that 27% of WTP’s discharged to natural water, 10% to sewer/WWTP, 40% to lagoons (¾ permanently, i.e. 30%), and 19% dewatered sludges (~½ in drying beds, i.e. 10%) [797]. In the Netherlands in 1982 KIWA and AwwaRF reported that 14% of WTP’s discharged to natural water, 10% to sewer/WWTP, 48% to lagoons, and 16% dewatered sludges (all on drying beds) [797].

Table 1-3 reports more recent data on the proportions of sludge disposed of by WTP’s in

New Zealand (122 plants, 1996) [161, 797], the U.K. (circa 1999) [827], and the U.S.A. (circa 2000) [282]. Major differences exist between the three countries. As suggested by Table 1-3, very few (~20%) water suppliers in New Zealand carry out any sludge dewatering [797].

Table 1-3: Popularity of various disposal routes, as percentages, for sludge generated at WTP’s in New Zealand (122 plantsa, August 1996) [161, 797], the U.K. (circa 1999) [827], and the U.S.A. (circa 2000) [282]. Major routes in bold.

Disposal route

New Zealanda

Freshwater

45

Wetland Marine Sewer / WWTP b

United Kingdom

U.S.A.

(50 plants)





2

(3 plants)

2 (“water environment”)

11 (“stream”)

1

(1 plant)

23

(26 plants)





25 (direct)

24

4 (trucked) Landfill

13

(15 plants)

57

20 (“landfill”)

Lagoon

11

(12 plants)

2

13 (“monofill”)

Land application

4

(5 plants)

9

25

Construction materials

–

(0 plants)

1



Other

–

(0 plants)

–

7

Note

a

Data for 10 plants at large industrial sites [see 797] has apparently been excluded.

b

WWTP = wastewater

treatment plant.


27

D. I. VERRELLI

In Australia each year more than 6000 dry tonnes of WTP sludge is produced [57]. Traditionally this sludge has either been dried and stockpiled on site for years, or sent to sewer (to be handled by the WWTP) [57].

A useful outline of key operating and capital costs for selected dewatering operations was presented in the AWWA Technology Transfer Handbook, along with a few real plant case studies [880].

Costs include equipment purchase and civil works, personnel, chemical

addition, haulage or transfer costs, fees and taxes, on-going maintenance and monitoring; associated costs can arise from the need for temporary storage prior to ultimate disposal [880].

1▪5▪2

Discharge to a natural water body

In the past almost all WTP sludges were ultimately discharged to surface waters; a 1953 U.S. survey of 1500 plant estimated the proportion as 96% [777]. In so-called ‘developed’ countries stricter and more rigorously enforced environmental regulations have “essentially terminated all direct discharges” to natural waterways [879]. This is increasingly the case also in the more advanced developing countries, such as Brazil [865]. In some parts of the U.S.A. discharge of WTP sludges to natural waterways was deemed to be (illegal) pollution even before 1969 [891] [cf. 521, 781, 782], although circa 1984 it was the final destination of ~50% of WTP sludges [880] — it is “no longer [circa 1996] a viable option for many” WTP’s [880] [e.g. 1023]. It is “no longer common” in the U.K., but individual cases are permitted [315]. Discharge to natural waters has been common in New Zealand — the material is normally of low toxicity, bacterial count and biological oxygen demand (BOD), especially due to the high raw water quality and treatment chemical standards — but a 1991 Act has tightened discharge consent requirements [797]. Regulations may focus on any number of environmental parameters, such as pH, suspended solids, dissolved solids, trace metals, nitrates, chlorine [879], radionuclides, toxicity, odours, dissolved oxygen levels, and hydraulic loading [281]. Alternatively, the regulations may explicitly ban this disposal route altogether — even though in such jurisdictions some

28



carefully monitored sites have been able to demonstrate that their high rates of dispersal and dilution of the sludge mean that its environmental impact would be minimal, if allowed [865]. In the U.K. aluminium and polymer (especially cationic) levels are of most concern [315]. In such cases it is useful to evaluate the cost (predominantly financial) of banning these discharges against the (essentially environmental) benefit [cf. 284].

Some discharge consent requirements are unrealistically onerous [781]: e.g. one consent issued in New Zealand stipulated that discharges contain “no chlorine”, while others required “no water treatment plant chemicals”: achievable nor verifiable [797].

true zero levels are technically neither

Tight discharge levels have also been set variously on

fluoride (1mg(Fl)/L) [797] and aluminium [315, 880] that are even tighter than the corresponding guideline values for potable water [34, 43, 59]. In the U.K. a limit of 0.5mg(Al)/L applies to soft, acidic watercourses [315].

For these

watercourses in the U.K. [315], and generally in the U.S.A. [880], the medium-term average should not exceed ~0.08mg/L dissolved Al. (At one New Zealand plant a l u m levels in the discharge were not permitted to exceed 1mg(alum)/L; equivalent to ~0.09mg(Al)/L [797].) Although the aluminium in WTP discharges is predominantly in the solid phase, the fact of receiving stream aluminium concentrations naturally exceeding 1mg(Al)/L in several regions has convinced some American states to “mandate complete elimination of any [direct] discharges that contribute to the [aluminium] load of the receiving stream” [880].

Residuals disposed of by direct stream discharge have relatively low solids concentrations: in the range < 1 to 8%m, as for discharge to sewer [879]. It must be ensured that the colour and turbidity of the receiving water is not excessively elevated by the sludge discharge, as this can block light from penetrating the water column, affecting aquatic life [797]. Solids may also collect in ‘pools’ at the bottom of the water body, which may become anaerobic due to microbial activity, and may also pose a hazard to visitors who cannot perceive the true water depth [797]. Discharge to natural water bodies is more likely to be permitted if: the waste volume (flowrate) is much less than that of the receiving water; the receiving water is naturally


29

D. I. VERRELLI

especially turbid; or no treatment chemicals were used in generating the sludge (e.g. waste from filtration-only plants) [161, 797]. Discharge problems can be aggravated if the receiving water is relatively quiescent, as the waste stream is then diluted much more slowly [161], forming more of a slug or plume, and may settle upon benthic zones [282, 284]. The sludge can block light penetration and bring about anaerobic conditions [282, 284]. C h l o r i n a t e d spent filter backwash water, sludge dewatering supernatant (or centrate), and bypass water may be discharged to receiving waters — but only if the chlorine levels are not ‘too high’ [562]. Some regulators have set limits on such levels based on the studies of workers such as TURNER & CHU [562]. Uncommonly an environmental benefit accrues from a l l o w i n g the discharge, principally where the flows downstream of the WTP would otherwise be too low to provide adequate support for aquatic life [782, 797] [cf. 781]. Discharge to a surface water is predominant, but discharge into deep wells is also practised [281].

The toxicity of aluminium has been extensively researched, with a recent review in CORNWELL [282]. A key dependency is pH: at pH < 4.0 fish are at risk irrespective of Al concentration; at 4.0 < pH < 5.2 aluminium can be lethal to fish at concentrations as low as 0.1mg/L; at 5.5 < pH < 6.9 aluminium is less toxic and has not been reported to affect fish; finally, at 7.0 < pH < 9.0 aluminium toxicity increases as pH increases (1984 WRc report) [161]. This seems to be consistent with the observation that dissolved aluminium is more toxic than suspended aluminium [161]. Certain dissolved aluminium species may be more toxic than others [cf. 148, 893, 894]. Aluminium toxicity to smaller lifeforms is generally less, although they can potentially be coagulated [161]. It is important to consider the phase(s) in which the Al is present: WTP’s discharge alum s l u d g e , not aluminium i o n s , and the toxicity of the different phases can be very different [284]. Natural organic matter can also significantly influence aluminium toxicity:

at high

concentrations of NOM, aluminium toxicity decreases [161, 284], presumably because

30



adsorption of NOM onto aluminium species makes them ‘unavailable’ for coagulation reactions on the gills of the fish.

1▪5▪3

Discharge to sewer

Sludges disposed of to sewer can be ‘treated’ together with sewage treatment sludges at sewage treatment plants, yielding economies of scale. The convenience of this route depends in part upon geography: in some situations a short pipe run will suffice to connect to the sewer main, while in other cases a longer pipeline may be required; when the distance becomes too great [797], or if volumes are small, material can be trucked directly to the WWTP [880]. Trucking is also required for disposal of lagooned or otherwise concentrated sludges [315, 880]. This disposal option ideally requires co-ordination (and hence communication) between the discharging WTP and the receiving WWTP [434, 781, 782]. Problems could potentially arise due to short-term ‘spikes’ following from spent backwash flows from the WTP, which may affect the loading upon digesters at the WWTP * or may even lead to non-compliance with the maximum allowable peak flows in the sewerage system [434, 782] [cf. 781]; a simple remedy is to install a balance tank [797]. The sludge may not be sent at too high a solids concentration lest it settle in the sewerage conduits [161] — perhaps also a problem for more dilute sludges with rapid settling properties [891]. Solids concentrations of sludges sent to sewer are in the range < 10 to 80g/L [879]; for coagulant sludges, typically ≤10g/L [315].

The effects of WTP sludge on sewage treatment appear to be poorly understood, and may vary greatly depending upon local conditions, including the point of addition. DILLON [315] recorded that the literature is full of contradictions: • beneficial and adverse effects on sludge thickening and dewatering characteristics; • negligible and adverse effects on aerobic and anaerobic digestion; and • negligible and adverse effects on sludge incineration.

*

Or decreasing volatile solids and hence affecting digestibility of the sludge [891].


31

D. I. VERRELLI

Numerous researchers have reported a decrease in sludge concentration in the primary clarifier underflow, with reduced floc settleability [cf. 161, 281, 880]; yet negligible effect or even improvement in primary clarification efficiency has also been reported [e.g. 107] — the discrepancy is likely due to different loading rates [see 879, 880]. Inclusion of water treatment sludge in the centrifugation of wastewater sludges has yielded marginal changes [161, 434] or enhancement (ferric sludge) [434].

Filtration of WWTP

sludges has been widely reported to improve with the introduction of WTP sludges, especially in regard to SRF (see §2▪4▪1▪4) [880].

Other potential drawbacks include reduced primary settler overflow quality, reduced digester efficiency [281, 557, 797], increased variability in loading (leading to more operational adjustments being required and/or a failure to attain the full dewatering enhancement potential), increased abrasion of the centrifuges and other plant items [cf. 781, 782], and the necessary increase in total material processed at the WWTP [434, 781, 782], possibly including additional heavy metal species [557]. One WWTP operator also suspected the inert WTP sludge was slowly accumulating at the bottom of the oxidation ponds [797].

Somewhat offsetting the disadvantages, the (alum) WTP sludge may bind phosphorus * [315, 880] and heavy metals present in the sewage sludge [161, 557]. Enhancements in the removal of suspended solids and turbidity [315, 557, 797, 880, 891] and nitrogen compounds [107] have also been reported upon dosing a WTP sludge.

One operator observed that the

additional discharges helped to ‘flush out’ the main sewer line, and another felt that IMHOFF tank performance improved [797]. Enhancement of BOD and COD removal in settling tanks has been variously described as “slight” [797, 880] and “significant” [315].

Ferric sludges were found in one study to remove sulfide and prevent struvite (MgNH4PO4·6H2O) formation, but trace metal concentrations were elevated [161].

*

Such

Provided the concentration of aluminium in the sludge is sufficiently high: SALOTTO, FARRELL & DEAN [891] worked with an alum WTP sludge that was less than 1% aluminium by mass of dry solids, and they did not detect any enhancement in phosphorus removal [see also 282]. Dosing of alum WTP sludge at the WWTP directly was reported to achieve in excess of 90% phosphorus removal [797].

32



results reinforce concern over toxicity to biomass in the WWTP [281]. Nevertheless, in 1989 in the Netherlands ferric WTP sludge was routinely added to more than ten WWTP’s, at least 10 municipal sewer networks, and a number of industrial works to reduce hydrogen sulfide evolution [282, 797] — alum sludges are apparently also suitable [315]. (An extension of this is the use of lime–softening sludges for flue-gas desulfurisation [282].)

According to DILLON [315]: It is generally accepted that if the proportion of waterworks sludge is less than about 15– 20% by weight of the resultant sludge, any detrimental effects on sewage sludge treatment and disposal are minimal.

Deleterious effects may be minimised by introducing the WTP sludge to the WWTP directly, rather than via the sewer main [880]. Various studies have concluded that the operation and final effluent quality of WWTP’s is not adversely affected by accepting WTP sludge [107, 880]. Despite concerns, metal content of the WTP sludges does not appear to cause problems [880]. (In the U.S.A. the sludge must be confirmed as non-hazardous by passing the TCLP test [282] — see p. 45.)

Sewer discharge appears to be more common in Europe, including the U.K. [797], than in the U.S.A. [557].

At Winneke WTP (see §3▪2▪6▪1) costs as at August 2003 were of order $0.90/kL, with flows of around 10 to 12ML per month; i.e. disposal cost circa $10000 per month. In New Zealand as at 1996 unit ‘trade waste’ charges of 0.07, 0.31, and 1.00 NZD/kL were quoted for three separate WTP’s [797]. Overall disposal costs are somewhat higher when additional operating expenses (e.g. maintenance) and capital costs or depreciation are accounted for [797]. US WWTP rates follow various formulæ, with most charging by volume but some charging a flat monthly fee [880]. An indicative range for the ‘base rate’ in large cities circa 1992 is 0.11 to 0.90 USD/kL, and several works impose surcharges for BOD or TSS loading (up to 0.33 and 0.25 USD/kg, respectively), or other operational factors [880].


33

D. I. VERRELLI

Charges for discharging tradewaste to sewer in the U.K. follow the Mogden formula [315]. The form is consistent throughout the U.K., but the numerical values vary between water authorities; also, different rates may apply for ‘large water users’ [234]. For example, the standard 2007 rates were [234]: • Yorkshire Water —

(S) 0.3147  Charge [£/kL] = 0.6259 + 0.5533 (TSS [g/L]) (P) 0.6259 + 0.5533 (TSS [g/L]) + 0.3372 (COD [g/L]) (B) 

[1-1]

• United Utilities — (S) 0.4871  Charge [£/kL] = 0.3380 + 0.4909 (TSS [g/L]) (P) 0.3600 + 0.4909 (TSS [g/L]) + 0.4260 (COD [g/L]) (B) 

[1-2]

in which ‘S’ denotes sea outfall, ‘P’ denotes primary treatment, and ‘B’ denotes biological treatment; TSS is total suspended solids, COD is chemical oxygen demand. (It is important to note that the Convention for the Protection of the Marine Environment of the North East Atlantic (1992) committed to end marine discharge of sewage sludge by the end of 1998 [315].) Both TSS and COD * depend directly upon the sludge concentration — i.e. the extent of dewatering — and are generally of order 10–1 to 101g/L for WTP sludges discharged to sewer [282, 315, 797, 880]. In comparing with the tax rates per unit of wet sludge for landfilling in Figure 1-3 it must be remembered that volumes discharged to sewer will be greater.

1▪5▪4

Discharge to lagoons

Usually lagoons are periodically emptied — the period varies from months to years [797] — and the contents disposed of as landfill or land cover material [161]. Permanent lagoon storage is feasible for some smaller treatment plants. OGILVIE [797] quoted lagoon volumes of ~9 and 150ML. If the cumulative on-site volume exceeds 10ML in the U.K. then additional waste management licensing provisions apply [315]

*

34

For WTP sludge COD may be of order 10 times greater than BOD [e.g. 282].



As noted, a dry crust can form over a still-wet bulk, which can create a dangerous situation in the case of a lagoon, where — despite appearances — the crust cannot support the weight of a human, or livestock, or a vehicle or infrastructure [137, 161]. A full lagoon “may take many, many years” to completely dry out [797, cf. 1139] — for comparison, it is suggested that a dedicated WTP sludge landfill operated for 20 years would require a “postclosure care period” of around 30 years [880]. Groundwater contamination must be avoided [315].

Although lagoon storage is conceptually an interim step, some utilities see lagoon storage as ultimate disposal [879]. Alternatively, the costs and difficulty * of emptying the filled lagoon, and uncertainty over where to transfer the contents, may prevent removal [797].

(Such a situation can be

envisaged where the design lifetime of the lagoon system is long — e.g. 80 years at one site [1139] — so that no provisions for disposal are deemed necessary in the initial design.) As such, it is similar to landfill and, to a lesser extent, land spreading. On-site disposal is attractive if the sludge quantities are small and ample land is available [557]. Another permutation of permanent on-site disposal arises when, say, a disused quarry is located on site [557] (or on adjacent land).

Regulations recently implemented in the U.S.A. have made lagoon storage less attractive [797]. In the U.K. lagoons will be regulated as landfill sites (see following sub-section) [196]: Lagoons fall within the definition of landfill, unless the waste is stored for less than one year before disposal or three years before recovery.

DILLON [315] described permanent lagoon storage as “no longer acceptable” in the U.K..

*

It can take days or even weeks to empty a lagoon, and specialised equipment is usually required [315].


35

D. I. VERRELLI

1▪5▪5

Waste landfill

For the purposes of this study, “landfill” refers to the deposit of waste material at a site whose primary purpose is to ‘store’ the waste. This differs from use as an engineering material or agricultural material, as discussed in the following sections. Landfill is generally understood as surface storage, either in ‘areas’ (above ground) or trenches (in ground) [282, 1098]; however, discharge into deep wells (below ground) is also occasionally practised [281]. ‘Area’ landfills can take the form of mounds, layers, or dikes [281, 282, 1098]. Mounds tend to slump [282]. Layering allows significant air drying [281].

For landfill purposes the sludge must be dewatered prior to disposal — to meet legal obligations [13, 88] as well as for economic and practical handling reasons [281]. Solids concentrations of sludges sent to landfill depend upon whether other waste is being sent to the same landfill (“co-disposal”) or whether the landfill is dedicated to sludge disposal (“monofill”) [879]. Co-disposal landfills can take sludges of 150 to 250g/L solids, while monofill landfill sites can only handle sludges that have been dewatered to > 250g/L solids [879].

In some jurisdictions minimum solids contents may be legislated [264].

Historically co-disposal has been more common in the U.K. [315]. New Zealand landfill operators have typically requested that sludge be ‘ s p a d e a b l e ’ or firmer, implying a solids concentration of 15% or higher [161]. More detailed acceptance criteria (especially for monofill sites), based on soil mechanics, include [161]: • Plasticity index (hence handleability) — this is relatively high for sludges (poor handleability) • Compaction data — moisture–density curves • Compressibility — controls settlement • Shear strength — determines stability, hence maximum height and slope of landfill, and maximum weight supportable.

Germany and the Netherlands adopted a

preliminary standard of 10kPa for the minimum shear yield stress, based on vane rheometer measurement, for a sludge that would support heavy equipment. (This was consistent with data of CORNWELL et alia (1992), except that there a more conservative

36



safety factor was then applied [880].) In the U.S.A. a minimum of only 2.9 to 3.8kPa was proposed, based on handleability [cf. 282, 580, 1098]. In the U.S.A. often concentrations of ~35%m are required for landfilling, and in some states as high as 50%m [880] or even 70%m [282]. CORNWELL [282] implies 30%m is indicative. Daily landfill cover material should be about 55 to 65%m solids [434, 562]. This could be achieved by extensive drying of sludge to 60%m solids *, or by drying sludge to about 40%m solids and mixing with soil [562].

As with land spreading (§1▪5▪7), the sludge to be disposed of should be shown to pose negligible risk of leaching toxins [562] or other regulated chemical species [27, 41, 44]. Leaching of freely-draining water from sludge is a concern to landfill operators and environmental regulators; as a result, sludges typically need to be dewatered to at least 20%m if the site has an impervious lining (a practical requirement for trucking in any case), and at least 40%m if not [557]. Heavy metal leaching is mostly of order only 1% of the fresh sludge content [797]. A problem arises with co-disposal sites if the landfill operator permits acidic industrial waste to be deposited with the WTP sludge [797]. The legal liability attaches to different parties depending on the jurisdiction: e.g. to the landfill operator or owner in New Zealand, but to the WTP operator or owner in the U.S.A. [cf. 282, 797]. Consequently, utility-owned monodisposal landfills are increasingly preferred in the U.S.A. [315].

Landfill disposal has become more difficult and more costly in the U.S.A. recently, due to new environmental laws brought in by regulators [780, 879], the disinclination of landfill operators [557, 562], and the simple economics of supply and demand — i.e. the sources of landfill waste are abundant, but the capacity of landfill sites is limited (and even decreasing) [281]. The landfill scarcity problem is a worldwide problem [cf. 501].

*

Filter press cakes take ~2 to 3 months to dry (in England) when spread on the ground to a depth of not more than about 125mm [137].


37

D. I. VERRELLI

50 Inactive waste Other waste

Tax rate [£/t]

40

30

20

10

2010–04

2008–04

2006–04

2004–04

2002–04

2000–04

1998–04

1996–04

0

Date Figure 1-3: U.K. landfill tax rates since inception [53, 70, 72, 315].

Landfill in the U.K. is taxed differently depending upon its composition. WTP sludge is typically n o t classified as “inert or ‘inactive’ waste” (see below), meaning that it attracts the higher levy under The Landfill Tax Regulations (1996) [315], which aim to discourage such disposal. (The taxes and disposal fees are usually levied on a wet basis, although Northern Ireland has used a dry solids basis [315].) Since inception of the Regulations the “standard” landfill tax rate has climbed relentlessly, while the inert waste rate has remained almost constant [53, 72]; even steeper increases have been announced [70], as shown in Figure 1-3 (note that this does not include operator-levied charges). 38



Some landfill operators in New Zealand were charging ~40 NZD/t for sludge disposal in 1997 [797].

Regulations governing the general operation of landfill sites in the European Union are also becoming tighter [88, 196, 395]. Among the most affected will be the United Kingdom, as it has relied more heavily on landfill for hazardous waste disposal than the E.U. average [88]. In fact, the U.K. Environment Agency (EA) predicted that the number of sites in England and Wales that accept hazardous waste would drop more than 90% from around 180 to 240 sites down to around 10 to 15 [38, 88]. This reduction is presumably due to classification of sites as receiving o n e of the following: hazardous waste; non-hazardous waste *; or inert waste † [13, 88]. Massive increases in landfill disposal fees were predicted for hazardous waste [40], but fees for the other two waste categories would likely increase sympathetically to some degree. WTP sludges tend to be classed ‡ as “non-hazardous”, but not “inert” [cf. 315]. (However the trend is for more waste streams to be recognised as hazardous [40].) WTP sludges are not normally classed as ‘hazardous’ in the U.S.A. either [282, 880, 1098].

*

According to Article 6 of Council Directive 1999/31/EC [13], landfill sites for non-hazardous waste may take: municipal waste; other non-hazardous waste; and “stable, non-reactive hazardous wastes”. (The latter two categories should include inert wastes [27].) “Non-hazardous waste” is literally any waste not defined as hazardous by Article 1(4) of Council Directive 91/689/EEC [2, 13].

†

Defined in Council Directive 1999/31/EC [13] as “waste that does not undergo any significant physical, chemical or biological transformations” (e.g. glass [27]). Inert waste should generally also be suitable for disposal in a landfill designated for non-hazardous waste [27].

‡

The classification is made in the so-called Hazardous Waste List of the European Waste Catalogue [17, 31], which applies E.U. Council Directive 91/689/EEC [2] and is of regulatory importance [41, 44]. The relevant categories are “Wastes from the preparation of drinking water or water for industrial use” (# 19 09) in general, or “Sludges from water clarification” (# 19 09 02) in particular [17].


39

D. I. VERRELLI

As of 30 October 2007 England and Wales implemented two key requirements of E.U. Council Directive 1999/31/EC [13] on landfilling of non-hazardous waste *, namely [196]: • the wastes must undergo a documented “ t r e a t m e n t ” , if possible [as in 41, 44]; and • n o “ l i q u i d ” wastes can be accepted. In general the treatment must reduce the quantity of material or the hazards to human health or the environment, or constitute recycling or re-use [13, 76]. The U.K. Environment Agency considers that waste streams originally deemed non-hazardous cannot have their hazard reduced (unless the risk assessment shows a clear benefit [76]); however, it will accept treatments that enhance recovery of materials or energy [76] or facilitate handling [196]. The U.K. Environment Agency also considers “sludge” acceptable, provided it “flows only slowly” and has limited “free-draining” liquid [196] (similarly in the U.S.A. [282]). Thus, both of these new conditions promote dewatering of WTP sludge that is to be landfilled, although one guidance document indicates that “no treatment” will be required if the sludges are not suitable for beneficial land application [76, 350]. Despite this, a 2006 conference paper stated that alum sludge from Irish WTP’s is “currently disposed of in landfill as a waste” due to its high aluminium content, whose agricultural impact is somewhere between a marginal benefit and a toxic effect [1147]. Although the additional regulatory provisions have been interpreted as implying increases in waste disposal costs, the U.K. Environment Agency [196] claims that rather: Waste audits and a review of waste production and management will often identify potential for savings, by avoiding waste production and by identifying alternative waste management routes.

1▪5▪6

Engineering fill

When aluminium water treatment plant sludges are dried, they form essentially insoluble ‘rocks’ and are inert (like gravel, though not as strong/hard) [254] [cf. 282]. With these qualities, dried aluminium sludge has been used as ‘road fill’ [254] (or road ‘subgrade’ [282, 832] or ‘aggregate’ [557]).

*

40

The Directive must be fully implemented by member states by July 2009 [196].



Dried aluminium sludges can also be poured, and so have been used for back-filling beneath fibreglass swimming pools [254]. Anecdotally lime–softening sludges appear to be especially popular for use as engineering fill in the U.S.A. [282].

A related area is land reclamation. This includes filling of disused quarries and mines, and covering over of landfills and lagoons [282]. Such usage implicitly relies on features of the sludge discussed under the topic of ‘land application’ (§1▪5▪7), in that the material is ultimately a substitute for natural r o c k s and s o i l . Land reclamation, however, generally involves much thicker applications.

1▪5▪7

Land application, including agricultural uses

Spreading or spraying of sludges on agricultural and forest land and on pasture has been trialled on numerous occasions [562, 797, 880], and has become routine at many sites [282]. Temporary site storage will almost certainly be required, as land application may not be possible at certain times due to weather or crop cycle or the like [880]. Yet at some plants the demand exceeds supply [880]! Spraying to land was common in the U.K. in the 1980’s, practised by about 20 WTP’s, applied often at 0.1 to 0.5%m, but sometimes thicker [315]. Circa 1997 this route was hardly used at all, due to legislation which requires that a demonstrable benefit of application exists unless an ad hoc consent is granted [315]. Dewatered sludge should be applied in layers no more than about 200mm thick in order to ensure a reasonable drying rate [797]. Applications of 20mm — repeated if need be — may be advantageous [797]. Typical solids concentrations of sludges used for land application are in the range < 10 to 150g/L [879]. Higher concentration ranges help minimise run-off [1139].

Dry WTP sludge has been described as similar to fine soil, varying from clay-like to sand-like depending on local conditions [880]. (Laboratory-dried samples generated at high coagulant doses formed hardened clay-like shards; presumably due to the dose, but also in the field ‘dry’ may really mean ‘not so wet’. VANDERMEYDEN & CORNWELL (1998) had a similar


41

D. I. VERRELLI

experience in which dried WTP sludge samples could not be hydrated and resuspended [282].) Alum and ferric sludge mineralisation rates and levels of organic carbon are similar to those of many soils and levels of organic nitrogen may be similar to or somewhat less than those of many soils [161, 880]. In fact [161, cf. 880]: “Water treatment plant sludges are [...] more like soil than sewage sludge (biosolids)” — in particular, they often contain a high proportion of clay particles;

furthermore, soils naturally contain some aluminium hydroxides [684].

Increases of nitrates and nitrites tend to occur only in the first 6 months or so, and may be due purely to disturbance of the soil, rather than the chemical properties of the sludge [393].

Once dried, ferric sludges form very friable (i.e. crumbly) granules, which are good for adding to clay soils as a mixture with topsoil [254]. One large-scale application has been addition to mulch, which otherwise forms a firm paste [254]. Some ferric sludges are currently used to dress football fields [48, 254], mixed with compost, and used for professional landscaping application [26, 47, 65]. They are applied as a layer immediately beneath the surface topsoil to improve drainage [254].

The New Zealand

sludge management guidebook [161] suggests a topsoil blend of 10% (or less) WTP sludge. It has been claimed that the high iron content of ferric sludges “improves the quality” of soil [48]. Similarly, alum WTP sludges have been “successfully” applied to horse training areas and tracks [36, 57, cf. 73]. It was found to provide a firm but “low impact” surface that remained stable and did not absorb water [36, 57].

Studies have found that alum WTP sludges used as potting media improved air- and waterholding capacity [281, 282, 669].

In general, application or blending of WTP sludges

improves soil structure or ‘tilth’, increases water retention and minimises effects of fertiliser run-off [161, 281, 880]. Improvements in pH buffering capacity and capacity to adsorb heavy metals [cf. 1098] have also been reported [315]. (Sludges containing significant proportions of lime are especially welcome in areas of low soil pH [232, 880], but even ‘regular’ sludges can amend pH [282].)

42



WTP sludge loading must be sufficiently low for the sludge to crack and fully dry so that plant roots are not waterlogged or starved of air [161] and seed germination is not hindered [879]. GEERTSEMA et alii [393] used a special “sludge grinder” to allow the sludge to be applied as small particles. Alternatively the dry crust can be broken up after spreading [879].

Unlike sewage sludges, water treatment sludges do not contain significant quantities of nutrients beneficial for plant growth (although the risk of dangerous microbial contamination is reduced). However, spreading of lime–softening sludges has been shown by ROBINSON & WITCO to have positive effects on vegetation [562]. WTP sludges are especially suited for turf farming, as turf has a low nutrient demand and requires high moisture levels, especially in the initial growth phase [281, 282].

Water treatment sludges have been shown to bind or precipitate out soluble reactive phosphorus (SRP) in soils to which they are applied [669]. SRP levels up to 75mg/L are required for plant growth; above this concentration soils are considered to be ‘eutrophic’ and run-off leads to the eutrophication of surface water bodies [669]. Such conditions may be created by excessive fertilisation or manuring, with high-density poultry farming being the most commonly quoted example. In such situations it would be desired that the SRP ‘captured’ is not later released from the sludge matrix; some experimental evidence suggests that disintegration of the sludge matrix may occur over extended periods of time which may reduce both removal and retention [1147]. While depletion of SRP below the required level adversely affects plant growth or ‘yield’ [393], a beneficial effect could be realised by applying * the sludges to eutrophic soils [669, 880]. (Treatment of a eutrophic lake with thickened alum sludge has even been trialled, with reasonable success [161]!) Aluminiumbased sludges appear to produce greater reductions in SRP than iron-based sludges, typically achieving 60 to 90% removal, depending upon the application rate, soil type, rainfall, et cetera [669, cf. 880]. Prior freeze–thaw conditioning appears to partly mitigate the phosphorus depletion, according to a study by DEMPSEY, DEWOLFE & MCGEORGE (1993) [282]. Although SRP depletion may seem to be a problem, l o n g - t e r m field studies have *

The application may be by spreading over the entire affected area [669], or by constructing buffer strips around the periphery to act as ‘barriers’ to high-phosphorus run-off entering surface water bodies.


43

D. I. VERRELLI

shown soil phosphorus levels u l t i m a t e l y unaffected by alum sludge application; this is attributed to the pre-existence of significant concentrations of natural P-binding constituents in the soil [393]. An alternative proposal is to apply (alum) WTP sludges in combination with a phosphorus-rich material such as WWTP sludge [281, 684, 832]. A further option is to inject the sludge deep below the soil surface (T 20cm) [782] to minimise the effect on seedlings, which generally have higher phosphorus demands [880].

Coagulation and flocculation sludges should also be shown to have a low toxicity potential. A concern has been the release of heavy metals such as copper, zinc, manganese and cadmium following sludge application [281, 669, 684]. One study (conducted at neutral to high pH) suggested that leaching of heavy metals from ferric sludges would be more likely if the iron phase transformed from ferrihydrite to hæmatite, rather than remaining stable or transforming to goethite [957]. Heavy metal leaching appears to be a problem where soil pH values are very low, as when ferric sludges are applied, but generally not for alum sludges [669], where trace heavy metals tend to remain strongly adsorbed (i.e. they are not mobile) [161, 393, cf. 880]. Leaching of the coagulant metal itself follows the same pattern, with aluminium leaching being negligible at practical loadings [281, 684] but iron leaching being excessively high [669]. In fact, one study reported that levels of s o l u b l e aluminium actually dropped after application of alum WTP sludge [880]. (Aluminium toxicity is not expected to be a problem for soil pH values below 5.0 * [684].) The iron that is leached from ferric sludges is toxic to animals such as grazing cows [669]. Although it is not toxic to vegetation, neither is it an aid to plant growth, as it is present in a non-chelated form that can precipitate [669]. Nevertheless, CORNWELL [282] reported that citrus-growing regions in the southern U.S.A. have iron-deficient soils, and can make this up by applying ferric WTP sludges; indeed, many regional WTP’s have upgraded ferric sulfate quality to enhance marketability. Alum sludges may be composted with a range of other organic materials [161, 282, 797]. Composting a WTP sludge with sewage sludge reduces the concentration of heavy metals in the final mixed product [161], and balances phosphorus availability [315, 880].

*

44

An

Or below 5.5 for kaolinitic soils [684]. ELLIOT & DEMPSEY (1991) reported pH 6.0 to 6.5 as a safe range [281].



alternative successful trial mixed four parts leaves and one part alum sludge by volume [161]. Similarly, alum WTP sludge has been mixed with green waste to provide a ‘capping’ material for a local rubbish tip, accounting for close to 100% of the WTP’s sludge output [36, 57, 73]. For composting the concentration needs to be T 15%m [282].

Overall, both short- and long-term studies both in the laboratory and in the field have consistently shown that land application of alum sludges has no significant ill effects [281, 797], with the possible exception of SRP reduction, for application rates at least up to 2.5%

dry mass (in the first 15cm of soil) [393]. “It has been demonstrated [in many studies] that mobilisation of [heavy] metals is not an issue” in land application [797]. Ferric sludges appear to have essentially the same ‘neutral’ effect, although they may have a slightly higher phosphorus-binding effect [797].

1▪5▪7▪1

Regulatory issues

In the absence of specific regulations, local authorities often ‘informally’ apply the criteria specified for sewage sludges (or ‘biosolids’), or develop separate guidelines based thereon [797]. This has been the case in the U.S.A. — where WTP sludge disposal to land is unlikely to be constrained by either sewage-sludge-based contaminant limits or the TCLP test (see below) [880] — in New Zealand [797], and in the U.K. [315, 1139].

(Nevertheless the

applicable U.S. regulation on, “Standards for the Use or Disposal of Sewage Sludge” (1993) s p e c i f i c a l l y e x c l u d e s , at §503.6, application to “drinking water treatment sludge” [56].)

The U.S. toxic characteristic leaching procedure (TCLP) identifies 8 metals and 25 organic components that are considered to be at risk of leaching into groundwater [562]. (Cf. §257.3– 5 “Application to land used for the production of food-chain crops (interim final)” and §261.24 “Toxicity characteristic” of the U.S. Code of Federal Regulations (CFR) Title 40 [56], which lists 8 metals and 32 organic species [see also 282].) The German equivalent is DIN 38414-4 (1984) [797]. The U.S. TCLP test has been criticised as largely irrelevant, at least in the New Zealand context, where raw water and treatment chemicals are normally of high quality, and WTP sludges will always be expected to pass the TCLP test without difficulty [797, cf. 880]. (Even 1▪5 : Sludge disposal

45

D. I. VERRELLI

in the U.S.A. itself, no failures have been documented in the literature, and many jurisdictions effectively assume all WTP sludges are satisfactory without individual testing [797] [cf. 282, 880].) Indeed, OGILVIE [797] makes an excellent case for pollution avoidance through ensuring that the contaminants never enter the system to begin with: a typical American commercial “alum” contained ~600mg(As)/kg [cf. 880], compared to the New Zealand Specific Impurity Limit of 10mg(As)/kg. (Compare also to the South Australian limit for land application of 20mg(As)/kg in the sludge material [75], which matches the Australian guideline Ecologically-based Investigation Level for soils * [16].

[Cf. 315.]

Note that natural

background soil levels are of order 1 to 50mg(As)/kg in Australia [16] and 0.2 to 8mg(As)/kg in New Zealand [797].) However, U.S. “chemical suppliers are [circa 1996] more conscious of heavy metals contaminants in coagulants” [880], and accordingly have improved product purity. Ferric chloride derived from reprocessing of pickle liquor usually contains especially high levels of contaminant metals [797].

Another risk is that the discharge consent requirements lean too far in the other direction: as discussed on p. 29.

The South Australian EPA [75] presently † allows WTP sludges to be applied to land (by spreading or injection) provided that the land is not used to grow food intended for direct human consumption, that the sludge itself does not exceed the intermediate biosolids ‘Contaminant Grade B’ levels of selected heavy metals [cf. 9], and that significant adverse environmental impacts are avoided. Particular concerns are raised over potential deficiency of phosphorus, and over increases in nitrogen, alkalinity, and copper. The sludge copper content may be excessive due to dosing of copper sulfate in the event of an algal bloom; however the restriction does not apply to application on horse tracks [75].

*

Cf. 100mg(As)/kg in “‘standard’ residential” zones [16].

†

This is an interim guideline, which is to be updated based on an “intensive research project [currently] being undertaken” [75].

46



Exemption from certain discharge levies may apply if the application provides direct agricultural or ecological benefit [315]. Where a benefit is derived, the practice is classed as “waste recovery” in the U.K., rather than “waste disposal” [315].

1▪5▪8

Chemical reuse

Between 60% and 80% of dosed aluminium may be recovered by thickening aluminium sulfate sludge, acidification to pH 3.0 to 1.8 (or even pH 1), and decanting the remaining solids from the aluminium solution [107, 161, 557, 879, 880] [cf. 1139]. Lower pH values are required for hydrochloric acid compared to sulfuric acid [107]. Contact times of 10 to 20 minutes are generally sufficient [161]. Popular in Japan prior to 1972 *, and apparently also in the former U.S.S.R. [see 107], this process lost favour due to concerns about impurities in the recovered product, especially in terms of accumulation of redissolved heavy metals, such as chromium and iron, in the sludge [557, 879] (not an issue where high-purity chemicals are dosed into high-quality raw water [797]; a 1973 U.S. study also concluded that impurities did not accumulate [282]). The process was practised in the U.S.A. too, where operation was also found to be cumbersome [783]. Operation in the 1970’s was reported to be sensitive to process fluctuations, as in daily operation, and comparable difficulties were faced in attempting to apply the technology from one (pilot) plant to another [797]. More recently, aluminium sulfate has been recovered by acidification of sludge to pH 2, sedimentation to remove the remaining solids, followed by ion exchange to extract the aluminium [879]. The yield of the process is good, with about 95% recovery †, as is the selectivity [879].

In recent times coagulant recovery has come to be considered truly

economically viable [827]; recoveries as high as 98% are quoted [797]. Yet practice in Brisbane over a few years demonstrated that despite the advantages of recovering (85% capture) an effective coagulant ‡ and producing one-third the amount of sludge, which dewatered “much more readily”, high ‘hidden’ corrosion and maintenance

*

Fifteen plants were using this technology in Japan in 1978 [797].

†

Under laboratory conditions.

‡

The recovered product appears to be effective even at concentrations an order of magnitude less than usual operation [315].


47

D. I. VERRELLI

costs meant that the process was not truly cost-effective [797]. The high acidity of the sludge can also present a disposal problem, although the material appears to possess favourable dewatering properties [797, 1139]. Several more published case studies were summarised by CORNWELL [282].

Between 90 and 95% of dosed sodium aluminate may be regenerated from sludge by dissolution at pH 12 to 12.5 using sodium hydroxide [879]. Organic chemical solvents have also been investigated [107].

Between 60% and 70% of dosed iron may be recovered by thickening ferric sludges, acidification to pH 2.0 to 1.5, and decanting the remaining solids from the iron solution [879]. This process is not popular, due to difficulties in dewatering the sludge and the high cost [879]. Ion-exchange resins have also been employed to investigate recovery of iron from ferric WTP sludges for recycling back to the plant as a coagulant [395].

The solids concentrations of sludges sent to chemical recovery vary widely, from < 10 to > 250g/L [879].

In 1973 FABER & TARAS [353] wrote: Logic dictates that the reclamation of water-treatment chemicals such as alum, lime, and magnesium carbonate will eventually prevail in many locations as the long-term solution to the waste-disposal problem.

[....]

The economics of byproduct recovery are

continually improving [...]. Accordingly, the movement of waste to distant landfills is losing its former competitive advantage [...].

Despite their confidence, such a situation has not yet come to pass. The reference to magnesium carbonate relates to the family of processes proposed by BLACK at around this time.

M a g n e s i u m use as a coagulant was largely predicated on the

recovery and reuse of the chemical, given a suitable raw water stream — see §R1▪2▪7▪1.

The small quantities of “unmarketable and useless residue” produced by “most” recovery processes have been disposed of via landfill, subterranean disposal, and barging to sea [353]. 48



Circa 1992 “few” full-scale plants were operating in the U.S.A. [880]. Circa 1997 full-scale

plants were operating in the U.S.A., Japan and Poland [315]. Echoing the above quotation, DILLON [315] wrote: The economic and technical feasibility for coagulant recovery may be more favourable now as a result of increasing waste disposal costs and improved technologies such as activated carbon adsorption and ion exchange for the purification of recovered coagulants.

Circa 2006 CORNWELL [282] reported that implementation of coagulant recovery was

“limited”.

1▪5▪9

Other beneficial uses

Various studies have investigated uses in building materials, mainly focussed on two aspects: • cement production [161, 282, 557, 827, 832, 880] (or use in asphalt or concrete [107]); and • bricks for paving or general purpose [281, 282, 501, 557, 827, 832, 880]. Incorporation in tiles [501], refractory bricks and other ‘ceramics’ [107] has also been investigated.

In the case of tiles and bricks, the WTP sludge may be advantageously

combined with sediments dredged from the supplying dam or reservoir, say, to reduce water absorption and shrinkage [501]. It would be reasonable for the sludge solids to comprise 5%m of the raw materials in brick making [e.g. 282, 501].

A limitation on incorporation in building materials is the need for an amenable and potentially very large production factory to be sited close by [282, 797]. It is unlikely that the factory would pay for the sludge [315]. Disincentives include [315]: • the possible need for further processing, including dewatering; • the presence of specific contaminants; • variability in sludge quality; 1▪5 : Sludge disposal

49

D. I. VERRELLI

• variability in market demand for the factory product, such that disposal of at least part of the sludge by an alternative route may sometimes be required. On the other hand, raw material consumption by typical cement and brick factories is far greater than typical WTP sludge outputs [282]. Although these are subject to cyclic trends, as essentially commodity items they are not sensitive to changes in fashion. In brick-making the sludge is most conveniently deposited at the quarry, and blended with the natural quarry materials prior to delivery to the brick works, although blending at the plant is also feasible [282].

Leaching from the fired bricks and tiles is low [501]. By appropriate blending of the WTP sludge and firing temperature selection, compressive yield stress and water absorption requirements can be met [501]. A perhaps unexpected drawback of the use of WTP sludges in the production of commercial bricks and tiles is the adverse colouration that they may impart [501], limiting their practical use.

One study considered the feasibility of firstly pelletising and then sintering alum WTP sludge with rice hulls in order to produce a material that could function as a filtration medium for water treatment [249] — i.e. in the filter beds where media such as gravel are usually specified. Evaluation of the sintered particles in terms of porosity, pore size and “leachability” * indicated they were suitable for the intended use as WTP filter bed media [249].

The phosphorus-binding ability of WTP sludges described in §1▪5▪7 has been considered of possible benefit in wastewater treatment. In that case it is desirable to remove both ‘free’ orthophosphates as well as condensed phosphate species, and experimental evidence shows that WTP sludges can accomplish this [1147]. (In fact, removal of other contaminants such as

*

Here “leachability” is defined with respect to mass loss of the sintered particles upon washing with concentrated HCl, and thus does not distinguish the specific chemicals contained in the leachate [249]. Although this may seem an insufficient test in view of the possibility of heavy metal release, for example, it is stated that the test results demonstrated that the samples were “in compliance with the Taiwan Water Supply Corporation’s criteria” [249].

50



Cr, Hg, Fl, Cu and Pb may also be achieved [1147].) It appears that an inner-sphere complex is formed [1147], which should be relatively stable.

1▪6

The nexus between sludge generation, sludge dewatering, and sludge disposal Despite the strong linkage between the treatment process and its waste streams, however, water treatment plant waste management has historically been treated as a stand-alone management issue. [...]

With increasing costs associated with

managing waste streams, it has become prudent to consider

the

waste

stream

quality

and

characteristics as part of the overall evaluation and design of the main treatment process. — CORNWELL (1999) [281]

WTP sludges are not simply WTP sludges. Different treatment conditions and different raw waters produce sludges with different characteristics [281]. The sludges dewater differently. If they dewater differently, then the range of disposal options may be different. Alternatively, if external requirements determine a particular disposal route, then the costs of disposal will be different [281]. As is natural, the greatest research effort has gone into investigating the effect of water treatment on the product water [525], which we may call the supernatant. Relatively little research has been carried out into the influence of upstream conditions upon drinking water sludge dewaterability, with a few notable exceptions, such as the pioneering work of KNOCKE, DULIN and HAMON [331, 577]. They reported improvements in dewaterability at [331, 577]: • lower coagulant doses; • lower coagulation pH values; • higher incorporation of raw water turbidity; and • lower incorporation of raw water organic content. 1▪6 : The nexus between sludge generation, sludge dewatering, and sludge disposal

51

D. I. VERRELLI

(Unfortunately, these also tend to correspond to inferior product water quality [577]!) Along with similar studies by other researchers, these results did not systematically quantify the sludge dewaterability across the full range of solidosities in such a way as to allow performance prediction in a variety of dewatering devices. In fact, several researchers have reported results at an arbitrary mass concentration, following dewatering for an arbitrary period of time in a single arbitrarily-configured dewatering device. These factors may also have influenced industrial thinking.

It is a common view in industry that the only reliable way to design dewatering devices such as thickeners, centrifuges or filter presses, or to evaluate polymer performance, is to perform pilot-scale testing and make inferences from other full-scale installations [e.g. 315, 376, 797, 1076]. This was eloquently expressed by FREE [376]: Most engineers seem to have concluded that advance in laboratory study of slimes is of little help in the design of thickening plant and that one must go at it blindly, guided only by such general good judgement as has resulted from empirical experience. With this pessimistic conclusion I cannot agree. [...] Probably most of the past failures are to be attributed to misinterpretation of laboratory data, due, in turn, to neglect of the fundamental mechanics of suspension.

Despite being made in 1916, the comments still have resonance today.

1▪7

Aim of this work Although sludge dewatering and disposal have traditionally not been of major concern at many treatment facilities, more emphasis will be placed on them in the future. — KNOCKE, HAMON & DULIN (1987) [577]

Several problems exist with the conventional approach to drinking water treatment and the associated sludge by-product: • demand for higher quality potable water leads to more sludge;

52



• availability of source (raw) water is increasingly restricted, especially when limited to sustainable abstraction; • scarcity of land discourages lagooning and landfilling; • increasing value of environment — traditional disposal routes are prohibited or too expensive.

According to OGILVIE’s [797] assessment based on New Zealand WTP’s: The cost of sludge handling and disposal may approximate 10 [to] 20% of the cost of water treatment, with the cost reducing as the water treatment plant size increases.

An important contribution can be made to the environmental and economic efficiency of the water treatment process by specifying operating conditions that will minimise the amount of sludge produced and/or maximise the ‘quality’ of the sludge produced — subject to compliance with drinking water quality requirements. In the context of the present work sludge ‘quality’ is synonymous with sludge dewaterability. All of the disposal options covered in §1▪5 would benefit from improved dewatering performance.

The present work is intended to lead to models or correlations that can be used to predict the dewaterability of a sludge produced under given conditions, and hence optimise the process.

To achieve this, a better understanding of the formation and behaviour of floc particles and sludge is essential. Many influences will be considered, including the following: • The quality of the raw water — amount and composition of contaminant. • The coagulation and flocculation operating conditions (the type of coagulant or flocculant, dose, pH, mixing rate and time, et cetera). • Further (mechanical) processing of the floc particles, especially as shear from pumping, flow through pipes, et cetera.

These influences are classified in Table 1-4 in terms of how readily they may be controlled and when they arise.

1▪7 : Aim of this work

53

D. I. VERRELLI

Table 1-4: Classification of key parameters influencing sludge properties.

Control

Situation

Daily operation

Generation

Post-formation

Coagulant dose

Polymer conditioning dose

Coagulation pH Flocculant dose Periodic assessment

Design or major review

Flocculant type

Polymer conditioner

Raw water quality a

Addition of PAC

Coagulant type

Shear

Mixing rate

Freeze–thaw conditioning

Mixing time Note

a

Raw water quality is often out of the control of the plant operator, although it is subject to natural

periodic variation, and will be routinely monitored on site. In a limited number of cases the WTP may have the ability to select a different raw water source, or a different blend of sources. More often the abstraction point in the reservoir can be changed.

It is acknowledged that operational plants may be considerably constrained in their ability to vary critical aspects of the treatment, such as coagulant dose or PAC addition. Nevertheless, Table 1-4 demonstrates that, in principle, sludge dewaterability can be optimised on any plant without necessarily jeopardising product water quality, such as by attention to the shear that sludges are exposed to. A further important outcome will be the ability to p r e d i c t dewatering performance, and the effect of process changes. For example, if regulatory changes mean that the coagulant dose must be increased, it would be very useful to know in advance whether the sludge resulting from the new configuration will dewater in the same way, or whether different devices would be more suitable. Similarly, systematic characterisation of dewaterability would allow the operator to anticipate the increase in sludge volume corresponding to an increase in coagulant dose of 50% (say), and hence determine in advance whether existing infrastructure (piping, pumps, tanks, et cetera) will be adequate, or determine the specifications of new equipment items required.

54



The effects of the variables in Table 1-4 will be measured by experimental, rheological characterisation of the sludge. Given the importance of shear on sludge quality, if not quantity, care will be taken to ensure that exposure is well characterised. Although practical on-site dewatering of sludge may occur by centrifugation or by filtration, experimental techniques in this study will build upon expertise gained in pressure filtration to generalise results for any mechanical dewatering technique. Low-concentration behaviour will be characterised by analysis of batch settling. Limited centrifugation testing will be carried out for validation and comparison purposes.

Naturally, the supernatant produced must still be of acceptable quality for drinking water supply after normal processing. Hence turbidity, true colour, and ultraviolet absorbance (as an indicator for organics) will be monitored. Nevertheless, some treatment conditions will be explored that would not necessarily be acceptable on a real WTP. Exploration of such conditions will inspire more confidence in trends identified in sludge dewaterability over the narrower range of plant operating conditions, and may assist in establishing the responsible mechanisms.

A subsidiary aim of this work is to evaluate, extend and validate existing theories and analyses related to sludge generation and dewatering. Although the present application focusses on WTP sludges, the theoretical framework is more generally useful for a wide assortment of particulate systems. Hence it is hoped that the present work will also support developments in more fundamental areas such as aggregate structure and compaction.

1▪7 : Aim of this work

55

2.

BACKGROUND

Models, of course, are never true, but fortunately it is only necessary that they be useful. — BOX (1979) [185] [see also 970]

A study of WTP sludge production and dewaterability requires background knowledge in a diverse range of fields. At the heart these deal with two broad themes. First, the nature of the m a t e r i a l of which the sludge is composed. Second, the b e h a v i o u r of the sludge once formed.

The material making up the sludge is a product of coagulation, and flocculation. Metal salts and polymers are mixed into the raw water in order to combine with natural impurities, so that they can all be removed together. The outcome of coagulation depends upon cation hydrolysis and polymerisation, followed by precipitation, which governs the phase of solid that forms. Flocculation mechanics are similarly complex at the most fundamental level, with the outcome depending upon e.g. polymer (re)conformation kinetics and electrostatic interactions. In each case, if the operation is successful, the result is a porous aggregate or floc, often with a fractal structure, that is composed of a mixture of substances, each with their own properties. A moderately concentrated mixture, or suspension, of these aggregates then makes up a sludge. The technology of water treatment is very well established, and has a heritage of several thousand years [289, 358]. With the state of modern science and engineering, it can be expected that most professionals working in this area have a good understanding of the foregoing processes. Nevertheless there are numerous fundamental aspects of coagulation and flocculation that are greatly simplified in standard engineering textbooks [e.g. 129, 142, 289, 557, 653, 854]. Furthermore, even in more scholarly works the level of understanding of

certain elements is surprisingly sketchy. It has not been the primary aim of the present work to survey the literature on these topics. Yet it is important to ensure that results are interpreted in the light of a satisfactory 57

D. I. VERRELLI

knowledge of the fundamental processes underlying coagulation and flocculation. In order to properly address this, a critical review of these topics is presented at the back of this thesis. See Appendix R1.

The behaviour of sludges can be described by their t r a n s i e n t properties — usually in terms of the kinetics or dynamics of the ‘transformation’ process — and by their e q u i l i b r i u m properties. (Occasionally it may be convenient to include model parameters for a state that is ‘practically’ at equilibrium.) These principles hold equally for mechanical dewatering or thermodynamic rearrangement, and form the basis of both good theoretical models and meaningful empirical correlations. Significant examples are presented and discussed in the following sub-sections.

This chapter focusses on the rigorous development of theories describing dewatering as practiced industrially. This is not to imply that other theories, developed with different motivations, are irrelevant.

Examples of these include equations describing soil

consolidation under load, ‘spontaneous’ gel shrinkage, and certain macrorheological models. These additional topics are examined in the second part of the critical review presented at the back of this thesis (Appendix R2).

2▪1

Introduction to dewatering

Dewatering theory deals with the opposing ‘flow’ of a liquid phase (nominally water) and a solid phase [e.g. 1037]. Dewatering cannot happen without the action of an external ‘force’, needed to overcome the resistance to this flow. These terms can be quantified in numerous ways. More concretely, the dynamic resistance arises because the entire cross-section is not available to either phase for flow *. Although their volumetric flowrates must be constant (by

*

Inertia is not a persistent resistance in the sense intended here. Wall effects are also neglected. Osmotic resistance is ‘static’ on physically meaningful timescales.

58

Chapter 2 : Background


mass balance, with constant phase densities), the local relative velocity is increased by this partitioning of the cross-section, which amplifies the resistance. These fundamental considerations mean that is most appropriate to analyse dewatering processes in terms of volumetric flows and areas — or, more conveniently, volumetric fluxes and volume fractions. (The volume fraction being taken as equal to the area fraction [see 204] [cf. 753, 875].)

The volume fraction of pores in the sample is the p o r o s i t y , o. The volume fraction of solid phase in the sample is the s o l i d o s i t y [203, 255, 257, 406, 408, 585, 604, 642, 765, 1026, 1027, 1028, 1029, 1032, 1034, 1036, 1037, 1040, 1143], φ, which is the complement of the porosity: o + φ = 1 always. As desaturation (i.e. gas penetration) is not considered in the present work,

it is only necessary to specify φ. Solids that have dissolved are assumed not to take part in the dewatering process except to perhaps modify (say) the density and viscosity of the liquid phase. Occasionally reference is made to the void ratio, e = (1 ‒ φ) / φ [e.g. 629, 1013] [cf. 1011].

An important distinction exists between the a m o u n t of pore space, the s i z e of the pores, and the c o n t i n u i t y (cf. tortuosity) of the pores — and thereby the compressibility and permeability [375];

These are controlled by particle arrangement, including aggregate

structure, aside from primary particle properties.

The other characteristic feature of dewatering processes is that the spacing between particulates comprising the solid phase is progressively reduced, such that the solidosity increases. Ultimately this must give rise to a class of ‘static’ resistances to dewatering, as described in §2▪1▪4.

2▪1▪1

Solidosity

The solidosity can be simply expressed in terms of the solid- and liquid-phase volumes:

φ≡

VS VS = . Vtotal VL + VS

[2-1]

2▪1 : Introduction to dewatering

59

D. I. VERRELLI

The solidosity of a real sample is obtained from

φ=

1 ρ  1 1 +  − 1 S  x  ρL 

,

[2-2]

where ρS and ρL are the solid- and liquid-phase densities, respectively, and x is the s u s p e n d e d solids mass fraction, defined x≡

mS , mL + mS

[2-3]

where mS is the mass of suspended (non-filterable) solids, mL is the mass of the liquid phase. The liquid phase may include dissolved (filterable) solids, with mass mDS, in addition to the expected evaporable liquid. Experimentally x can be obtained by gravimetric analysis of the dried sample and its supernatant according to x=

y sample − y supernanant 1 − y supernanant

,

[2-4]

where the yi are mass fractions of t o t a l solids, defined in general:

 m + mS   , y i ≡  DS   m L + mS  i

[2-5]

and it is recognised that mS for the supernatant should be zero.

For the sample often

mS [ mDS. Note that if mDS = 0, then x = ysample. In contrast to commonly studied particulate systems [e.g. 737], the low solidosity of WTP sludges makes accurate knowledge of the relevant densities and salt concentrations essential.

2▪1▪2

Dewatering regimes

Dewatering is commonly categorised according to the concentration of solids in the system. This is truly a spectrum [1034], in which it is merely for the sake of convenience that different labels are applied to different ranges, much as dilute systems are called ‘suspensions’, more concentrated systems are called ‘sludges’ (or ‘muds’ et cetera), sediments are called ‘beds’, and the most concentrated systems are called ‘cakes’. Similarly, the separated liquor is variously termed ‘supernatant’, ‘permeate’, ‘centrate’, ‘filtrate’, and even ‘expressate’ [e.g.

1034].

60



The solidosities corresponding to each range vary from material to material.

The regimes may be labelled as follows, in order of increasing solidosity: free settling; hindered settling; and consolidation or compression [cf. 206].

F r e e s e t t l i n g describes dewatering in systems that are so dilute that interaction between particles is negligible. If there is a dispersity of particle size, shape or density, then this results in preferential sedimentation of some classes, while others may remain in suspension [298, 376]. The term h i n d e r e d s e t t l i n g may be applied to systems in which there is some interaction between the particles resisting the dewatering motion, but in which the particles have not formed a network.

This regime is s o m e t i m e s called ‘zone settling’ (see

§2▪4▪1▪2(a)).

Particles may be said to have formed a n e t w o r k when contact (or interaction) between particles is ongoing (unlike the transient nature of slow ‘collisions’ that characterise hindered settling), and when this chain of interactions may be followed between any two particles in the network. That is, compressive * stresses can be transmitted via the network throughout the system [435, 628]. In a network it can be said that the interparticle connections ‘percolate’ (read ‘chaotically span’) the space: hence, these are also described as ‘percolation networks’ [175, 906] [cf. 347]. (Note that percolation per se is generally n o t relevant to a g g r e g a t e f o r m a t i o n [see e.g. 588, 590, 705]: see notes to Table R1-13.) The solidosity at which the particles first form a network is known as the g e l p o i n t , φg †. The gel point has been described as “an important indicator of the state of aggregation” *

The criteria of TILLER & KHATIB [1035] are that the structure must be “capable of resisting [both] shear and compressive forces”.

†

Also called the p e r c o l a t i o n t h r e s h o l d , φc [604, 691, 906] — the term ‘percolation’ is used loosely [cf. 590, 841]. LOIS, BLAWZDZIEWICZ & O’HERN [681] explained that for attractive particle systems percolation — and by analogy ‘gelation’ — strictly comprises t w o distinct transitions:

“connectivity

p e r c o l a t i o n ”, when the network spans the system volume, followed by “ r i g i d i t y p e r c o l a t i o n ”, when the network backbones are rigid and cannot be deformed without storing energy [cf. 705]. The ‘gel point’ intended in the present work adheres more closely to the second description.


61

D. I. VERRELLI

[1035]. (Traditionally only particulate systems with relatively weak interactions (~100 kB T) are described as forming ‘gels’, however the c o n c e p t of a gel point applies regardless of the strength of the resulting network [cf. 241].) At the particle lengthscale, the network resists deformation through ‘force chains’ [83, 151,

452, 460, 692, 772, 794, 1052] or ‘mechanically resistant columns’, which can be visualised as connected aggregate ‘backbones’ in coagulated systems [347, 567, 813, 990, 991] [cf. 1087], with fractal conformations [175, 366, 844, 845, 967] [cf. 681]. Thus, the applied load is not borne equally by all particles. Indeed, recent models consider that force chains aligned roughly in the major principal stress direction bear the greater part of the load, and particles between force chains (which are also part of the larger network) provide more laterallyoriented forces to prevent the force chains from buckling (i.e. ‘failing’) [83, 585, 772, 794] [cf.

1052].

Dewatering of this network structure may be described as c o n s o l i d a t i o n or compression. The compressive stresses are conventionally taken as ‘superficial’ pressures over the entire cross-sectional area of solids and fluid, rather than the true pressures existing at individual points of contact, which would be difficult to measure or analyse [200, 207, 771, 1040]. In sedimentation processes, i.e. batch settling or continuous thickening, the consolidation is driven by the (buoyant) self-weight of all the superposed particles in the network, as described by FREE (1916) [see 218, 376] and DEERR (1920) [298].

A t r a n s i t i o n zone

between the hindered settling zone and compression zone is observed [274] [cf. 233]. A similar mechanism applies in centrifugation, except that a (‘fictitious’) centrifugal force is substituted for the gravity term. In filtration an applied load drives the consolidation. The total particle ‘pressure’ (see p. 107), pS, is made up of a range of contributions: selfweight under gravitational or centrifugal acceleration;

external load due to a pressure

differential imposed across the sample (as in filtration); and the ‘osmotic’ pressure [630].

2▪1▪3

The dewatering ‘spectrum’

Settling operations are often interpreted as separation of solid particles from liquid, while consolidation operations are often seen as separation of liquid from (porous) solids. While

62



these distinctions are sometimes useful conceptually, they are entirely artificial. In reality, dewatering — the separation of solids and liquids from each other — covers the entire spectrum [1034].

Often a material that dewaters readily in one regime (e.g. in clarification, at low φ) dewaters well in other regimes (e.g. centrifugation, filtration, at high φ) [860]. Unfortunately, this has promoted the misconception that this is always the case [860].

A key point of the theory developed by LANDMAN, WHITE and BUSCALL (§2▪4▪5) — and applied in the present work — is that the concept of flow past a set of particles is applicable for solidosities in a range from that corresponding to single, isolated particles all the way up to consolidated ‘beds’ of particles [424, 607] [cf. 604, 1028]. This feature is not unique, and had been considered before. It is also possible to derive exact conversions between the parameters used to characterise dewatering in several different models [604, 607, 975, 976, 1027, 1028]. An advantage of the LANDMAN–WHITE approach is that it starts from a general mathematical theory and employs appropriate boundary conditions to suit each operation [607].

Alternative approaches have been obtained by

generalising models developed for specific dewatering processes.

CAETANI (circa 1913 [373]) had also made a link between settling and permeation through his reasoning that “as [...] particles sink the water must rise through the tortuous channels between the particles and must hence overcome a frictional resistance” [856]. In the ensuing decades others — such as RUTH (1946) [882] [see also 881, 884], KYNCH (1952) [617] and HAPPEL & BRENNER [442] — have occasionally published similar comments.

SHIRATO, MURASE and co-workers (1983 [932], 1989 [765]) combined dewatering data from settling, centrifugation, permeation and filtration to obtain ‘master curves’ for both kinetic and equilibrium parameters (αm(φ) and φ∞(Δp)) [1027, 1028], although they regularly work in terms of cake-averages and allow up to ~10% deviation from equilibrium [see 765]. Also the effect of network stress on the initial settling rate (relevant for φ ≥ φg, cf. §2▪4▪5▪3(a)) was effectively disregarded [932].


63

D. I. VERRELLI

TILLER & HSYUNG (1993) [1034] also advocated a “unified approach” to the analysis of dewatering operations.

2▪1▪4

Driving ‘forces’ and resistances to dewatering

Dewatering can be driven mechanically, or by chemical potential [745]. M e c h a n i c a l p r o c e s s e s rely on [cf. 1040]:

•

hydrodynamic drag (generally frictional drag [847]) — as in rotary vacuum drum filtration;

•

direct surface–surface transmission of forces (pressures) imposed externally through pistons or membranes — as in filtration; and

•

self-weight arising from gravity or centrifugal acceleration — as in gravity settling or sedimentation and centrifugation.

C h e m i c a l p r o c e s s e s rely on a chemical potential gradient applied to the liquid phase [745]:

•

capillary forces arising from surface tension — as in slip casting, where liquid is drawn into a porous substrate;

•

exogenous osmotic pressure — as in osmotic consolidation, where a colloidal mixture is sealed in a semi-permeable membrane and immersed in a concentrated (high activity) solution; and

•

molecular kinetic energy — as in drying or evaporation.

Less common techniques include electrophoresis and electro-osmosis, which rely on an applied e l e c t r i c field which motivate the solid or the liquid (respectively) [105]. Interparticle attraction may provide an endogenous ‘force’ for dewatering (see synæresis, §R2▪1). The listed mechanisms dominate the respectively suggested operations, but do not necessarily occur in isolation. When a combination of mechanisms occur together, they can act synergistically, but may also act against each other. In the present work only mechanical dewatering mechanisms are investigated.

64



Dewatering can also be categorised according to the prevailing mode(s) of r e s i s t a n c e [cf.

363]: 1.

D y n a m i c f l u i d f l o w . This resistance always exists when there is r e l a t i v e m o t i o n of liquid and solid phases. a.

Normally it is encountered when a particulate or arrangement of particulates moves with respect to the liquid, so that the liquid can be described as deviating a r o u n d the solid.

This resistance is directly

proportional to the velocity difference (cf. equations 2-9 and 2-18). b.

An ‘enhanced’ dynamic effect is important at high particle velocities — or, more precisely, velocity gradients — such as may arise at a discontinuity [363]. The effect can be illustrated by considering the excess forces on two approaching particles, due to the fluid ‘squeezed out’ from b e t w e e n them [363], compared to the resistance when an isolated particle moves (at the same speed) (§2▪2).

2.

E n d o g e n o u s o s m o t i c e f f e c t s . By treating the solid phase as a ‘solute’, an analogy may be drawn to solutions in which differences in osmotic pressure act to equilibrate solute (particle) concentration in adjoining volume elements [cf.

211] *. The origins of osmotic pressure in a suspension are (static) interparticle repulsions

or (dynamic)

collisions:

the repulsions could be e.g.

electrostatic; the collisions would arise from BROWNian motion (just as for a gas) [585, 628, 630] [cf. 363]. The underlying mechanism is that higher solidosities require smaller interparticle separation, and therefore increased repulsion and collision frequency. Dewatering (or indeed swelling, cf. §R2▪1) in this mode is thus expected to be r e v e r s i b l e [cf. 363] until a solidosity is reached that favours particle bonding. The lengthscale of BROWNian motion fluctuations is likely to be much smaller than at least the aggregate diameters in the present work. Also, the liquid phase ionic strength is sufficiently high that electrostatic-type effects would also be of short range compared to the interparticle spacing [628, 630]. Hence osmotic *

Fundamentally these osmotic effects arise as a chemical potential due to entropic (statistical thermodynamic) considerations.


65

D. I. VERRELLI

pressure becomes significant only as the system reaches close packing, φcp [211,

628, 630]. (In the present work on ‘compressible’ WTP aggregates, very large external pressures need to be applied to approach this state!) For these reasons osmotic pressure is generally assumed negligible [630], except for very small, non-aggregated particles [cf. 363], essentially engendering only a slight shift in behaviour around φcp. 3.

S t r e s s o f w e a k b o n d s . For materials that are w e a k l y c o a g u l a t e d o r f l o c c u l a t e d , with bonding in a shallow (secondary) minimum of the interaction energy (say 1 kB T to 10 kB T) the particle network undergoes gradual, irreversible consolidation even under very small loads in a process commonly called ‘ c r e e p ’ [101, 140, 211, 213, 926]. This is an irreversible ‘thermal’ process, relying mainly on bond fluctuations and particle hopping (cf. §R2▪2▪3, §9▪3▪2▪4).

4.

S t r e s s o f s t r o n g b o n d s . Particles are s t r o n g l y c o a g u l a t e d , and bonds are in the deep, steep (primary) minimum of the interaction energy. The particles are in contact, and stresses are transmitted across network from one particle to the next though the contacts [363]. The network is able to withstand moderate stresses with barely any deformation (all of which is elastic). Beyond a critical ‘yield stress’ bonds fail and the structure consolidates irreversibly.

5.

S t r e s s o f a g e d b o n d s . Particles have been held together for a long time and formed enhanced bonds, e.g. though increased contact area (see §S17▪1, p. 938). Stresses are transmitted across a coherent network, which strains through (possibly elastic) deformation of the solid particles until (irreversible) catastrophic failure at very high loads.

6.

P r i m a r y p a r t i c l e i n t e g r i t y . The primary particles themselves may deform under high loads [195].

Under moderate stresses only a slight, elastic

deformation would be expected for most solids [cf. 37]. As the stress is increased, plastic deformation of the solid phase could occur, and ultimately catastrophic failure [cf. 83, 884]. 7.

A t o m i c - s c a l e s o l i d l a b i l i t y [127].

Under sustained loads s i n t e r i n g

(§9▪1▪1▪1(b)) may progress over extended periods of time until only isolated

66



pores remain [550]. The rate (or extent) can be increased at elevated pressure, depending on the prevailing mechanism [550, 571]. (This summary is a synthesis of aspects described in more detail elsewhere in the present work.)

Systems will tend to be predominantly affected by a resistance further down the list as the solidosity increases. Nevertheless, combinations are possible, and in principle all of the resistances are additive. Aggregates or networks with intermediate bond strength may predominantly exhibit yielding on short timescales, but creep on long timescales [cf. 844,

845]. In some cases the i n e r t i a l terms may be significant [363], but more usually they may be neglected [e.g. 923].

Many studies of dewatering account for only point 1.a in the above list. The modelling of LANDMAN and WHITE (§2▪4▪5), applied in the present work, accounts for points 1.a and 4.

2▪1▪5

Packing

At the concentrated end of the spectrum, particle arrangement may be described as ‘close packed’. However, maximum practical solidosity is not well defined, due to the ability of particles to form stable arches [cf. 175]:

for spherical particles, s t a b l e packing

arrangements with solidosities from about 0.15 up to 0.7 have been reported [442]. The maximum theoretical solidosity of

π / 3 2 ≈ 0.7405 [375, 644] corresponds to

rhombohedral [442, 450] or hexagonal [636, 948] or face-centred cubic [151] close packing. Some form of ordered or crystalline packing can exist down to solidosities of 0.545 [151, 636]; in fact the theoretical limit of simple cubic packing is obtained at a solidosity of π / 6 ≈ 0.5236 [375, 948]. Interestingly, the adoption of an ordered arrangement is favoured by entropy,

which increases overall for the system, due to the increased space for small positional fluctuations by a given particle [636]. Randomly packed uniform spheres may be expected to attain the theoretical solidosity of between 0.63 and 0.64 [382, 644, 1040, 1052]. However in practice solidosities from 0.53 to


67

D. I. VERRELLI

0.64 * are commonly observed [218, 382, 442, 636];

and in principle random packing

solidosity could extend down to ~0.125, and theoretically may approach zero [151, 317, 1091]. Below a solidosity of 0.494 (cf. π / 6 ≈ 0.5236 [450], for simple cubic packing [151]) monodisperse hard spheres can generally be assumed to be disordered (although highly localised ordering is retained) [636]. The close packing fraction tends first to decrease slightly as polydispersity increases (for spheres); e.g. limiting solidosity of 0.715 [853]. Packing efficiency may be further reduced if the primary particles are highly elongated [e.g. 1091].

2▪2

Slow particle motion

Where all gradients are small, such as in the limit of slow motion, the assumption of NEWTONian behaviour should be a good approximation for many real fluids [442].

For incompressible fluids in the presence of conservative body force fields, the continuity and NAVIER–STOKES equations, respectively, may be written [442]:

∇⋅v = 0

[2-6]

 ∂v  ρ + v ⋅ ∇v  = −∇p + η∇ 2 v .  ∂t 

[2-7]

By purely dimensional arguments, it can be shown that the left-hand side of the NAVIER– STOKES equation goes to zero as the REYNOLDS number, Re, goes to zero [442]. I.e. − ∇p + η∇ 2 v → 0 as Re → 0 ,

[2-8]

and the time-dependent term has dropped out. “Creeping flow” may be defined as flow for which Re < 0.05 [442] †. Equation 2-8 is then the STOKES equation [954]. Recall that the

*

These variations have been attributed to the difference between bed construction in which all of the particles are settled at once so that the bed forms rapidly (producing a denser bed) and the case where individual particles are gently added to a stable, partially-constructed bed [442].

†

Inertial effects have been experimentally noted for Re > 0.25, while the deviation from STOKES’ law is ≤ 1% at Re ≤ 0.05 [442]. BIRD, STEWART & LIGHTFOOT allow Re ( 0.1 [154].

68



REYNOLDS number represents the ratio of inertial to viscous forces, and so small REYNOLDS numbers imply ρv∇∙v / ηL∇2v [442].

For the problem of a small sphere of diameter d moving slowly at velocity u in a quiescent unbounded fluid, STOKES solved the steady-state differential equations arising from the above assumption to obtain a drag force of [442, 992] FDrag = –3 π ηL d u .

[2-9]

This is STOKES’s law [154]. Various improvements can be made to this first approximation, and these often take the form FDrag = –(3 π ηL d u) я ,

[2-10]

where я is an appropriate ‘correction factor’ [418]. This implies that the actual velocity of the particle differs from the uncorrected velocity by a factor of 1 / я, that is u = uuncorrected / я.

When motion far from the sphere is properly accounted for, the correction is [442] [cf. 154] я = 1 + (3/16) Re + (9/160) Re2 ln(Re/2) + O(Re2) .

[2-11]

where the particle REYNOLDS number is Re = ρ v d/ηL. Because this has я → 1 as Re → 0, in practice the form derived by STOKES is normally used.

Particle shape can greatly affect the motion, and numerous corrections have been developed and compiled [see e.g. 418, 442]. Anisotropy will often result in a spread of values, reflecting various orientations [see also 898, 1003, 1069], which can be averaged [442].

Some other factors also influence settling, such as particle roughness, particle rotation, and turbulence, but for low REYNOLDS numbers (e.g. Re < 1) these appear to be negligible [418, 442]. The rate of energy dissipation would additionally depend upon the inability of a denser solid particle to deform and thereby accommodate dilation of the fluid *, but this is likewise negligible for “many macroscopic systems” [442].

*

This relates to the effective ‘viscosity’ of the suspension [442].

2▪2 : Slow particle motion

69

D. I. VERRELLI

By balancing the drag force of equation 2-9 with the weight, the t e r m i n a l s e t t l i n g v e l o c i t y of a single spherical particle can be obtained as [418, 442]: Δu∞ = u° = Δρ g d2 / 18 ηL ,

[2-12a]

where Δu∞ ≡ u∞ ‒ v *, u° is the STOKES settling velocity, g is the gravitational acceleration, and Δρ ≡ ρS ‒ ρL. Inclusion of the correction factor, я, would require Δu∞ = (Δρ g d2 / 18 ηL) / я .

[2-12b]

For very small particles, BROWNian motion becomes significant.

Given that BROWNian

motion is driven by collisions between water molecules and the particle, the speed and displacement will be greater for small particles, as the probability of the collisions not being balanced on all sides is increased [715]. In water at a 1 second timescale BROWNian motion could be neglected with respect to gravity settling for particles above about 3μm in diameter with a specific gravity of 2.0 [442].

Considering the ‘fuzzy’ boundary of a typical water treatment floc, which will be largely fluid, both the presence of the ‘hard’ core and the slow nature of the flow mean that the particle is not expected to deform while settling [442]. Further, the presence of the solid material in the ‘droplets’ means that the circulation patterns arising for fluid droplets [see e.g. 442] are unlikely to be significant. In any case, if the viscosity of the fluid inside and outside the particle boundary can be assumed to be identical, then 5/6 ≤ я ≤ 1 [442].

GRAF [418] and HAPPEL & BRENNER [442] also review some correction factors for interactions with boundaries or a second particle [see also 192, 489].

Corrections in the ‘ h i n d e r e d s e t t l i n g ’ regime, where there are multiple particle–particle interactions, have been published, but are generally not robust or consistent. As the name suggests, settling in this regime is s l o w e d d o w n .

*

70

This v is for the bulk liquid.



However, SMOLUCHOWSKI found that particles in a dispersed ‘swarm’ would move f a s t e r together than they would individually [442] [cf. 1049]. In fact, the resistance to the motion decreases as the number of particles increases [442]. In the first instance, particles following behind other particles will experience less drag force [442]. Secondly, once the following particle has caught up to the leading particle, they can form a “doublet” that moves about 55% faster than the individual particles would [442]. Swarms settling in shear-thinning fluids are especially hastened, as fluid in the interstices is essentially inert, and acts as part of the solid mass, due to the elevated fluid extensional viscosity [86].

A selection of fairly similar corrections has been published for dilute suspensions [see e.g. 131, 205, 442, 617] [cf. 211, 627, 691]. A great diversity of correlations has been proposed for settling of concentrated suspensions [see e.g. 101, 211, 442, 931, 932] [cf. 742].

2▪3

Flow through porous media

2▪3▪1

DARCY’s law

In 1856 DARCY [295, reprinted in 502] published a brief description of work carried out with RITTER and BAUMGARTEN establishing a relationship for the one-dimensional permeation of a fluid (water) through a porous medium (a bed of sand): qL = − K D 1856

d(P ρL g ) , dz

[2-13]

in which qL

is the volumetric flux of the fluid [m/s], equal to (1 ‒ φ) v,

KD 1856

is DARCY’s original permeability coefficient [m/s],

P / ρL g

is the modified pressure head [m],

z

P

is the modified pressure [Pa], equal to (p + ρL g z),

ρL

is the fluid density [kg/m3],

g

is the acceleration due to gravity [m/s2], and

is the linear dimension in the direction of flow (vertical) [m].

2▪3 : Flow through porous media

71

D. I. VERRELLI

Equation 2-13 and its ‘descendants’ (see below) have become known as D A R C Y ’ s l a w [502]. Strictly P represents a modified pressure that includes self-weight [e.g. 154] [cf. 200, 502, 1013, 1014];

fluid self-weight is usually negligible in pressure-filtration or pressure-

permeation, but not in gravity permeation. Formally, P reduces to p when dp/dz [ ρL g (= constant) — clearly this should be true for typical pressure-filtration or pressurepermeation. Analysing equation 2-13, the condition would also hold for gravity permeation in the special cases of large qL / KD 1856; this might result from an unusually high liquid head on the upstream side (dropping to atmospheric downstream of the filter) or by pre-forming a relatively impermeable bed under a sufficiently high pressure. (In equation 2-13 P is sometimes replaced by the excess pore-water pressure, p , especially in soil mechanics texts: cf. §R2▪2▪2▪1(a).)

As permeability is seen as a property of the solid phase, more modern usage typically emphasises the pressure, and decouples the influence of fluid viscosity, ηL [Pa.s], as in [442, 502, 954, 1040, 1097, 1103] * [cf. 1013]  K  dP qL = −  D  ,  ηL  dz

[2-14a]

or, in three dimensions K  qL = −  D  ∇P ,  ηL 

[2-14b]

where

KD

is the now-conventional DARCian permeability [m2].

This is a sensible reformulation, recognising that the true driving force is fundamentally P , rather than P / ρL g, and given the theoretical result:

K D 1856 ∝

d 2 ρL g , ηL

[2-15]

in which d is a dimension characteristic of the ‘grains’ in the porous bed [502]. HUBBERT [502] presents a derivation of equation 2-14 from the NAVIER–STOKES equation (equation 2-7,

*

72

In fact, many of these also implicitly set P = p.



p. 68). With some further assumptions regarding the form of the pores, the approximate proportionality  (1 − φ) d 2 , KD ∝

[2-16]

is obtained [502] (cf. equations 2-20 and 2-121). Other definitions of DARCian permeability are possible, e.g. either including φ or removing ηL as divisors in the group multiplying the derivative [931] (cf. equation 2-20).

The formulation of DARCY’s law in equations 2-13 and 2-14 assumes:

• NEWTONian fluid behaviour [153], • ρL and g constant * [502], • a porous material that is homogeneous, isotropic, insoluble, chemically inert with respect to the given fluid, and ideally rigid [442, 502],

• inertial forces are negligible (stricter than a laminar flow requirement) [502], • zero solid-phase flux (qS = 0) [cf. 442, 934, 1040] (note that by overall mass balance this implies constant qL, given constant ρL) [cf. 1034, 1036]. The need for homogeneity and isotropicity are a consequence of continuum modelling: e.g. there is no explicit account taken of variations in component velocities over a cross-section, due to variation in pore sizes and tortuosity of different flow paths. The requirement is asymptotically satisfied in the limit of large cross-sections relative to d. A particulate network (or aggregate) can be treated as a porous medium in this way provided that there are “enough particles to form a valid statistical ensemble” and “the length scale over which velocity gradients change [is] large with respect to the particle radius” [954]. The latter constraint is satisfied where KD / d2 [ 1; physically this implies a relatively open structure [954]. (It is not clear whether d should refer to primary particles or some larger unit.) DARCY’s law is implicitly based on the assumption that “the flow is uniform on a scale larger than the [...] pores, but smaller than the whole [porous] body” [1097].

*

The constant density assumption apparently is only required for equation 2-13 [cf. 502]. However, for g a s e s at a t m o s p h e r i c pressure the standard form of DARCY’s law generally does n o t hold [502].

2▪3 : Flow through porous media

73

D. I. VERRELLI

In the present work the fluid flow is likely to be NEWTONian, except possibly where polymers have been added. Also, the liquid density is essentially constant. However, the effective “g” would vary in centrifugation. A valid form of DARCY’s law can be written for flow through a n i s o t r o p i c , porous media — by writing equation 2-14a with different values of KD in different directions — provided that the nett direction of flow is determined by the bounding walls (which also counteract any sideways thrust from the particles) [442].

In DARCY flow, streamlines are not straight as they would be in POISEUILLE flow [154], and so there is potential for inertial effects to become significant at lower values of the REYNOLDS number (before turbulence occurs), at which point the model becomes invalid [442, 502] [cf.

1012]. According to HUBBERT [502], inertial forces may be neglected when qL ( 1×10‒6 / d [m/s] *. This is likely to be true for d ( 10‒4m, for which qL ( 10‒2m/s is required; a number of studies [e.g.

417] have found Re < 1 for such typical industrial filtration scenarios. It will generally be untrue for depth filtration [1103]. Both HUBBERT [502] and HAPPEL & BRENNER [442] are critical of the various attempts to predict values of the DARCY’s law constant, including those of KOZENY [see also 414, 416] and CARMAN [see also 416, 881] (see §2▪3▪2). The methods were described as unable to produce satisfactory results “without invoking ad hoc assumptions or resorting to experimental data”; many assume the existence of POISEUILLE flow [442].

The issue of moving solids would simplistically seem to be resolvable by simply replacing ‒qL with Δq ≡ qS ‒ qL. symmetric;

However, this formulation suffers two, related, flaws:

it is not

and it does not scale proportionally to the true (local) velocity difference,

Δu ≡ u ‒ v, from which the resistance must arise. The symmetry argument says that it should not matter what (inertial) frame of reference one uses, e.g. whether the co-ordinates are defined with respect to the (nominally stationary)

*

This should possibly be inflated by a factor of, say, 1 / (1 ‒ φ) to more accurately reflect the true velocity in the pores. This factor would still not yield the true velocity, and would not affect the order of magnitude estimates.

74



solid bed or the (nominally moving) fluid [cf. 362]. Co-ordinates may even be defined with respect to a moving cake–suspension interface (i.e. material co-ordinates) [934]. SHIRATO and co-workers [934] proposed a definition of the nett flux of solids (in one dimension), such that [1040]:

1− φ  qS − qL Δ q ≡   φ   q qL  = (1 − φ )  S −  = (1 − φ )[ u − v] = (1 − φ ) Δ u  φ (1 − φ )

.

[2-17]

Essentially this converts the solid-phase flux to a ‘pseudoflux’ defined with respect to the liquid-phase cross-sectional area. The choice is arbitrary, but sensible to permit compatibility with the conventional equation 2-14. This may now be written [cf. 1040]: 



(1 − φ) Δ u =  K D  dP  ηL  dz 



(1 − φ) Δ u =  K D  ∇P  ηL 

,

[2-18a]

.

[2-18b]

For permeation through a stationary medium (u = 0) with constant porosity, the threedimensional continuity requirement is ∇∙(Δu) = 0, so that constant KD yields ∇2P = 0  ∇2p = 0 [153, 154]. Finally, it is of interest to note that equations 2-16 and 2-17 give KD ∝ Δ q ∝ (1 ‒ φ), so a further formulation could cancel the apparently common factor of (1 ‒ φ) from both sides of equation 2-18, yielding a coefficient more truly representative of the material properties. That is, K D∗ ≡ KD / (1 ‒ φ) .

2▪3▪2

Extensions and alternatives to DARCY’s law

Several extensions or alternatives to DARCY’s law have been proposed, notably those of BRINKMAN [see 153, 954, 1068, 1097] and KOZENY and CARMAN [416, 442, 1030, 1103]. The latter analyses [414, 416, 502, 881] and the resulting CARMAN–KOZENY equation [347, 416, 442, 642, 928, 1103] [cf. 598] have been criticised on numerous counts.

For concentrated suspensions, HAPPEL & BRENNER [442] derived an expression that is consistent with the empirical permeability coefficient correlation of DARCY, viz. 2▪3 : Flow through porous media

75

D. I. VERRELLI

qL = − K D

 6 − 9φ1 / 3 + 9φ 5 / 3 − 6φ 2 d 2  ΔP ΔP  ⋅ = − η Δz 6 + 4φ 5 / 3 18φ  η Δz 

[2-19]

where it can be assumed that the pressure varies linearly with bed depth.

qL is the

s u p e r f i c i a l velocity (i.e. volumetric flux). Note that qL = − K D

 d 2  ΔP ΔP  → −   η Δz  18φ  η Δz

as φ → 0

[2-20]

which is relevant for both dilute suspensions and, by implication, situations in which wall effects may be neglected [442]. Hence [442]

v v uncorrected

= 1 / я =

6 − 9φ1 / 3 + 9φ 5 / 3 − 6φ 2 ΔP 5/ 3 6 + 4φ ΔPuncorrected

[2-21]

where φ is the solidosity *, and я is the drag force correction factor. For settling, where the pressure drop is unaffected by the interaction of the spheres, ΔP = ΔPuncorrected [442]. For flow through porous media, where the superficial fluid velocity is held constant, v = vuncorrected [442].

2▪4

Dewatering analysis Sludge dewatering remains perhaps the most difficult

and

engineering

elusive challenges.

of

the One

environmental of

sludge

dewatering’s most bothersome aspects is that there seems to be no accepted means to evaluate [dewaterability]. — VESILIND (1988) [1076]

Understanding dewatering allows the design of more efficient or more effective dewatering operations — including construction of the equipment as well as addition of chemical additives such as flocculants — and can also be used for the optimisation of existing operations [628, 745]. To be effective, such predictions often need to be applied to large-scale

*

The solidosity will generally neglect particle porosity for sedimentation, whereas the distinction becomes harder to make for fluid flow through a porous bed.

76



operations from small-scale tests. In such cases the more fundamental, less empirical models are generally more reliable.

In general, dewatering depends upon both kinetic (i.e. rate) and equilibrium parameters. The rate of dewatering describes quantitatively the rapidity with which solids and liquid are separated from each other. The extent of a dewatering operation as described here implies that an equilibrium has been reached, in which the resistance has asymptotically risen to exactly counter the ‘driving force’ of dewatering (which is often due to a pressure and/or density difference) and separation of solids and liquid has therefore ceased. That is, the extent describes a s t a t i c equilibrium. Clearly particles settling under gravity, whether in the free or hindered settling regime, reach an equilibrium at their so-called terminal settling velocity (as the drag force increases with velocity difference between phases). This is a d y n a m i c e q u i l i b r i u m , as the dewatering can be seen to be ongoing, and so no extent can be defined for these systems *. An extent of dewatering can only be defined for networked systems, in which the increasing resistance (decreasing permeability) is caused by the increase of solidosity in response to the applied pressure. This means that the gel point, which separates the two cases, also has special importance.

Flocculent aggregates typically have larger mass-to-size ratios than the constituent particles, so they settle faster [628]. However, they tend to form a bed in which the network is more open than for sedimentation of the primary particles, and so the extent of dewatering is lower [628]. This also suggests a greater permeability.

In all cases the shear history of a sludge can significantly affect its dewaterability [e.g. 628] (see §7).

Ad hoc methods attempting to standardise shear history by some pre-

characterisation agitation may allow comparison on a common basis, but that basis may not

*

A static equilibrium is impossible for these systems, as the resistance is due precisely to the relative motion.

2▪4 : Dewatering analysis

77

D. I. VERRELLI

be relevant to real plant conditions [cf. 117]. Conversely, p r o t e c t i n g a sludge from shear may also yield a material different to that on a real plant!

2▪4▪1

Empirical methods There is a strong feedback: we measure what we care about, and those measurements alter what we believe is important. — STERMAN (2002) [970]

Most empirical methods for characterising dewatering used in the drinking water sector are described in the U.S. Standard Methods [334]. Empirical methods have clearly been used for as long as equipment has been produced. The main drawbacks of empirical models are the lack of insight gained into the mechanisms at work [628], and the difficulty in scaling up or down [cf. 1006]. These empirical methods are often simplified, bench-scale versions of pilot tests, and in the same way are often unable to provide information about any other condition other than for the given unit operation at the given solidosity. Thus they are in no way material parameters. Just as with the less empirical tests, certain of these techniques are more relevant to particular unit operations. For example, the capillary suction time (CST, §2▪4▪1▪3) has been found to be more relevant to centrifuge dewatering, while the specific resistance to filtration (SRF, §2▪4▪1▪4) has been found to be more applicable to filter press dewatering;

some

techniques (e.g. belt press filtration) or materials (e.g. freeze–thaw conditioned sludges) defy valid characterisation by these methods [810]. The investigation of PAPAVASILOPOULOS & BACHE [815] suggests that each empirical characterisation technique predicts a different ‘optimum’ operating condition [117] [cf. 225]. Perhaps for the above reasons, and also due to a need for specialised equipment or for timeconsuming testing or analysis, [117]: experienced operatives often circumvent this problem by assessing the optimum dosage by ‘the look’ of a sludge.

78



It is a common view in industry that the only reliable way to design dewatering devices such as thickeners [435], centrifuges or filter presses, or to evaluate polymer performance, is to perform pilot-scale testing and make inferences from other full-scale installations [e.g. 315,

376, 797] [cf. 1006]. KNOCKE & WAKELAND [580] actually performed de facto compressive yield stress testing, but concluded that the limited (or indirect) practical applicability did not justify the time demanded (of order weeks). Yet for typical empirical settling tests in small stirred or static cylinders, DILLON [315] acknowledged: The actual clarities and sludge concentrations obtained should not be expected to be repeated at full scale.

The empirical methods provide no insight into the dewatering process, often are not transferrable between operations, and are not supported by theoretical arguments. Most of the methods have not been employed in the present work. Brief descriptions are provided in Table 2-1, with extended discussions of the more important parameters following.

Table 2-1: Conventional empirical methods. (a) Gel point:

• Synthesizing mixtures of increasing or decreasing φ0 and identifying the transition

between “gel” and “sediment” formation [1151]. An arbitrary definition of ‘gel’ was used [1151], and aggregation at different φ0 produces different structures [e.g. 590, 841]. • Basic analysis of batch settling solidosity profiles [see 257]. (b) Extent:

• Sludge volume — o Settleable solids.

Sedimentation in an IMHOFF cone with ad hoc gentle

agitation [334] [cf. 521]. Applicable only to dilute systems [334]. Equilibrium is not guaranteed.  Volumetric procedure — volume of sediment is reported [334].  Gravimetric procedure — straight subtraction of total suspended solids of


79

D. I. VERRELLI

the supernatant from that of the unsedimented sample [334].

Gives

practically no information about the extent of dewatering whatsoever. o Settled Sludge Volume.

Reports consolidated volume of sample in a

cylinder under gentle agitation at 5 to 15min intervals [334]. Equilibrium may not be attained. The indicated rate is not transferrable.  A M o d i f i e d S e t t l e d S l u d g e V o l u m e test has been described [334].

Although the set-up is only slightly different, results “are not currently considered comparable” [334]. o S l u d g e V o l u m e I n d e x ( S V I ) is the ratio of fractional Settled Sludge

Volume [L/L] at 30min to total suspended solids of the original sample [mg/L] [334]. Equilibrium may not be attained [310]. “Although SVI is not supported theoretically [FINCH & IVES (1950)], experience has shown it to be useful in routine process control.” [334] o A g g r e g a t e V o l u m e I n d e x ( A V I ) is the ratio of the ‘settled’ sludge volume

before and after d r y i n g [577, 821]. (CHEN et alia [246] define it rather as 1/φagg.) o C a k e S o l i d s C o n t e n t ( C S C ) was defined as the “solids content” of a filter

cake formed under arbitrarily specified vacuum filtration conditions [821]. • B o u n d w a t e r . Water associated with the sludge is classified according to how

readily it can be evaporated or frozen [cf. 121] or centrifuged off [580], indicating whether it is “free” or tightly “bound” to the solid phase [1055, 1077]. Results are often interpreted in the context of free, interstitial, vicinal, and (bound) water of hydration [1077] [cf. 113, 349, 538, 595, 877, 882, 1079, 1099].

Bound water “is [...] an

operationally-defined value” that when “measured via different techniques could be very different” [1137]. The classifications are arbitrary and application to dewatering unit operations is unclear. • Geomechanical tests. o A T T E R B E R G l i m i t t e s t . Essentially quantifies the solids concentration at a

number of arbitrary transitions (e.g. from “viscous fluid” to “plastic” material to “semisolid”) [281, 1012] [cf. 37, 282, 580, 1098] [see also 267, 946], which must broadly, implicitly correspond to certain values of the shear and compressive yield stresses [cf. 281, 850, 1012].

80



o Standard and modified P R O C T O R c o m p a c t i o n tests [267, 282, 880, 1014,

1098] [cf. 267, 946]. • ‘Compressibility’ has been given special definitions by various researchers. o C o m p r e s s i b i l i t y c o e f f i c i e n t . Many definitions —  Exponents in quasi-power-law empirical correlations of αm or αV (§2▪4▪4)

[881, 1033, 1037, 1040] [see also 867], φ [1032, 1037, 1040] and 1 / KD [1032,

1037, 1040] as functions of stress (pS or py) in filtration.

(Also called

“compactibility coefficients” [1036] [cf. 1032].) Only two are independent, as φ αV KD = 1 [see 1036, 1037]. o Various soil and geotechnical science parameters [see 1014], e.g.:  Co e f f i c i e n t o f c o m p r e s s i b i l i t y , av c.  Co e f f i c i e n t o f v o l u m e c o m p r e s s i b i l i t y , mv c. o See §2▪4▪1▪1 for details.

• S h e a r y i e l d s t r e s s e s , τy, have been directly reported [281] [cf. 390, 722, 880]. (c) Rate:

• ‘ Z o n e s e t t l i n g r a t e ’ or ‘ z o n e s e t t l i n g v e l o c i t y ’ ( Z S V ) — see §2▪4▪1▪2. • C a p i l l a r y S u c t i o n T i m e ( C S T ) and derivatives — see §2▪4▪1▪3. • T i m e - t o - F i l t e r ( T T F ) . The time taken to vacuum filter a given volume of filtrate

(50% of the original sample volume) through a BÜCHNER funnel with a paper support filter [334].

May be ‘normalised’ by dividing by the initial suspended solids

concentration [334]. A “simplification” of the SRF test [130, 282], which it is claimed to correlate with [334]; both are sensitive to the volume of sample assessed [282]. o Earlier versions (characterising “filterability”) measured the time until the cake

cracks [130, 390]. • S p e c i f i c R e s i s t a n c e t o F i l t r a t i o n ( S R F ) and adjusted SRF — see §2▪4▪1▪4. • Hydraulic conductivity.

Used in soil and geotechnical science [e.g. 1013];

identical to KD 1856 (see §2▪3▪1) [cf. 604, 605, 975, 976]. (d) Hybrid rate and extent parameters:

• C o e f f i c i e n t o f c o n s o l i d a t i o n , cv c. A ‘diffusivity-like’ term, used in soil and

geotechnical science [see 11, 37, 361, 771, 912, 946, 975, 976, 1013, 1014]; can be related


81

D. I. VERRELLI

to py(φ) and R(φ) using the parameter D (φ) (§2▪4▪5▪1(d)), as shown in §R2▪2▪2▪1(b). • “ C o m p a c t i b i l i t y ” and “super-compactibility” have been loosely associated * with

the compressibility coefficients (see above) relating to resistance variables αm, αV and 1 / KD [1034, 1036, 1037].

Compactibility has also been loosely associated with the

absolute and relative increases in φ under load [1036]. • Other ad hoc procedures — see §2▪4▪1▪5.

2▪4▪1▪1

Compressibility

In the present work the term ‘compressibility’ is used to indicate the magnitude of φ∞ in the range of py studied (generally 0 to 300kPa). This is similar to the usage of DE KRETSER et alii [605] and others. However, other authors often intend a different meaning with the term “compressibility”.

Isothermal compressibility The fundamental definition of compressibility employed in thermodynamics and the study of fluids is

βT ≡ −

1 ∂V V ∂p

,

[2-22]

T

which is the ‘isothermal compressibility’, βT, [87] (cf. equation 9-12).

An ‘adiabatic

compressibility’ can also be defined in the same form of equation. These parameters characterise e l a s t i c — i.e. r e v e r s i b l e — deformations.

Extension to particulate systems By analogy the conventional fluid compressibility can be extended to particulate systems:

*

82

The relationship is “significant” [1034], but the behaviours are “crudely” demarcated [1037].



βVS = −

∂ [(VL + VS ) / VS ] VS (VL + VS ) ∂pS V

= −φ =

∂ [1 / φ] ∂pS V

1 ∂φ φ ∂pS

S

[2-23] S

, VS

with variations due to T assumed negligible. This equation is quite general. However, unlike fluids, particulate systems manifest both e l a s t i c and p l a s t i c (i.e. irreversible) deformation (§2▪1▪4).

Ordinarily the plastic

contribution dominates the response, and so this is the focus of the discussion below. A ‘true’ elastic compressibility is discussed in §9▪4▪2. Strictly the compressibility is defined for isotropic normal stresses (i.e. pressure), while true uniaxial stress is characterised by YOUNG’s modulus of elasticity [758]. However, practical tests often involve a major axial stress and minor lateral stresses, especially where lateral deformation is constrained. Rigorous treatment of such cases is also deferred to §9▪4 (see also §3▪5▪3▪4(b)).

Provided the dewatering can be assumed to occur instantaneously and irreversibly:

β∗ =

1 dφ∞ . φ∞ dp y

[2-24]

For β∗ to be constant for a given sludge, the compressive yield stress would need to have the form: py = pref +

1  φ∞  , ln  β∗  φref 

[2-25]

in which the most obvious choice for the reference values is φref = φg and pref = 0. Empirical py(φ) correlations do n o t generally follow this form of variation (cf. §2▪4▪5▪1(a), p. 109), so β∗ evidently varies with φ∞: the sludge at two quite different solidosities would conventionally be considered as two different materials. Hence it is not meaningful to state that a given WTP sludge has a large or a small compressibility by this definition. For typical py(φ) curves further approximations can be considered: β∗ ≈

1 φ∞ − φg 1 Δφ∞ , ~ φ∞ Δp y φ∞ py

[2-26]


83

D. I. VERRELLI

given py(0) = 0. For WTP sludges often φ∞ [ φg, so that β∗ ~ 1 / py .

[2-27]

Coefficient of volume compressibility Various ‘compressibility’ parameters have been defined by TERZAGHI, PECK & MESRI [see 1014] inter alia for use in soil and geotechnical science. Of most interest are the following.

Table 2-2: Important ‘compressibility’ parameters of TERZAGHI, PECK & MESRI [see 1014].

Parameter

Definition a

‘Coefficient of compressibility’

av c ≡

‘Coefficient of compressibility with

 ∂(1 / φ)  av c t ≡    ∂t  σ axial

respect to time’ ‘Coefficient of compressibility with respect to vertical stress’ c ‘Coefficient of volume compressibility’ — D e f i n i t i o n 1 ‘Coefficient of volume

d(1 / φ) 1 d εaxial, con. = d σaxial con. φ0 d σaxial

 ∂(1 / φ)   av c σ ≡ −   ∂σaxial t mv∗ c ≡

‘Coefficient of vertical compression’ mV c ≡

b

d εaxial, con. d σaxial

Uniaxial

b

deformation Uniaxial deformation

con.

Uniaxial deformation

con.

= φ0

d(1 / φ) = φ0 av c d σaxial con.

d

Uniaxial deformation

φ ∗ mv c φ0

Uniaxial

Δ(1 / φ) Δ εaxial = φ0 Δ σaxial Δ σaxial

Uniaxial

mv c ≡ φ av c =

compressibility’ — D e f i n i t i o n 2

a

Conditions

deformation

stress

The subscripts are: “v” for volume (or vertical); “c” for compression; “con.” for laterally confined. Also defined as a secant. The strict distinction between a finite and an infinitesimal difference, and thus

between a derivative and a secant, is routinely disregarded [e.g. 946, 1014] [see also 771, 850] — probably because of linearity assumptions [cf. 1011, 1013]. c

It is taken as understood in the present work that this refers to the “effective” stress, i.e. that additional to

hydrostatic stress (liquid-phase pressure). d

Defined as a secant, like mV c, but here assumed equal to the derivative for generality and compatibility with av c.

ε denotes uniaxial (linear) strain; σ denotes stress, and is equivalent to a (local) ‒pS.

84



(

av c t represents consolidation due to creep (§R2▪2), while av c σ −

d σ axial dt

) represents dewatering

in the absence of creep [1014] [cf. 238, 933].

From Table 2-2 it is evident that mv c represents a (confined) compressibility [see also 912]. It can be simply obtained from py(φ) — see §R2▪2▪2▪1(b). In general mv (or m∗v ) has been called the ‘coefficient of volume change’ [912], with mv c (or m∗v c ) then called the ‘coefficient of volume decrease’ [e.g. 18, 1013] [cf. 320]. Its reciprocal has been called the ‘constrained modulus’ [267, 850] (or ‘œdometric modulus’ [361] or ‘bulk modulus’ [320]) of compression, or the ‘one-dimensional stiffness modulus’ [850]. The conflicting definitions of the ‘coefficient of volume compressibility’ (in the source text [1014] mv c is used for both, and they are taken as identical) are discussed further in §R2▪2▪2▪1(b).

Reciprocal ‘confined elastic modulus’ Other ‘compressibility coefficients’, ai, have been defined as compact parameters for primary, secondary and tertiary consolidation in the macrorheological model of SHIRATO et alii [933] (§R2▪3▪2) [see 238]. For primary consolidation: aE = −

d(1 / φ) 1 = , dpS con. φ E1

[2-28]

E1 is the spring elastic modulus (i.e. stiffness) to model the cake formation stage, and tc is the time at which cake formation ends and cake consolidation (or compression) begins [238] [cf. 765]. Equation 2-28 can be rewritten d(1 / φ) 1 = −φ . E1 dpS con.

[2-29]

and comparison with the foregoing shows that 1 / E1 is a “compressibility” for confined consolidation (it is strictly n o t a YOUNG’s modulus).


85

D. I. VERRELLI

Compressibility coefficients At best the exponents relating 1 ‒ φ or φ to pS can be shown to be directly p r o p o r t i o n a l to the volume compressibility, differing by some (variable) factor.

The exponents in

correlations between ‘pressure’ and the rate parameters are tenuously associated with ‘compressibility’ insofar as those rate parameters are functions of φ.

2▪4▪1▪2

Zone settling rate

2▪4▪1▪2(a)

Definition of zone settling

The concept of ‘zone settling’ probably gained popularity through the description by COE & CLEVENGER [273] of four zones in a (continuous) thickener corresponding to different materials or dewatering regimes [cf. 42, 298]. These are [133, 273]: 1.

Clear water (supernatant), with φ ≈ 0

2.

Material settling at uniform rate (hindered settling), with φ = φ0

3.

Transition settling, with φ0 < φ < φg

4.

“Compression”, where the material has formed a network, with φg ≤ φ ≤ φ :z=0

The implication is that the settling columns exhibit discontinuities in solidosity that bound the various zones [cf. 205, 274, 363, 390, 483].

The main feature of this settling mode is that φ0 is of such a magnitude that particulates in the suspension settle e n m a s s e at the same velocity due to particle interactions [293, 363, 390, 1034, 1035] [cf. 376].

The precise values of φ0 will depend upon the form of the

particulates — e.g. solid spheres or flocculent aggregates [293, 376] — but the mode should be attainable for most materials [cf. 205, 274, 334]. A lower φ0 would lead to free settling, in which heavier, larger, or more compact particles could quickly sediment while a haze of light fines remained [376, 1034, 1035] [cf. 298]. (For a true monodisperse suspension zone settling is more likely, but not guaranteed.) A higher φ0 would lead to network consolidation, with non-uniform (generally decreasing) rate of fall of the interface with the supernatant, or perhaps to channelling [830].

86



Zone settling is sometimes used to describe the entire pattern of settling in this mode — i.e. the evolution and disappearance of the listed zones over time, and especially their fall (and build-up) [246, 483, 560, 1035] [cf. 42]. However sometimes the phrase is used essentially as a synonym for ‘hindered settling’ [431, 864], in which case ‘zone settling velocity’ refers only to the initial, uniform, constant settling rate of the suspension at φ0. (TILLER and co-workers [1034, 1035] extend the definition to encompass also consolidation or compression — uniform for all particulates — regardless of rate decrease.)

2▪4▪1▪2(b)

Measurement

The U.S. Standard Methods [334] describe a technique to measure a hindered settling rate. Their recommended apparatus consists of a graduated cylinder of height at least 1m and width (at least) 0.1m [334] — at the upper limit of ‘benchtop’ scale. The cylinder is to be equipped with a stirring mechanism to agitate at least the material at the walls of the cylinder (with a peripheral speed of ≤ 0.01m/s) [334].

The sample is of known solids

concentration (as total suspended solids). The height of the interface is monitored at about 1min intervals until a constant settling rate is attained [334]. It is assumed that this settling rate corresponds to the “zone settling rate”.

The agitation seems to run counter to the characterisation of the settling regime as “quiescent” [334]. It is agreed that high agitation speeds “may interfere with the thickening process and yield inaccurate results” [334], yet it is not clear what the threshold rate would be. The picture is further confused by the insistence upon agglomeration of the suspended solids and formation of “a coarse structure with visible fluid channels, within a few minutes” [334]: “If [the] suspension does not agglomerate, [then the] test is invalid [...].” Confidence in the method is further eroded by statements such as the following [334] [The described methodology should minimise experimental artefacts.] However, even with careful testing suspensions often may behave erratically. Unpredictable behaviour increases for sludges with high solids concentrations and poor settling characteristics [...].


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D. I. VERRELLI

Measurements of “zone settling velocity” (ZSV) under other conditions, e.g. without agitation, are also possible [236, 246, 247, 507, 528, 1146].

2▪4▪1▪3

Capillary suction time (CST) and derivatives

Capillary suction time (CST) is a measure of the readiness with which a sludge sample ‘releases’ its water. The sample is placed in a reservoir above a sheet of chromatography paper *, and the time taken for the liquid to be drawn a certain radial distance † by capillary action is measured [130, 334, 1076]. The test was originally developed by BASKERVILLE & GALE [130], who estimated the suction pressure as of order 1kPa ‡. Similar techniques are used in other fields, such as food science [1045]. Much of the appeal of the method lies in its speed, simplicity [130], and need for only small sample volumes [e.g. 788, 789]. It is noted that “comparison of CST data from different sludge samples [...] cannot be made with confidence unless suspended solids concentrations are comparable” [334]. Method error is of order ±10% [334] [cf. 130].

NOVAK & BANDAK [789] noted: [...] values of CST cannot be directly related to the performance of dewatering equipment [...].

Prediction based on CST measurement has been widely reported to overestimate the amount of polymer needed for effective sludge conditioning [810]. On the other hand, BACHE et alia [113] found that CST (and SRF — §2▪4▪1▪4) predicts an optimum polymer dose below the saturation level.

VESILIND [1076] proposed a normalised ‘filterability coefficient’, χ [kg2/s2.m4], based on DARCY’s law (§2▪3▪1) [1080].

χ is inversely proportional to the CST, and purportedly

*

If properties vary between lots, then distilled water flowrates can be used as baselines for correction [334].

†

The U.S. Standard Methods [334] stipulate flow between references at 15.9 and 22.2mm from the centre of the reservoir (the reservoir being of inner radius 9mm and height 25mm) [cf. 130].

‡

An early suggestion to utilise multiple paper types with different capillary suction strengths to better characterise sample ‘compressibility’ (cf. §2▪4▪1▪1) [130] does not appear to have been pursued.

88



independent of CST device and insensitive to small changes in solids concentration [821, 1079]. This permits at least approximate comparison of results at different solidosities or from different devices. It is defined [1080]:

 χ =  Do 2 − Di 2 

(



η C ) πA δp   CST , 

 

L



[2-30]

in which Do and Di are the outer and inner sensor diameters (CST is thus the time to travel (Do ‒ Di) / 2) [m], δ is the filter paper thickness [m], A is the cell area [m2], p is the “capillary suction force” [m], ηL is the filtrate viscosity [Pa.s], and C is the “solids concentration” [g/L]. Note that the term in brackets will normally be constant for a given device [1076, 1080]. The capillary suction force can be estimated by measuring the liquid rise in a vertically-hung strip of paper above a reservoir of water [1076, 1081]. The reliance upon DARCY’s law implies that no allowance is made for any cake compression. Also, the precise f o r m of dependence on the ‘equipment parameters’ such as p has not been verified [cf. 1076]. The purported linear correlation between viscosity and CST [cf. 1076] has not been adequately demonstrated, given that p must also vary with temperature. Finally, the premise of constant χ for a given material with various values of φ0 was not conclusively demonstrated — this premise could only hold for incompressible particulates. However deficient the theory on a fundamental level, these approximate corrections are useful on a practical level. 1/χ was shown to correlate reasonably well with SRF (§2▪4▪1▪4), albeit with one outlier; such correlation had not been observed between CST and SRF [1076] [cf. 130, 789]. The greater experimental ease of CST measurement over SRF measurement [1076] and small additional effort required to compute 1/χ suggests that 1/χ could be used as a convenient surrogate for SRF.

Although the filterability coefficient ‘normalises’ the CST value, the experimental procedure is identical to that for CST measurement [1080]. For both of these measures problems can arise when the permeability of the sample is very high, so that it is essentially free-draining, such as for freeze–thaw conditioned sludges or ‘super flocculated’ sludges [1080]. The ratelimiting step then becomes the movement of water through the filter paper, rather than release from the sample [1080]. In other words, the resolution of the CST (or 1/χ) is poor


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D. I. VERRELLI

when the permeability is very high, and such samples cannot be differentiated from each other or from a sample of pure water [1080]. To accommodate highly permeable samples, VESILIND & ÖRMECI [1080] proposed a modified CST procedure, in which once loaded into the cell the sample is first allowed to drain to waste under gravity through a 530μm mesh assembly. The capillary forces exerted by the mesh are negligible. After a few seconds or minutes, when dripping ceases, the mesh assembly is slid off so that the drained sample directly contacts the filter paper, as in the usual CST procedure [1080]. A disadvantage of the test is that precision and reproducibility may be slightly poorer than the conventional CST test, due to the incorporation of additional steps [1080]. It may be possible to further improve the procedure [1080].

2▪4▪1▪4

Specific resistance to filtration (SRF)

The specific resistance to filtration (SRF), αSRF [m/kg], of a unit mass of sludge per unit area of filter is a kinetic parameter. and may be obtained from [e.g. 282, 402, 598] α SRF =

2 Δ p d(t /V ) , φ 0 ρ S η L dV

[2-31a]

or, equivalently, αSRF =

dt Δp , φ0 ρS ηL V dV

[2-31b]

in which Δp is the applied pressure, φ0 is the bulk or initial solidosity, and ηL is the liquid viscosity *. This concept goes back to the work of RUTH and CARMAN in the 1930’s [402, 416, 580, 598, 881, 882, 883, 884, 934, 1039]. However the practical industrial test procedure is credited [598, 1076, 1080] to COACKLEY & JONES (1956) [271].

*

Note that for filtration with V :t=0 = 0 [1059] (see §2▪4▪4, p. 100) — but not generally — A2 d(t/V )/dV = d(t/V )/dV = dt/d(V 2) = (1 / 2V ) dt/d(V) .

90



While the cake resistance would normally be assumed to be independent of the solids concentration in the bulk, researchers recognised before 1970 that actually an inverse relationship exists [402]. CARMAN found that αSRF also depended upon the pressure according to a power-law relation [402]. This is consistent with equation 2-135, given that often R is able to be fit empirically as a power-law function of Δp * in the domain corresponding to filtration.

OGILVIE [797] mentions 1012m/kg as the upper limit to achieve satisfactory dewatering. FU & DEMPSEY [382] gave 1 × 1013 to 5 × 1014m/kg as a typical range for the SRF of “hydrous metal oxides” found in raw waters.

SRF is said to give “large errors [...] when dealing with sludge of low solid content” [810]. SRF also apparently does not yield information suitable for scaling up industrial processes [1076].

2▪4▪1▪4(a)

Adjusted SRF

ZHAO, PAPAVASILOPOULOS & BACHE (1998) proposed an adjustment to the SRF measurement with the intention of removing the effect of filter-pore blocking, which occurs at high (‘excess’) polymer doses † [117]. The method derives from a traditional DARCY equation [117, 293] (cf. equation 2-40)

Δp dV = d t ηL (α m C V + rmembrane )

[2-32]

in which C is the mass of dry solids per volume of filtrate, rmembrane is a resistance due to the membrane (and drainage system), and the remaining symbols have their usual meanings. The novel approach suggested estimating rmembrane by performing some supporting experiments in parallel with supernatant taken from samples settled for 30min, such that

*

More usually py is expressed as a power-law function of φ (in the domain corresponding to filtration); this can also be done for R, leading to the required outcome.

†

In fact the pore blockage mechanism was found to be a synergistic interaction of both the excess polymer and particulate material [117].


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D. I. VERRELLI

C ≈ 0 * [117]. The procedure involves fitting data to the empirical equation dV/dt ∝ 1/t to

determine the parameters in the function rmembrane = α′ e β′ V [117].

The SRF, αSRF, can be related to αm (by comparing equations 2-31 and 2-45a) according to:  φ αm =  1 − 0 φcake 

2▪4▪1▪5

  αSRF .  

[2-33]

Other ad hoc methods The great advantage of the model-based over the ad hoc approach [...] is that at any given time we know what we are doing. — BOX (1979) [185]

While some researchers criticise empirical methods such as SRF and CST as expedient tests lacking a proper theoretical grounding, there are also industrial practitioners and others who lament those same empirical methods for their difficulty, slowness, and dissimilarity to dewatering in industrial devices [e.g. 797]! While the former group work to develop more rigorous characterisation protocols, the latter propose yet simpler and faster tests which they claim to possess practically the same — or more — relevance to industrial operations.

OGILVIE [797] describes a very simple procedure that is used as an alternative to the CST (or TTF):

*

1.

Dose (say) 500mL of thickened sludge with the desired conditioner.

2.

Transfer the sludge gently back and forth between two beakers (say) 10 times.

3.

Tip some of the material into a “funnel” constructed of filter cloth †.

4.

Record the time taken for (say) 50, 75, 100, ... mL to pass through.

Presumably the intention is that some small amount of particulates would remain in the supernatant — enough to block the pores (see preceding footnote), but not enough to form a cake of significant resistance — otherwise the resistance would be estimated by adding the polymer to pre-filtered water, say.

†

92

This element bears a resemblance to the standard ‘paint filter test’ [797].



BACHE & ZHAO (2001) [117] presented a convenient method dubbed “CML30”, a mnemonic for the procedure of observing the extent of sample settling in 100 (“C”) millilitre (mL) measuring cylinders after 30 minutes. This could be reported as a bed moisture content after 30min settling, however comparison of bed heights of tests run in parallel (fixed initial solids) gives the same result at a glance [117]. To its advantage are its speed, simplicity (both in equipment and calculation), and agreement with CST and adjusted SRF analysis [117]. To its disadvantage are its narrow application to “a particular type of alum sludge” which relies on the “coincidence” of a “physicochemical quirk” that the method yields reasonable predictions for the 100mL plastic cylinder and 30min duration specified — but not for other cylinder sizes (i.e. larger diameters with reduced ‘wall effects’) or other (longer) settling times [117]. The measurement is sensitive to any latency period (§9▪1), due to the short observation time [cf. 1145]. See also §9▪2▪1▪1.

2▪4▪2

Early dewatering theory

Scientific description of dewatering operations first began to be published around 100 years ago. An overview of milestones in early development of the theory is presented in §S1.

2▪4▪3

Kinematical batch settling theory of KYNCH

While LIGHTHILL & WHITHAM [663, 664] wrote the first general treatment of the kinematic wave theory (see §S2), aspects of it had been applied before this. In particular, KYNCH (1952) [617] described dewatering (specifically, sedimentation) based upon the concept of kinematically propagating concentration waves [274]. According to this model the suspension is treated as a continuum, called an “ideal suspension” [274, 628]. It is assumed that the settling velocity is a function of the local solidosity, φ, only * [274, 363]. The system is described by the continuity equation of the solid phase:

*

Variation with position, z, due to (say) varying cross-sectional area can be contemplated as a simple extension [see also 362].


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D. I. VERRELLI

∂φ ∂qS + = 0 , 0 ≤ z ≤ L, t > 0 ∂t ∂z

[2-34]

in which qS =qS(φ) = φ.u is the “solid flux–density function” satisfying the conditions qS(0) = qS(φmax) = 0 qS(φ) < 0 for 0 < φ < φmax with u being the solid-phase velocity [205, 274]. It is further commonly assumed that qS′′ > 0 [205]. Equation 2-34 is a first-order quasilinear hyperbolic partial differential equation [206, 218]. In comparison with a comprehensive force balance, KYNCH’s model neglects the effects of inertia and solid phase stress [363]. Hence both qS and u correspond to the physical situation when there are no solid phase stress gradients (except on reaching φmax), i.e. for i n c o m p r e s s i b l e sediments [cf. 233, 363]. The consequence of neglecting inertia is that it is assumed that particulates can accelerate and decelerate instantaneously in response to the ‘extrinsic’ forces (hydrodynamics, gravity, solid phase stress) without compensation for their own ‘intrinsic’ change in momentum [e.g. 923].

At the d i s c o n t i n u i t i e s which appear in solutions of the above scalar conservation law a jump condition is used: c o m m o n l y that of RANKINE–HUGONIOT, viz. c = ΔjqS / Δjφ ,

[2-35]

where c is the speed of propagation of the discontinuity and Δj here represents “the jump in a property from one side of a discontinuity to the other” [203, 205, 206, 218, 274, 617, 664, 923]. (Traditionally the m e c h a n i s m of formation and maintenance of discontinuities has been disregarded in the analysis [617, 923].

Cf. §2▪4▪3▪1.)

Alternatively, shock-capturing

(approximate) numerical schemes can be used [202]. Following BUSTOS, CONCHA, BÜRGER and co-workers [274] an entropy (weak) solution criterion — c o m m o n l y that of OLEĬNIK — is imposed to ensure a unique, physically-relevant solution can be found [202, 205, 206, 218]. In these solutions zones of constant concentration are separated by (compressive) shocks, rarefaction waves, or combinations of these [202, 205, 274] [cf. 101].

The shocks and

rarefaction waves are related to points of inflexion in the flux density functions, qS(φ) [205, 274].

94



Application to the settling of a suspension with initially uniform φ0 showed that the h(t) profile would commence with a linear section (i.e. constant interface settling rate), but at some time would slow in a curved region corresponding to the influence of a rarefaction wave (or ‘fan’), terminating in a transition to the equilibrium state [617]. The theory assumes a “continuous but extremely rapid” increase of φ to some “maximum” at the base of the cylinder, whereupon qS → 0 [617]. Nowhere is it considered that this maximum is itself a function of the self-weight of the overlying network — reasonable for (say) hard spheres, but a poor assumption for ‘deformable’ particulates such as aggregates (cf. §2▪4▪5▪1(a)). Still, KYNCH [617] did recognise that as φ → φmax, the dewatering became “analogous” to the problem of liquid flow through a porous solid medium.

Attempts to apply KYNCH’s theory to compressible systems * (e.g. containing flocculent particles), such as those by FITCH (1983) [cf. 362] and FONT (1988), were not successful [274, cf. 281].

2▪4▪3▪1

Shock thickness

DIXON (1978) [317] recognised through mathematical analysis that the presence of d i s c o n t i n u i t i e s in solidosity and velocity implied local expenditure of energy at an infinite rate. Thus g r a d i e n t s in both variables must exist through the settling column [317, cf. 1057]. (Following the LAGRANGian material co-ordinate approach, discontinuities are permitted only where there is no transport of particles across them, such as at the suspension–supernatant interface.) DIXON [317] suggested that this could be explained physically by the existence of a r e s i s t a n c e to dewatering at a l l solidosities, such as that arising due to permeation of fluid through either a n e t w o r k e d bed or an u n n e t w o r k e d ‘zone’. Thus, even for a model

*

KYNCH’s theory may be applied to systems which have the potential to undergo consolidation when in the fully-networked state (φ ≥ φg), provided that only the un-networked state (φ < φg) is actually modelled [274].


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D. I. VERRELLI

system of incompressible spheres the settling particles would decelerate rapidly in the vicinity of the sedimented bed due to the sudden increase in drag locally [see 101, 1057]. In many cases the gradients would be predominantly contained in a very thin layer above the bed, so that in practice negligible error would result from treating it as a discontinuity [317].

An alternative approach to equation 2-35 presented by AUZERAIS, JACKSON & RUSSEL [101] relies on consistent balances over the shock and outside the shock. An interesting outcome of their [101] analysis is the finding that real shocks in the suspension region generally have non-zero ‘thickness’. The thin, non-zero width of real shocks in the suspension region implicitly resolves the inconsistencies identified by DIXON on a practical level [see 101].

2▪4▪3▪2

Polydisperse suspensions and instability

An extension of KYNCH’s kinematic theory was presented by BATCHELOR & JANSE VAN RENSBURG [131] to account for particle polydispersity.

Although settling (or creaming)

would be the dominant effect, giving particle motion parallel to the vertical axis, contemplation of (transient) channelling and other flux-plane heterogeneity suggests a threedimensional vectorial expression, namely [131]: ∂φi = − ∇ ⋅ [φi (w + ui )] + ∂t

 [∇ ⋅ (D 2

j =1

ij

)]

⋅ ∇φ j , i = 1, 2 ,

[2-36a]

for two distinct particle species; w is the local mean velocity of the mixture relative to the container, and ui is a mean velocity of the i-particles relative to local zero-volume-flux axes. The diffusivity tensor (or matrix) D ij is determined by the sum of velocity fluctuations arising from BROWNian motion and hydrodynamic interaction with neighbouring particles; the latter contribution dominates for moderately large particles (above about 1μm) [131]. While diffusion normally has a stabilising (or damping) effect on disturbances, hydrodynamically-driven diffusion can have a destabilising effect on the system for certain

96



permutations of D ij [131]. When the component solidosities have ‘small’ spatial gradients *, then diffusion can be ignored, thus [131]:

∂φi ≈ − ∇ ⋅ [φi (w + ui )] , i = 1, 2 . ∂t

[2-36b]

Omission of diffusion effects is almost an essential simplification, given the current lack of knowledge of the relative magnitudes of the components of D ij [131].

By linearising equation 2-36b, conclusions may be drawn regarding the response of a given bidisperse particle system to a small perturbation or disturbance [131]. A key result is the condition for i n s t a b i l i t y of this linearised system, namely [131] [cf. 204]: 2

 ∂(φ1 u1 ) ∂(φ2 u2 )  ∂(φ1 u1 ) ∂(φ2 u2 )  +4 ⋅ < 0, I =  −  ∂ φ2 ∂ φ1 ∂ φ ∂ φ 1 2  

[2-37a]

where the ui = ui are oriented vertically down, and the derivatives are evaluated at the initial (undisturbed) condition. It was implicitly assumed that φ1 and φ2 do not depend on each other (under the pre-disturbance conditions), in which case [131]: 2

 ∂(φ1 u1 ) ∂(φ2 u2 )  ∂ u1 ∂ u2  + 4 φ1 φ2 ⋅ < 0. I =  −  ∂ φ2 ∂ φ1 ∂ φ2   ∂ φ1

[2-37b]

This predicts that disturbances will not persist if either φ1 → 0 or φ2 → 0 — i.e. approaching a monodispersion [131]. Stability is also predicted when the particles have very different diameters, in which case the suspension of small particles is practically a continuum with respect to the larger particles [131]; motion of the small spheres is affected by the presence of the larger particle in their immediate vicinity, but not in an unstable sense. Condition 2-37b can in turn be crudely simplified to ∂ u1 ∂ u2 ⋅ /0 , ∂ φ2 ∂ φ1

[2-37c]

i.e. instability requires the interactions to be strong and oppositely-signed [131]. Condition 2-37c clearly will not be satisfied if the particles are sufficiently similar — again approaching a monodispersion [131].

*

More precisely, variation in the φi is only significant on lengthscales much larger than the particle diameter — provided the total solidosity is not too high, and disturbances are oriented horizontally [cf. 131].


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D. I. VERRELLI

For particles that are both heavier than the liquid phase, the derivatives tend to be likesigned, predicting stability, except where the (buoyant) particle densities are very different [131] [see also 204]. It is worth emphasising the foundations of this powerful analysis technique [as in 131]: The explanation involves only the movement of particles through the fluid due to gravity and hydrodynamic interaction of the particles, the same two processes that alone are believed to be at work in the dispersions observed in the laboratory.

The above predictions do n o t allow for h i g h t o t a l s o l i d o s i t i e s and long-range correlations [131]. As solidosities increase, approaching “maximum packing” — either ‘close packing’ or φ∞ — two sedimenting particle species are wont to settle together at a common rate (cf. ‘zone settling’, §2▪4▪1▪2) intermediate to their individual tendencies as pure suspensions [131]. This means that the presence of a second component has a retarding effect on one species, but an accelerating effect on the other, so that condition 2-37c c a n be satisfied, and instability results [131]. Instability has been experimentally observed in systems where both particle species are denser than the liquid phase [131]. Despite the above predictions regarding the ‘absolute’ stability of monodispersions, macroscopic structures can develop in such systems, e.g. if the disturbances are formed on scales on the order of the particle diameter [131].

Empirically, the characteristic lengthscale, or wavelength, of the fastest-growing disturbances at intermediate total solidosities is about 13 particle diameters [131].

FITCH [362, 363] discussed related instabilities that would arise in thickening, settling, and fluidisation. Several other researchers have also investigated settling of polydisperse suspensions [see

202, 204]. In particular, BÜRGER et alii [202] extended the above analysis to show that model instability can be related to the ellipticity (or lack of hyperbolicity) of the system of conservation laws, which for bidisperse systems manifests as a type change from hyperbolic to elliptic (cf. §2▪4▪5▪3(b)). (They [202] also emphasise that model instability does not always reflect instability in the physical system; furthermore, model instability can be ‘damped’ by 98



‘numerical diffusion’ arising from the implementation scheme.) Non-linearities can expand the domain of instability beyond the type-change boundary [204].

2▪4▪3▪3

Influence of BROWNian motion

A PÉCLET number for settling (cf. §R1▪5▪6▪4(a)), Pésett, that indicates the magnitude (or rate) of gravitational effects relative to BROWNian motion effects can be defined, viz.:

Pé sett =

π d3 Δ ρ g l , 6 kB T

[2-38]

in which l is a characteristic length [101, 102, 211, 795, 878]. (The equivalent parameter for centrifugation can be obtained by substituting the centrifugal acceleration for g [1057]. Modification is necessary to account for fractal structure [cf. 841].) In the limit * Pésett → ∞ hydrodynamic forces dominate and the settling of hard spheres is modelled exactly by KYNCH’s solution [878]. For finite Pésett the settling of a suspension of hard spheres will deviate from kinematic wave behaviour, with the thermal diffusion causing a ‘blurring’ of the interfaces between different settling zones [101, 878] [cf. 257]. Several specifications of l in equation 2-38 have been made:

• AUZERAIS, RUSSEL, and colleagues [101, 102, 878] specified l ≡ h0. However, the implied linear dependence of Pésett upon h0 is not justified (e.g. the sedimenting of particles in a still lake will not be affected by the local height of the liquid column).

• BUSCALL [211] called that specification a “rescaled” PÉCLET number, and inferred that fundamentally l ≡ d / 2 — although in settling applications, at least, this may rather overstate the influence of d upon the settling behaviour. AUZERAIS, JACKSON & RUSSEL [101] called this the “microscopic” or “particle” PÉCLET number, a constraint on the validity of modern continuum models of sedimentation to settling of dispersed (or weakly flocculated) suspensions. This was also used by ODRIOZOLA et alia [795].

• AUZERAIS et alii [101] set l = d2 / 4 h0 for direct (fundamental) comparison of stresses arising from bulk viscosity and network interparticle forces. In no case is it clear how d should be interpreted for fractal aggregates.

*

Although for coagulation the criterion for hydrodynamic control was stated as Pé [ 1, in settling it was found that the influence of BROWNian motion was noticeable even at Pésett = O(105) [878] (for l ≡ h0).


99

D. I. VERRELLI

Directions to a stochastic modelling framework are presented in §2▪4▪8.

2▪4▪4

Permeation theories of settling and filtration

A modified version of the equation developed by DARCY was used by SHIRATO et alii and other researchers to analyse batch and continuous s e t t l i n g [1035]: dpS = dz

φ Δρ g  Buoyed weight

η Δu , + (1 − φ) KD 

[2-39]

Drag on solids

in which KD is DARCY’s permeability and the ‘nett’ density and speed (solid minus liquid) are used for brevity [cf. 140].

Following RUTH et alia [881, 883, 884], the work of SHIRATO, TILLER, and others also led to development of a model for f i l t r a t i o n which attributed the dewatering resistance to contributions from passage of the fluid through the membrane and through the (growing) cake [628]. The membrane was assigned a hydraulic resistance, rmembrane [m‒1], while the cake was assigned a ‘specific’ resistance *, α [628, 881, 884, 1039]. Various related forms of specific resistance can be used, which have the general form [117, 271, 293, 416, 867, 881, 983, 1059,

1103]: Δp dV dh = = − , dt ηL (rcake + rmembrane ) dt

[2-40a]

with

rcake

= α {amount of cake} ,

[2-40b]

where V is the filtrate volume (V) per unit cross-sectional area (A), and h is the piston height. Comparison with equation 2-14 shows that 1 / rcake and 1 / rmembrane represent permeabilities (KD) of the relevant material per unit length. (The resistances in series can be summed.)

*

Although it was recognised that specific resistance could v a r y l o c a l l y , RUTH, MONTILLON & MONTONNA [884] found empirically that the a v e r a g e over the cake ( f o r m i n g at constant pressure) was p r a c t i c a l l y c o n s t a n t with time.

The formulation of the average was later refined by TILLER &

SHIRATO [1039] to account explicitly for varying average cake solidosity with time and varying liquid flux over the height of the cake.

100



In engineering practice it is common to use a resistance, αm [m/kg], based on the solid-phase mass in the bed per unit filter area, such that [255, 271, 414, 416, 628, 631, 881, 934, 1033, 1039,

1063, 1103] rcake

= αm {mS / A} = αm { ρS φ

cake

z cake }

,

[2-41a]

where zcake is the cake thickness (equivalent to the total cake volume per unit membrane area) and CφDcake is the average cake solidosity. (Note: ‘cake’ and ‘bed’ are used interchangeably here.) A form closer to the volume-focussed theories of modern permeation theory uses a resistance, αh [m‒2], based directly on the cake thickness [414, 867, 1059]

rcake

= α h { z cake } .

[2-41b]

Finally, referring the resistance to the volume of solid-phase component in the bed per membrane area, using αV [m‒2], retains the features of the previous two forms [271, 983, 1034,

1036, 1037, 1040, 1063]:

rcake

= αV { φ

cake

zcake } .

[2-41c]

GRACE [417] reported that for many systems rmembrane ~ 0.1 αm.

Although less-permeable

materials may be expected to dominate the overall resistance to a greater extent, GRACE [417] reasoned that such materials tended to be filtered by finer media, so that effectively rmembrane increased in rough proportionality to αm. (For highly compressible materials this may be easier to accept if it is recalled that in practice rmembrane will include any existing f o u l i n g .) More precise estimates of rmembrane are required for thin cakes [417].

DARCY’s equation was first formulated for permeation through a fixed bed of porous material. In adapting the equations for filtration, it is necessary to account for growth of the bed, which is conventionally related to the specific filtrate volume, V [m]. In this case zcake can be obtained by combining overall and solid-phase volume balances [1059]:

z cake =

φ0 V , φ cake − φ0

[2-42]

so that e.g.


101

D. I. VERRELLI

dV = dt

Δp    ηL αV V    

 1 1  −  φ0 φ cake 

   

   r +  membrane   

−1

.

[2-43]

As a first approximation it is assumed that the cake solidosity is uniform, φcake ≈ CφDcake, and αV is constant [cf. 1039]. Integration of equation 2-43 with initial condition (t0, V 0) then yields [628, 631, 1059]  1 (t − t 0 ) η  1 ≈ L  12 αV (V + V0 )  − (V −V0 ) Δp   φ0 φcake  d(t / V ) ηL α V  ≈ dV 2 Δp

 1 1  φ − φ cake  0

   

   

−1

 + rmembrane  , 

[2-44]

−1

≈ constant ,

iff (t0, V 0) = (0, 0),

[2-45a]

given that n o c o n s o l i d a t i o n occurs (i.e. the piston is still in contact with material at φ0) *. Alternatively, equation 2-43 can also be rewritten (without integrating): dV 2 = dt

2 Δp   1 1 ηL α V  −   φ0 φcake

   

−1

 + rmembrane / V  

,

[2-46]

yielding V →∞ lim

η α dt = L V dV 2 2 Δp

 1 1  φ − φ cake  0

   

−1

≈ constant ,

[2-45b]

essentially as before [cf. 1059]. The key d i s a d v a n t a g e s of equations 2-45a and 2-45b are [cf. 1059, 1060]: • equation 2-45a has not been derived exactly for a varying cake profile; • equation 2-45a only holds when no prior filtration has occurred (or asymptotically for t0 / V and V 0 / V ), and so is not helpful in stepped-pressure filtration experiments †; • equation 2-45a only holds when no time elapses before filtration occurs, and so it is invalid when the set pressure is not reached quickly; and

*

Understanding of this cake-formation stage is more complete than of the consolidation stage [631].

†

The observed discrepancy may be less than this suggests [see e.g. 764], as the ‘error’ terms in t0 and V 02 have opposite signs, and so will at least partially cancel.

102



• equation 2-45b is affected by membrane resistance, so early-time data cannot be used (unless corrected). On balance equation 2 - 4 5 b is more useful, due primarily to its applicability in steppedpressure filtration [1059, 1060]. Despite the constraint that early-time data must be avoided due to possible membrane resistance, in practical work such data tends to be more ‘noisy’ and is best discarded in any case due to the time taken for the applied pressure, Δp, to be reached [cf. 1059]. The technique has been validated both experimentally and theoretically (by applying the model of LANDMAN & WHITE) [1059, 1064].

The above approach can be applied to produce a s i m p l i f i e d conceptual illustration of the progression of a stepped-pressure ‘permeability’ filtration run (§3▪5▪3▪1) [1059]: 1.

A cake of solidosity φ1 is formed at low pressure from the suspension at φ0.

2.

When the constant value of dt/dV 2 has been estimated, the pressure is increased.

3.

A compact layer of solidosity φ2 is formed within the existing cake of solidosity φ1.

4.

After a short time the entire cake has been compacted to φ2, and it continues to grow from suspension still at the initial solidosity, φ0.

5.

An estimate of constant dt/dV 2 is obtained for the second pressure, following which the pressure is increased again.

This procedure continues until all of the desired pressures have been applied, or until the cake has grown to reach the piston and no more suspension at the initial solidosity, φ0, remains.

These formulations have been found to provide good fits to (most) experimental data in the cake-formation stage [e.g. 631]. LANDMAN, WHITE & EBERL [631] outlined the disadvantages of this approach: There are considerable variations in the [model parameters for different materials]. The inherent weakness in this sort of modeling (its ability to summarize the data notwithstanding) is that no insight is gained into why [the parameters] behave in the observed way [...]. There is little predictive power [...] — to design an industrial filtration process [...] one reproduces in the laboratory the process itself. The rheological model[,] 2▪4 : Dewatering analysis

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D. I. VERRELLI

for all its greater level of complexity[,] does reduce the process to a set of measurable rheological parameters that control the process.

2▪4▪5

Phenomenological dewatering theory of LANDMAN, WHITE et alia

The inability to solve sedimentation problems for compressible (i.e. non-rigid) particles using KYNCH’s theory has motivated the development of phenomenological theories. A phenomenological theory is concerned with modelling macroscopic behaviour through the means of macroscopic (i.e. bulk) properties of the material [845]. It can also be thought of as an ‘engineering’ or ‘continuum’ approach [200, 211].

This contrasts with the use of

fundamental microscopic models to predict macroscopic behaviour [see e.g. 460, 772, 813] (§2▪4▪7). For the present applications a ‘two-fluid’ model is used, in which the continuity and momentum balance of the solid and liquid phases are formulated separately, rather than a ‘mixture’ (diffusion) model [see 1057]. Early research in this area was carried by ADORJÁN, who presented a satisfactory, “ad-hoc” theory of sediment compression [274]. An improved basis was introduced by BUSCALL & WHITE (1987) [213] — first revealed by DE GUINGAND (1986) [435] — and AUZERAIS, JACKSON & RUSSEL (1988) [101]. This basis was extensively developed by LANDMAN, WHITE and coworkers, as described in the following. Contributions to the mathematical formulation have also been made by BÜRGER and co-workers [see e.g. 200, 205, 274].

The theory can be considered an application of the “Theory of Mixtures” of continuum mechanics [see 218, 274]. Typical assumptions are [201, 206, 207, 274]: • the particles are small with respect to the containing vessel; • the particles are identical (i.e. in size, shape and density); and • each phase is incompressible and inert. Note that this last point still allows consolidation of a b e d of settled particles.

A further consideration is the current inability to correctly predict dewatering behaviour based on modelling of interactions on the primary-particle level [e.g. 745].

104



The LANDMAN–WHITE models assume a uniform volume fraction in the differential volume [628]. This means that the following behaviours will not be well modelled [628]: • build-up of immobile layers on vessel walls and ‘rat-holing’; • channelling; and • concurrent shearing [cf. 243, 585, 842] or agitation (e.g. raking) [cf. 107, 928]. More generally, the models assume that dewatering occurs in o n e d i m e n s i o n , so that there is no variation in any property over the cross-section. Effectively this means that w a l l e f f e c t s are assumed negligible [cf. 934]. (Likewise inertial terms and shear forces in the bulk of the fluid [627].) Shear stress and polydispersity effects have not been explicitly accounted for as yet [628]. Osmotic effects have generally been disregarded, although an extended model incorporating osmotic pressure has been outlined [211].

2▪4▪5▪1

Model parameters

The two key parameters used in the LANDMAN–WHITE models are the compressive yield stress, py, and the hindered settling factor, r. In practical contexts the hindered settling function, R ∝ r, is normally used in place of r.

A further fundamental parameter, the

dynamic compressibility, κ, is generally assumed to be large in magnitude and therefore negligible in effect [628]. Both py and R are m a t e r i a l properties b y d e f i n i t i o n : it is assumed that for a given particulate system they are functions only of the local solidosity, φ [140, 435, 598, 604, 605, 628, 745] [cf. 256, 422, 425] *. If estimates vary depending upon the measurement technique [cf. 646], then the conclusion is either that the characterisation procedure has changed the

*

Apparent φ0 dependence has been attributed to either [422, 425]: •

preparation of samples at different φ0 resulting in the creation of different ‘materials’ with real differences in aggregate microstructure (that persist to subsequently attained φ∞) [cf. 241, 590]; or

•

particle arrangement following different ‘pathways’ in sample preparation and in device dewatering from a common ‘preliminary’ solidosity [see following two footnotes].


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D. I. VERRELLI

nature of the material [see 241] (or the material has aged, or restructured *, differently in each [cf. 102]), or that the measurements are otherwise flawed †. Both experiment and theory support the status of py and R as material properties [604, 605, 745, 928]. A solids diffusivity, D, has also been defined based on r and the function py(φ).

2▪4▪5▪1(a)

Compressive yield stress

The c o m p r e s s i v e y i e l d s t r e s s , py, is a measure of how much applied stress the particle system can resist without being irreversibly deformed — i.e. dewatered, with the liquid phase free to drain from the system [628]. This is, in turn, “an implicit function of the strength of the interparticle bridging forces” [628]. (Micromechanical aspects are discussed further in §2▪4▪7▪1.)

This basis implies that py(φ) = 0 for φ < φg (not networked) and

py(φ) → ∞ as φ → φcp, in which φcp ≤ 1 is the close-packed solidosity. The function py(φ) can be inverted to provide a measure of the e x t e n t of dewatering at e q u i l i b r i u m under a given applied stress, because py(φ) → py(φ∞) = Δp as t → ∞.

py is assumed to be a function of the local solidosity only [140, 435, 598, 604, 605, 628, 745] for a given particulate system. (Conversely, the local solidosity depends on the stress history [cf. 317].) However, AUZERAIS et alia [102] proposed that when a system is far from equilibrium py may additionally depend on the deformation history. Restructuring of the aggregated

*

Differences in structure could arise if the characterisation techniques directly favour different packing configurations [cf. 422] (see e.g. ‘System anisotropy and osmosis’ and Figure 2-1), or through other factors such as damage to the sample upon transfer to the device.

†

If the dewatering is made to proceed extremely rapidly, at timescales shorter than the material’s characteristic relaxation time, then the values of py and R might be affected, as a consequence of the irreversibility of the process [101, 175, cf. 347, 363]. appropriate term in their momentum balance.)

(BÜRGER and colleagues [200, 207] included an

This does not appear to be an issue in practical

(compressible) systems: in filtration a kind of self-limiting mechanism exists, as the relatively large stresses needed to induce rapid dewatering soon yield a compact layer that slows the process; centrifugation would seem a more likely candidate to generate these dynamic effects. Failure to consider creep effects (cf. e.g. §9▪3▪2) could also lead to erroneous estimates.

106



particles over the course of the dewatering may affect py [cf. 102]; this may be equivalent to a change of material, so that naturally the ‘material properties’ may change.

LANDMAN & WHITE [628] use the common assumption that compression is i r r e v e r s i b l e . In mechanical terms, all ‘deformation’ of the particulate system (i.e. dewatering) is assumed to be plastic rather than elastic. This will be essentially true only for aggregated systems with φ ≥ φg, but in modelling practical dewatering processes the assumption has proven to be reasonable for many systems [605]. Mathematically the above may be summarised as [628] Dφ  = 0 , p S ≤ p y  Dt  > 0 , p S > p y

[2-47]

where pS represents the (static) s u p e r f i c i a l stress acting on the particles through the network, with the contact forces normalised by the entire cross-sectional area, rather than the (much smaller) contact area [200, 207, 771, 1040]. Measurements or calculations of pS(φ∞) are assigned to py(φ).

It is recognised that for pS ≤ py deformation can occur, but it is elastic, hence fully recoverable, and not considered in the model [627, cf. 745]. This assumption could equivalently be obtained by assuming that the elastic modulus approaches infinity. LANDMAN, SIRAKOFF & WHITE [625] also included a brief discussion of elasticity effects. Assumptions of one-dimensional, irreversible dewatering are not always valid, as discussed in §3▪5▪3▪4(b), §9▪2 and §9▪4.

Elastic cake re-expansion in centrifugation or filtration

experiments would lead to underestimation of φ∞ for the given stress (py) [cf. 1137].

System anisotropy and osmosis

The particle ‘pressure’, pS, is strictly “the zz-component of the network stress tensor”, where z is the macroscopic strain axis [624, 628] [cf. 218, 1032]. (The simplistic implication of this is that py ‘must’ represent a “uniaxial yield stress” [see also 211, 213]. In fact dewatering operations are almost always carried out in a c o n f i n e d geometry, so that in general a lateral restraining stress must also act — §9▪4▪2.)


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D. I. VERRELLI

For flocculated or coagulated suspensions the particle ‘pressure’ is taken as being due to (nett repulsive) interactions between particles [628]. If both e n d o g e n o u s osmotic pressure and ‘network pressure’ contribute to the particle pressure in a certain system (perhaps for a stable suspension), then [cf. 628] pS = pnetwork + posmotic(φ) ( py(φ) .

[2-48]

In contrast to pnetwork, posmotic can only be isotropic. As suggested in §2▪1▪4, posmotic can generally be safely ignored. The model should not be greatly affected in any case.

It has been reported that e x o g e n o u s osmotic consolidation can lead to greater equilibrium dewatering than mechanical means [745]. One of the key physical differences between these two processes is the geometric application of the driving force. In osmotic consolidation the imposed pressure gradient is typically two- or three-dimensional, whereas one-dimensional action is more common in mechanical operations [745]. This could lead to different packing arrangements [83, 585, 753, 1038] (see Figure 2-1, cf. §2▪1▪2) — although no manifestation was observed in the experiments of CHANNELL, MILLER & ZUKOSKI [241].

Apply axial pressure

Figure 2-1:

Apply lateral pressure

Final state

Simplified schematic of hypothetical equilibrium particle packing resulting from

sequential application of axial and lateral stresses. (drained) POISSON’s ratio of ν = 0.

Note that the process shown implies a

(It is assumed that the structure does not buckle

macroscopically — otherwise a minor perpendicular confining stress would be required.)

108



Experimental analysis of one-dimensional strength properties of a pre-consolidated sample in ‘axial’ and ‘lateral’ orientations, as suggested by Figure 2-1, could be used as a test of isotropicity.

Empirical and model functional forms of py(φ)

Experimental compressive yield stress curves in the domain φ > φg are often fitted with power-law curves such as [201, 203, 205, 628, 631, 642] [cf. 256, 1032, 1034, 1035, 1036, 1037, 1040]  φ  py = ξ     φg 

n    − 1 ,    

[2-49]

where n and ξ are positive constants.

(In practice φg may also be treated as a fitting

parameter, depending on the application and the information available.) A relation in the form of equation 2-49 can be derived by a simplified MOHR–COULOMB failure analysis [see 83]. Typical values for n are between 4 and 10 [495]. However, TILLER & KHATIB [1035] (who quote it in a different form, from BENDER & REDEKER) state that it “has not been particularly useful for the few substances tested” by them. The fits tend to be best for φg / φ / φcp [cf. 604, 605, 1040]. Numerous other correlations have been proposed [see e.g. 101, 102, 140, 203, 242, 416, 435, 628, 631, 642, 918, 975, 1032, 1035, 1052]. USHER, SCALES & WHITE [1061] recommended a correlation of the form: ξ1   φg      py = 1 −   exp ξ2 φξ3 + ξ4 ,    φ  

(

)

[2-50]

where the ξi are fitting parameters. A further recommended correlation is presented as equation 2-89 (p. 125).

Creep effects at low stresses

A physical interpretation of the compressive yield stress presented by BUSCALL & WHITE [213] is that below this stress flocculent or hard particles behave as solids due to electrostatic attractions or frictional and steric forces, respectively [629].


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D. I. VERRELLI

As with shear rheology [e.g. 127, 690, 691, 839], there is a question as to whether the yield stress still adequately describes the material for very low applied loads but very long times — i.e. where the very low strain rates of creeping deformation could be significant. In principle it can be argued that all real materials will contain gaps between particles, and vacant sites into which they can more compactly be arranged: however, for suspensions and fractal aggregates the primary particles may appear to ‘jam up’ [262, 263, 286, 567, 681, 1052] [cf. 165] on moderate length and time scales, so that creep might proceed only towards the limit of the atomic level [see 127]. The suggestion is made by BARNES [127] that material creep at loads far below the (shear) yield stress will proceed at a constant (shear) strain rate. This evidently cannot be applied to compressional rheology, where by its very nature any ‘deformation’, i.e. dewatering, results in a change of the material properties through the increase in solidosity.

Instead, to

distinguish creep and yielding behaviour, some practical ‘engineering’ threshold must be defined that implies negligible movement over the relevant lengthscale of the sample and timescale of the observation — which should be compatible with the intended application [127, 285, 779, 1056] [see also 243]. LANDMAN & WHITE [629] make the point that the typical model of py(φ) that they proposed is valid for suspensions and networks of fractal particles provided that the time for the dewatering operation of interest is less than the time for “spontaneous rearrangement of the network”. Experimental work suggests that creep is important, or even dominant, for weaklyaggregated systems (1 kB T to 10 kB T), so that no true yield stress exists [101, 140, 211, 213, 926] — albeit that an equivalent threshold stress could still be incorporated in models accounting for multiple dewatering modes [see 412, 844, 845] (see §R2▪2▪3, §S17). Effects may still be discernible at ~20 kB T [212, 844]. Attempts to model BERGSTRÖM’s data [140] in terms of py and R seemed to produce better agreement for more strongly aggregated systems (‒U = 35 kB T [140] and ‒U = 29 kB T [203]) than for the most weakly aggregated system (‒U = 11 kB T [140]). However, this may be partly an artefact of poor parameter optimisation, because POTANIN & RUSSEL [845] obtained substantially different (and arguably superior) re-predictions for the latter system using the

110



same model — albeit still distinctly inferior to results from their enhanced model incorporating ‘bulk viscosity’.

Elastic behaviour

There have been a number of accounts of compressed sludge materials expanding upon removal of the applied stress (see §9▪4▪1).

This is especially pertinent in the case of

centrifuge settling, where the settling of a suspension is monitored as a function of time.

BOTET & CABANE [175] conceived two forms of elastic deformation: in the first, particles essentially maintain their relative positions, and the entire system is compressed — this was called “ s t i f f ” behaviour; in the second mode, particle force chains b u c k l e under the load and the network rearranges, although interparticle bonds do not generally break.

FIRTH, HUNTER and VAN DE VEN developed models for rupture of elastic flocs [1069].

2▪4▪5▪1(b)

‘Hindered settling’ parameters

The h i n d e r e d s e t t l i n g f a c t o r , r, accounts for the hydrodynamic interaction between neighbouring particles [628]. This may be expressed mathematically as FDrag = ‒(λ Δu) r,

[2-51]

in which FDrag [N] and λ [kg/s] are the drag force and coefficient (respectively) for a single particle *, Δu [m/s] is its velocity relative to the fluid [cf. 628], and r [–] is a dimensionless ‘correction factor’. The drag coefficient, λ, is expected to be directly proportional to the fluid viscosity and particle size; for a sphere λ = 3 π ηL d (cf. equation 2-9) [442, 628, 631]. (LANDMAN & WHITE [628] present these interactions as though their effect is always to increase the drag on a particle. As is clear from §2▪2, it is possible for particle interactions to decrease the drag force on a given particle, although the nett effect of summing all interactions may still be to increase the drag force.)

*

The drag force imparted on the fluid by the particle has the same magnitude and opposite sign [628].


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D. I. VERRELLI

If the drag force is expressed with respect to the average v o l u m e per particle, Vp, then FDrag / Vp = ‒λ Δu r / Vp = ‒ Δu R,

[2-52a]

in which R ≡ λ r / Vp

[2-53]

is the h i n d e r e d s e t t l i n g f u n c t i o n [Pa.s/m2] for a given particulate system [608]. The drag may alternatively be expressed with respect to the average s u s p e n s i o n volume associated with a s i n g l e particle [629]: FDrag φ / Vp = ‒λ Δu r φ / Vp = ‒ φ Δu R,

[2-52b]

which is the basis used in the force balances following (equations 2-64 & 2-65, p. 117). R is a convenient parameter to work with, as the value of λ / Vp is often uncertain, especially for flocculent particles and aggregates [608]. As a first approximation, λ / Vp ~ O(1 / d02), where d0 is the particle diameter [631] — or 18 ηL / d02 for a sphere [e.g. 424, 425]. This implies that R will increase as the particle size decreases, in accordance with the commensurate decreases in the dimension of the fluid pathways between particles.

The parameter r (or R) can be interpreted as a correction to the STOKES settling velocity of the single particle (of given form), just as the factor я in §2▪2. Due to the form of the force balance (equations 2-64 and 2-65) — viz. the conceptually separate action of weight and pressures on the liquid and solid phases — and the conservation-of-mass requirement (equation 2-71), the correction includes an additional factor of (1 ‒ φ)2 (equation 2-78).

The hindered settling factor may be considered to be inversely proportional to a permeability (see equation 2-121). It quantifies a r e s i s t a n c e to dewatering due to fluid flow relative to the solid phase, normalised to the case of free settling. As noted previously (§2▪1▪4), this mechanism is commonly taken to be the dominant resistance. The hindered settling factor governs the (hypothetical) r a t e of dewatering in the absence of other resistances — principally load-bearing by the network.

It is notable that this kinetic term, whether expressed as r or R, is a function of φ only [see also 598]. It is clear that r(φ) → 1 as φ → 0 (free settling). It is also the case that r(φ) → ∞ as φ → 1 [628]. The same limits must apply for R(φ).

112



If the form of λ is known or can be reasonably approximated, then in principle Vp (and perhaps d0) could be estimated from R(0) = λ / Vp [424, 425]. In practice it can be difficult to obtain a reliable extrapolation of R back to φ = 0 [cf. 424, 425], and the form of λ is uncertain for most real particles (or aggregates), so the estimate would be of low accuracy. A more useful application may be rather to estimate — or validate — R(0) based on accurate particle size measurements.

Empirical and model functional forms of R(φ)

Model functional forms of R(φ) include [652]: R = ξ (1 − φ)− n ,

[2-54]

where ξ and n are positive fitting parameters (e.g. ξ = 1010, n = 20). This form is more-or-less compatible with the semi-empirical relation [495]: r = (1 − φ)−4.5 .

[2-55]

USHER, SCALES & WHITE [1061] recommended a correlation of the form: R = ξ1 (φ − ξ2 )ξ3 + ξ4 ,

[2-56]

where the ξi are fitting parameters. A further recommended correlation is presented as equation 2-90 (p. 125). Several other functional forms have been employed [see 203, 1032] (cf. the ‘compressibility coefficients’ described in Table 2-1). Equations 2-85 and 2-121 are useful for converting formulæ based on qS∗ and KD.

2▪4▪5▪1(c)

Dynamic compressibility

The d y n a m i c c o m p r e s s i b i l i t y , κ, is a measure of how quickly the network collapses in response to a pressure in excess of the compressive yield stress [628]. Including this in the mathematics yields [628] pS ≤ p y Dφ  0 , = Dt  κ ( pS − p y ), pS > p y

[2-57]

in which it is clear that a linear dependence upon a particle ‘overpressure’ (pS ‒ py) has been assumed for simplicity [see 213].


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D. I. VERRELLI

Note that from the definition of a material derivative, and given u = ‒u kˆ , then Dφ ∂φ ≡ + u ⋅ ∇φ , Dt ∂t

[2-58]

Dφ ∂φ ∂φ . = −u Dt ∂t ∂z

[2-59]

(Naturally the solid-phase velocity is chosen here [cf. 154, 314].)

Generally κ = κ(φ, pS) [628]. For pS not too much greater than py, κ may be assumed to be a function of φ only, because py = py(φ): that is, κ = κ(φ) [628]. In principle κ could also be ratedependant, but this too is conveniently ignored [213].

The dynamic compressibility quantifies a resistance to dewatering, and hence influences the rate. As noted above, this contribution to the overall resistance is commonly taken to be negligible [628]. This translates to κ → ∞, so that

 pS ≤ p y Dφ  0 , = Dt  lim c , p > p S y  c →∞

;

[2-60]

i.e. if ever pS exceeds py, then collapse is assumed “so rapid that, locally, φ moves immediately to the value at which py exactly balances the applied network pressure” (expressed as pS) [628, 630]. More simply, it may be required that at all times [cf. 630]

pS ( py .

[2-61]

Experimental results for flocculated systems generally support this assumption [628]. However selected experimental results indicate that the network’s inherent resistance to restructuring can affect the dewatering rate. Specifically, tests on soils have shown that even when the liquid pressure is “virtually [...] zero throughout” the sample, so that the applied stress ought to act without diminishment throughout the structure, “considerable further consolidation occurs” [317]. (This is referred to as ‘secondary consolidation’ [317], and can be thought of as a form of c r e e p — §R2▪2▪3.)

MILLER, MELANT & ZUKOSKI [745] identified the assumptions of large κ as equivalent to taking the “compressive viscosity” to be negligible.

114



Provided κ can be taken as large and consolidation is controlled by viscous fluid drainage, then knowledge of the precise magnitude of κ (and dependence upon φ) is important only in a small boundary layer at the top of the consolidating zone, and this region can be neglected in practice [630].

It is of interest to consider the closeness of the approximate equality between pS and py. This result derived from the implication that κ ~ φ / ηL, which is in turn based on the assumptions that the primary particles pack together in a uniform arrangement *, i.e. a ‘crystal’ arrangement, and that most of the work of compression is dissipated in the fluid [see

213]. The direct implication of this is that fluid drainage is very rapid [630]. The entire dewatering analysis also rests upon the assumption that bond breakage and reformation (i.e. densification [213]) occur essentially instantaneously, so that the fluid drainage is rate-determining: under these conditions the predicted form of κ means that consolidation itself will be as rapid as the fluid drainage [630]: [...] the existence of a constitutive relationship for flocculated suspensions is predicated on the assumption of rapid collapse when [the] yield stress is exceeded.

The assumption of instantaneous bond breakage and reformation has never been rigorously tested, although it is apparent from experimental work that in the vicinity of φg and at early times the assumption is a good approximation at least. M a t h e m a t i c a l l y it can be argued that — in the context of the LANDMAN–WHITE models — the dynamic compressibility a s d e f i n e d cannot influence dewatering behaviour at long times [419]. Yet this does n o t mean that slow network failure at long times governed by bond breakage kinetics p h y s i c a l l y cannot occur. The latter mechanism is treated outside LANDMAN–WHITE theory, under the category of ‘creep’ (§R2▪2▪3). When solid-phase failure processes (rather than liquid drainage) are rate-limiting, then many of the previous arguments no longer apply; for example, κ could become smaller as the solids become more

*

It turns out that any regular (i.e. periodic) arrangement yields the same result. At first this analysis seems a little dubious, given the accepted fractal nature of many aggregates (§R1▪5▪1▪1), which may result in the presence of fractal strands, or ‘backbones’ (§2▪1▪2).

However networked ‘beds’ of particles do not

necessarily have fractal scaling.


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D. I. VERRELLI

compacted, corresponding to slower network breakage at higher φ (for a given overpressure).

Scaling arguments suggested that [630]

pS ‒ py = py :z=0 ∙ O([d0/2 h0]2) ,

[2-62a]

in which h0 is the initial suspension height and d0 is the primary-particle diameter *. Continuum modelling requires in any case d0 / h0. For a typical settling system [630], with

h0 ~ 10‒1m and d0 ~ 10‒6m, say: (pS ‒ py) ~ 10‒10 py :z=0 .

[2-62b]

For d0 as small as 20nm: (pS ‒ py) ~ 10‒14 py :z=0 .

[2-62c]

(This seems to swamp even the range of timescales explored, say in batch settling, of order ~100 to 107s — filtration kinetics are ~102 times faster.)

2▪4▪5▪1(d)

Solids diffusivity

The s o l i d s d i f f u s i v i t y , D, is defined as [629] †

D ≡ (1 − φ)2

py ′ R

,

[2-63]

the prime indicating differentiation with respect to φ.

It is a common misconception that the solids diffusivity alone can summarise all of the information contained in the corresponding py(φ) and R(φ) functions [e.g. 443, 444] [cf. 975]. This misconception stems partly from the implicit use of py as a p a r a m e t e r in plotting

D (φ). In fact the D (φ) function is always used in combination with py(φ) [cf. 105, 787], and so the material properties are generally best expressed in terms of py(φ) and either R(φ) or

D (φ). D is unable to describe unnetworked suspensions (φ < φg), for which py′(φ) = 0.

*

An equivalent formulation has pS :z=0 on the right hand side [213]. Several misprinted versions exist [e.g. 628].

†

116

This was originally defined with an extra factor of φ in the denominator [627].



2▪4▪5▪2

General equations

General equations relevant to dewatering are derived as follows. It is assumed that inertia is negligible [as in 598, 1034], as are shear stresses at the walls [628].

F o r c e b a l a n c e s on the particles and on the fluid yield [628] ‒φ R (u ‒ v) ‒ φ ∇pL ‒ ∇pS + φ ρS a = 0

[2-64]

φ R (u ‒ v) ‒ (1 ‒ φ) ∇pL + (1 ‒ φ) ρL a = 0 ,

[2-65]

and

in which u and v are the particle and fluid velocity vectors (respectively), pL is the (hydrostatic) fluid pressure, pS is the (network) particle pressure, ρS is the density of the particles, and a is a linear acceleration vector (often due only to gravity). Balances including inertial terms are presented inter alia by AUZERAIS, JACKSON & RUSSEL [101] and BÜRGER and co-workers [200, 201, 207]. It is important to notice that here the solid and liquid phase stresses are both written as pressures, i.e. as scalars. A more rigorous general treatment in which the stresses (CAUCHY stress tensors) are each decomposed into the sum of a (scalar) pressure term and viscous stresses has been presented by BÜRGER and colleagues [200, 202, 207, 218]. These viscous stresses depend upon phase ‘partial viscosities’ [1057] and are not to be confused with the hydrodynamic flow resistance term linked to R [see 200, 207]. At low solidosities the solidphase partial viscosity may be practically zero; however, under certain circumstances it may influence (or even dominate) the behaviour, although there is very little guidance on a suitable constitutive equation [1057] — for expedience all of the viscous effects might therefore be assigned to the fluid phase [202]. (A separate discussion of bulk viscosity is presented in §S17.) Dimensional analysis indicated that the inertial and viscous terms are both likely to be small in most situations of interest [200, 203]; nevertheless the viscous terms must generally be retained for solution in more than one dimension [207] [cf. 202]. In practice neglection of these terms is common [207].


117

D. I. VERRELLI

Equations 2-64 and 2-65 may be combined to yield [628]

−

φ R ⋅ ( u − v) − ∇pS + φ Δρ a = 0 1− φ

[2-66]

and ‒∇(pL + pS) + (pL + φ Δρ) a = 0 ,

[2-67]

in which Δρ is the particle–fluid density difference. To account for friction between the particles and the vessel wall, a term proportional to pS can be added to equation 2-64 (hence also 2-66, 2-67, et cetera); for adhesion between the particles and the wall, a constant can be added [intuitively this should also be a strong function of φ] — the magnitude of both terms will also depend upon the vessel geometry [930, 1033].

Conservation of particle and fluid mass yields the c o n t i n u i t y e q u a t i o n s [495, 628]:

∂φ + ∇ ⋅ (φ u ) = 0 ∂t

[2-68]

and

−

∂φ + ∇ ⋅ ((1 − φ) v ) = 0 , ∂t

[2-69]

from which [cf. 495] ∇∙(φ u + (1 ‒ φ) v) = 0 .

[2-70]

Integration of the last equation depends upon the application [628] [cf. 203, 206]:

φ u + (1 ‒ φ) v = 0

for batch settling

[2-71]

φ u + (1 ‒ φ) v = qu

for a continuous-flow gravity thickener

[2-72]

for pressure filtration

[2-73]

φ u + (1 ‒ φ) v =

dh dt

where qu is the operating flux (based on the underflow mixture), and h is the height of

material above a membrane.

The models have been applied to uniaxial dewatering only, and so the general equations are cross-sectionally averaged to yield one-dimensional equations.

118



In applying the above general equations to specific processes, usually some terms will be neglected (e.g. gravity), and occasionally new terms will be introduced (e.g. input or output fluxes).

2▪4▪5▪3

Batch settling

As the LANDMAN–WHITE model accounts for interparticle stresses, it is valid in both unnetworked (φ < φg) and networked (φ ≥ φg) regions. Analysis is simpler for φ < φg.

2▪4▪5▪3(a)

Early time

For settling the only forces are in the vertical, such that u = ‒u kˆ , v = v kˆ , and a = g = ‒g kˆ . The overall force balance equation may be s i m p l i f i e d by removing the network pressure gradient term (i.e. φ ≤ φg) to give −

φ R ⋅ ( u − v) + φ Δρ g = 0 . 1−φ

[2-74]

Combining this with a rearranged continuity equation (equation 2-71), v=−

φ u, 1− φ

[2-75]

and simplifying gives u=

Δρ g (1 − φ)2 . R

[2-76]

Recalling that as φ → 0 then r(φ) → 1  R(φ) → λ / Vp, so the settling velocity of a single particle in an infinite, quiescent medium, u (or u° for a sphere), is given by u =

Δρ g . λ / Vp

[2-77]

Comparing with the more general equation leads to * u=

*

u (1 − φ)2 r

[2-78]

LANDMAN & WHITE [628] state that the velocity here, u, represents a m e a n settling velocity. Earlier formulations of the f o r c e b a l a n c e result in a different interpretation of r [e.g. 213, 624, 631].


119

D. I. VERRELLI

— equivalent to an earlier derivation in terms of αm (§2▪4▪4) by SHIRATO et alia [932] [see also 1027].

When the network stress term is retained (i.e. for all φ), then the settling velocity of the solids is given by [cf. 213]:  ∇p S  Δρ g −  φ   u (1 − φ) 2  ∇p S  =  1 −  r φ Δρ g  

u=

(1 − φ) 2 R

[2-79]

which shows the a d d i t i o n a l ‘hindering’ effect of the solid phase stress. Several alternative theoretical and empirical relations have been proposed [see 628] [cf. 495].

If the network pressure cannot be assumed to be zero, then i n i t i a l l y [628] h

t →0

=

u (1 − φ) 2 (1 − ι(φ0 )) , r

ι(φ0) < 1,

[2-80]

where ι represents the ratio of the critical (threshold) stress to the maximum actual stress * evaluated at the initial solidosity (assumed uniform), viz. ι( φ0 ) =

p y (φ0 ) φ0 Δρ g h0

.

[2-81]

It is evident that the critical stress will increase as φ increases, while the maximum actual stress will be constant due to conservation of material, that is ι( φ) ≡

p y ( φ) φ0 Δρ g h0

≥ ι(φ0)

for φ ≥ φ0 .

[2-82]

The above three equations may be summarised in practical terms [605]: R(φ0 ) =

Δ ρ g (1 − φ0 ) 2 h t →0

p y (φ0 )   , 1 −  Δ ρ g φ0 h0  

for settling of an initially-uniform suspension given py(φ0) < Δρ g φ0 h0. h

[2-83]

t →0

is just the initial

rate-of-fall of the supernatant–suspension interface, equal to the particle settling rate at the top of the column. It is only affected by h0 if φ0 > φg.

*

120

Actually the stress at the bottom of the vessel, neglecting hydrodynamic forces (i.e. at static equilibrium).



Past experiments in the literature showing a dependence of settling upon h0 could be caused by large values of φ0, material-specific mechanisms (e.g. concurrent bio-flocculation), or sideeffects of the characterisation procedure itself (e.g. biased exposure to shear) [see 309, cf. 356, 635].

2▪4▪5▪3(b)

General equation

Work by BÜRGER & CONCHA and LANDMAN & WHITE showed that batch settling can be modelled by [652]: ∂φ ∂qS∗ ∂  ∂φ  + − D =0 , ∂t ∂z ∂z  ∂z 

[2-84]

where D is the solids diffusivity (§2▪4▪5▪1(d)) and qS∗ is the ‘settling flux’ function given by qS∗ ≡ φ u∗ = −

(1 − φ) 2 φ Δρ g . R

[2-85]

qS∗ [m/s] is the ‘unsupported’ solid-phase flux, equal to the product of the solidosity, φ, and

the corresponding settling velocity in the absence of solid phase stress, u∗ [363, 604, 652, 1061].

Equation 2-84 is a quasilinear, second order, strongly degenerate hyperbolic–parabolic partial differential equation [206, 207].

Based on a transient profile of the falling interface between supernatant and settling suspension or consolidating bed, h(t), it is theoretically possible to obtain material properties

D (φ) and R(φ) — whence py(φ) — by solving the ‘inverse’ of equation 2-84 [652]. Although ‘possible’, it is not without difficulty: the non-linearity of equation 2-84 means that no analytical solution is available; numerical solution can be computationally demanding, and requires specification of functional forms for py(φ) and R(φ) [652].


121

D. I. VERRELLI

2▪4▪5▪3(c)

Practical solution

A significant simplification can be made while φ ≤ φ g , where D = 0 identically *, so that equation 2-84 reduces to the more tractable [652, cf. 1040]: ∂φ ∂qS∗ + =0. ∂t ∂z

[2-86]

(Cf. equation 2-34.) In practical terms, the condition φ ≤ φg is relevant when the material loaded is significantly below the gel point (φ0 < φg), so that φ ≤ φg for most of the column up until intermediate settling times, when most of the solid material is in the settled bed [cf. 652]. Equation 2-86 can be used to a n a l y t i c a l l y estimate [652] [cf. 420]: • R(φ) in the range

φ0 ≤ φt ≤

φ

≤ φmax ( φg

φ

≤ φ∞ :z=0

while equation 2-60 (p. 114) gives: • py(φ) in the range

0 ≤

(given t → ∞ so that ∂φ/∂t → 0 and pS(z) is equal to the buoyant particle self-weight per cross-sectional area,



h∞ z

φ g Δρ.dz ).

Here φ∞ :z=0 represents the equilibrium solidosity at the base of the cylinder, φt is the solidosity at the top of the bed when h(t) first diverges from linearity, and φmax is the maximum solidosity at which an analytic estimate of R is valid [cf. 652]. φmax is the solidosity at the top of the column of settling suspension when CφD = φg, that is, when h = φ0 h0 / φg [419]. As seen, the ‘flux curve’ qS∗ (φ) (⇔ R(φ)) is an essential input to — or output from — the model. It turns out that different modes of settling result depending upon the form of qS∗ (φ) and the value of φ0 [205, 652, 923]. The most important settling modes were described and analysed by LESTER et alii [652]. However, it is important to recognise that other modes of settling are possible [see 102, 205, 218].

*

Strictly the jump condition to ensure compatibility (§2▪4▪3) must be modified by subtraction of a limiting term D ∂φ/∂z (and writing qS∗ in place of qS) for compressible systems if one side of the jump has φ = φg [see 206, 218], as suggested by comparison of equations 2-84 and 2-34 (or 2-86). Although D (φg‒) = 0, in principle D (φg+) depends upon py′(φg+), which is not guaranteed to be zero — but could expediently be specified as such.

122



In order for the analytical solution to work and to produce useful outputs, it is necessary for the solidosity of the material beneath the supernatant to vary continuously, smoothly, and predictably over a significant interval [cf. 652].

Mathematically, it is required that the

solution contains a f a n radiating from the o r i g i n , i.e. a rarefaction wave of ‘characteristic’ lines of constant φ emanating from the origin [see 652]. For the predominant form of qS∗ (φ), with a single inflexion, this requirement is satisfied for most values of φ0 < φg, except those ‘close’ to either 0 or φg

*

[652]. In such cases a continuous variation of φ is obtained from

somewhere in the range φinflexion < φ < φmax to φmax (if φ0 < φinflexion then a discontinuity exists).

φ1 φmin

φ q∗

S, max

φinflexion

φmax

tangent at φg

tangent at φmax

φ [–]

φg

φ∞ φ0′

qS∗ [m/s]

tangent at φ0′

Range of φ for valid analytical output of R(φ) (along with φ0)

φ0 qS,∗ max

Figure 2-2: Typical flux plot [cf. 205], showing key features of the settling flux function, qS∗ (φ), and illustrating the range of solidosities for which R(φ) can be analytically evaluated for a given initial solidosity of φ0 or φ0′: the range is the same, as material loaded at φ0 jumps directly to φ0′ [cf. 652]. Not to scale.

*

Respectively: less than φmin or greater than φmax in Figure 2-2.


123

D. I. VERRELLI

This is best illustrated graphically, as in Figure 2-2, where the observable solidosities for the given input are indicated by a thick, unbroken line (and φ0). The construction follows the method illustrated by KYNCH (1952) [617] and others *. (Construction of the solid curve proceeds simply by successively running from the current point on qS∗ (φ) to the highestsolidosity point on the flux curve that can be reached without going below the curve [cf. 652].)

Although a continuous estimate of R(φ) can generally be obtained in the range φ0′ < φ < φmax, for clarity only the end-points of data extracted from gravity settling are explicitly plotted as points in the present work. Evidently the largest amount of information is obtained when φ0 = φinflexion [e.g. 419]; however, it is normally the case that little is known about qS∗ (φ) a priori [cf. 652] †. Furthermore, qS,∗ max is often of interest, so choosing φ0 ≈ φ q ∗

S, max

may be advantageous [652].

The discrete experimental data can best be used for analytic parameter estimation by fitting the h(t) profile with a smooth function [652] [cf. 450]. A reasonably robust and widelyapplicable choice is to model induction dynamics with a parabolic function, ĥ0(t), the constant-settling-rate region with a straight line, ĥ1(t), and the ‘fan’ region with one of two rather complicated functions given by LESTER et alii [652] ‡: hˆ 2 (t ) = hˆ1 (τˆ 1 ) + ξ0 t ξ1 + ξ2 t +

ξ3 − h2 (τˆ 1 , ξ ) , t + ξ4

t ≥ τˆ 1 ,

[2-87]

t ≥ τˆ 1 ,

[2-88]

or  τˆ + ξ  hˆ 3 (t ) = hˆ1 (τˆ 1 ) + ξ0 t ξ1 + ξ2 t −  1 − 1 3  h3 (τˆ 1 , ξ ) , t + ξ3  

where τˆ 1 is the estimated (or ‘predicted’) time when h(t) first diverges from linearity. ĥ2(t) has five parameters, ξ0 to ξ4, while ĥ3(t) has four; either set can be collectively referred to as

*

YOSHIOKA et alia (1957) applied this idea to develop a construction for continuous thickening [362, 363] [cf. 651].

†

Note that φmax can be estimated a posteriori without affecting preceding results [652].

‡

An earlier recommendation by LESTER [651] comprised only one form, which omitted the terms containing ξ3 and ξ4.

124



ξ. The terms containing τˆ 1 , including functions hi( τˆ 1 , ξ), are d e p e n d e n t terms that ensure

appropriate continuity with ĥ1(t). Choice of ĥ2(t) or ĥ3(t) is based on minimising the relative root-mean-square prediction error [652] (although the definition given appears statistically biased [cf. 755]). In the ensuing analysis the induction dynamics given by ĥ0(t) are ignored [652].

These procedures have been implemented in B-SAMS (§3▪5▪1▪1), where functional forms of py(φ) and R(φ) have been assumed.

For py [cf. 976]  0   k1  (φ − φg1 )    py =    a1 (φcp1 − φ) (b1 + φ − φg1 )    k2   (φ − φg2 )      a2 (φcp2 − φ) (b2 + φ − φg2 )    

∀ 0 ≤ φ < φg ∀ φg ≤ φ < φp ,

[2-89]

∀ φp ≤ φ < φcp2

with all of the parameters presumed positive, with φp < φcp1 ~ φcp2 and φg = φg1 ~ φg2. Typically the transition solidosity for the compressive yield stress, φp, is chosen such that it lies above batch settling data and below centrifugation and filtration data. In the present work φp was chosen such that py(φp)=2.5kPa;

alternative specifications were not

advantageous. The py(φ) curve estimation procedure is iterative, involving ‘guesses’ for φg, computation of the corresponding final height, ĥ∞, and comparison with the true final height, h∞ [1064]. It also extends by interpolation to data at higher solidosity obtained from (say) centrifugation or filtration. For R [1064]

( ( (

) ) )

 exp a1 φ 3 + b1 φ 2 + c1 φ + d1   R =  exp a2 φ 3 + b2 φ 2 + c 2 φ + d2   exp a3 φ 3 + b3 φ 2 + c 3 φ + d3

∀ φ1 ≤ φ < φ2 ∀ φ2 ≤ φ < φ3 .

[2-90]

∀ φ3 ≤ φ < φcp

This can be implemented such that the first and last domain are independently fitted to separate data, and the middle domain acts as a smooth, compatible interpolation function.


125

D. I. VERRELLI

Following the analytical solution, the ‘missing’ R(φ) data in the range φmax ≤ φ ( φ∞ :z=0 can be estimated n u m e r i c a l l y from equation 2-84 [652], if desired. (Given the infinitesimally small fraction of material actually at φ∞ :z=0, the estimates at this solidosity are likely to be less accurate.) A suitable algorithm was described by HOWELLS et alia [495].

GRASSIA et alii [420] recently developed an alternative analysis procedure, wherein a much simpler power-law approximation for h(t) in the fan region is chosen instead of ĥ2(t) or ĥ3(t). Although the fit is less accurate, a direct analytic conversion from h(t) to qS∗ (φ) (and hence R(φ)) is thereby permitted, without the need for reparameterisation [420].

As

reparameterisation itself often requires numerical methods, and the original data also contains experimental errors, the overall accuracy of the GRASSIA and LESTER methods may be comparable [420] *.

2▪4▪5▪3(d)

Settling in real systems

The simplest observations to make on settling systems are to monitor the height of the suspension (or bed) interface over time. Internal liquid pressure measurements can provide useful supporting information [see 203, 928] [cf. 1012] [see also 867, 1122].

Settling (and centrifugation and filtration) has also been monitored using x-rays [e.g. 102, 256, 257, 391, 742, 926], γ-rays [e.g. 140, 558, 1050] [see also 203], electrical conductivity † [e.g. 867, 1006] and capacitance [see 1122] [cf. 483, 1135], magnetic resonance imaging (MRI) (i.e. nuclear magnetic resonance imaging, NMRI) [see 256, 257], and ultrasound [e.g. 969]. (Ultraviolet light could be used too [713, 714].) This enables one-, two-, or even three-

*

The ‘verification’ presented by GRASSIA et alii [419] is, however, rather misleading.

While noise in

experimental h(t) data will indeed yield errors in estimated h′(t), these will almost certainly exhibit negative autocorrelation [see e.g. 755], but may have negligible systematic bias. If the LESTER method can be described as fundamentally ‘integrative’, then taking in turn the upper bound and lower bound of the envelope of estimated h′(t) data will greatly overestimate the m e t h o d error. A more meaningful estimate could have been obtained by bootstrapping (cf. §S15). †

More-or-less equivalent for this application are: resistivity [483]; resistance [867, 1122]; impedance [1135] [cf. 1122]; and conductance [1122, 1135].

126



dimensional representations of the suspension and settled bed to be created, yielding axial and lateral solidosity profiles, and permitting the identification of features such as channelling or wall effects. A helpful comparison of these techniques was presented in a very good review by WILLIAMS et alia [1122], which also included some less common techniques (for this purpose), including the monitoring of magnetic field or emitted radiation (either natural, associated with added ‘tracers’, or excited by neutron irradiation) and in situ pycnometry (e.g. utilising the ‘oscillating U-tube’ principle, cf. §4▪3▪1▪1).

Another option for generating solidosity profiles is local sampling or destructive testing (sectioning) [233, 1122].

If profiles are desired at several timepoints, then parallel

experiments should be conducted [233, 1122]. It may be feasible to suck material out from the column if the settling rate is slow enough [233]; other options include snap-freezing the column or the use of sliding partitions [1122].

In each of these techniques BUSTOS et alii [218] caution against interpreting an apparent discontinuity within the sediment as the interface between the bed and the suspension, i.e. the plane over which the material exceeds the initial solidosity; rather, the feature may be a steep gradient artefact w i t h i n the bed.

Numerous aspects relating to settling in real systems are discussed elsewhere in the present work: • delayed settling — §9▪1▪1▪1 — and the influence of o channelling — §9▪1▪1▪1(a); o densification — §9▪1▪1▪1(b); o wall effects — §9▪1▪1▪1(c);

• deterministic chaos: self-organised criticality and periodicity — §9▪1▪1▪2; • general wall effects — §9▪2▪1▪1 — and o torpid matter — §9▪2▪1▪1(a).


127

D. I. VERRELLI

2▪4▪5▪3(e)

Ideal settling

There are two distinct classes of behaviour of settling suspensions, depending upon whether the initial solidosity is above or below the gel point (it is assumed that the initial solidosity is uniform throughout the volume). These are depicted in Figure 2-3 and Figure 2-4.

φ0 < φg

φ = φ0

φ=0 φ=0

φ = φ0

φ = φ0

φ t=0

φ = φg φ > φg

φ t = t1

φ = φg φ > φg

φ t→∞

Figure 2-3: Schematic representation of typical batch settling behaviour with φ0 < φg.

φ0 > φg

φ = φ0 φ=0 φ=0 φ = φ0 φ = φ0

φ = φ0

φ t=0

φ = φ0 φ > φ0

φ t = t1

φ = φ0 φ > φ0

φ t→∞

Figure 2-4: Schematic representation of typical batch settling behaviour with φ0 > φg [495].

128



In certain cases somewhat different behaviour can arise, depending upon the precise form of the flux–density function, qS∗ (φ), the initial solidosity φ0, and the solidosity at the base [see 205].

According to the fundamental force balance (§2▪4▪5▪2) the initial consolidating ‘bed’ thickness (the region in which pS T py) in the second case is strictly non-zero, but vanishingly small in practice [213]. As alluded to earlier, inclusion of inertial effects would remove this condition.

The depicted transition from a concave to a linear and then a convex solidosity profile is consistent with direct experimental observation [102, 140, 203, 256].

However, the

implication in modern settling theories [101, 102, 495] that a ‘free fall’ zone of constant solidosity φ0 must exist above the consolidation zone is contradicted by numerous experimental studies [102, 140, 257, 483, 558, 926, 969, 1050] [cf. 256]. (This could be due to changes in φ0 over time [257] and size-segregation in polydisperse systems [483, 1122] [see also 1049].) Occasionally solidosity is even observed to increase with height [101, 558, 969, 1107]. Other variant observations were made by TILLER & KHATIB [1035]. Nevertheless, many investigations [e.g. 203] have shown good overall agreement between LANDMAN–WHITE phenomenological model profiles and experimental data, even for “natural slurries”.

2▪4▪5▪3(f)

Multiple-test theory

In many cases it is useful to know the solidosity at the bottom of the bed a t e q u i l i b r i u m , as the particle pressure can be simply calculated at this point from the known initial conditions. A useful parameter is the total volume of solids per unit area, ωtotal, [1035]: ωtotal = h∞ CφD∞ = h0 φ0 ,

[2-91]

(the latter equality follows from conservation of volume, given constant ρs) in which the subscripted ∞ represents the asymptotic value at infinite time and the angle brackets C · D indicate an average over the entire volume, viz. h

φ =

1 φ.dz , h 0



[2-92]


129

D. I. VERRELLI

where h is the height of the top of the bed at a given time. It is assumed that CφD0 = φ0. The pressure at the bottom of the bed at equilibrium (when Δu = 0 — see equation 2-66) is then [1035] py :z=0 = Δρ g ωtotal ,

[2-93]

where pS = py is assumed always to hold at the bottom of the bed. Rewriting the expression for ωtotal using equation 2-92, h∞

ωtotal =

 φ.dz ,

[2-94]

0

allows ωtotal to be differentiated by h∞ [1035] (using LEIBNIZ’s rule) to obtain the equilibrium solidosity at the base of the sediment bed, φ∞ :z=0: d ωtotal = φ∞ d h∞

z =0

,

[2-95]

as obtained by SHIRATO et alii [931]. The gel point, φg, is obtained by finding the limit as h∞ → 0. In practice the derivative may be obtained numerically either by estimating separate interpolation functions between successive pairs or sets of data points, or by fitting a single function to the entire data set. TILLER & KHATIB [1035] use the correlation *: ωtotal = a h∞b ,

[2-96]

in which a and b are arbitrary constants (characterising the “strength and openness” of the sediment). They [1035] warn that the equation is not valid for small values of h∞. The literature indicates that 1 < b < 2 (e.g. ~1.09 [931]; ~1.10 [932]; 1.06 to 1.33 [1035]), implying that the base solidosity varies with h∞ to a decimal power, so that φg = 0 is predicted. Equation 2-96 did fit a set of experimental data from the present work, however an excellent fit was also obtained with the function ωtotal = a h∞2 + b h∞ .

[2-97]

(The zeroth-order coefficient is chosen as identically zero to ensure zero volume at h∞ = 0.) This function has the advantage of predicting the gel point, through b ~ φg, which must be non-zero to fit the present work’s experimental data (see §S10 and §3▪5▪1▪2). Equation 2-96 predicts the following dependence of yield stress upon solidosity:

*

SHIRATO et alia [931, 932] preferred the reverse form of power-law expression, namely h∞ = a′ ωtotalb′ ; this yields a slightly more compact version of equation 2-98, viz. py = Δρ g (a′ b′ φ∞)1/(1 ‒ b′).

130



py =

Δρ g  φ∞    a1 /( b−1)  b 

b /( b−1)

.

[2-98]

In view of the values of b quoted above, this suggests a dependence on φ∞ of between 4 and 18 with a gel point of zero. The second-order polynomial (equation 2-97) predicts instead py =

(

)

Δρ g φ∞ 2 − b 2 , 4a

[2-99]

that is, a parabolic dependence, with non-zero gel point. Experimentally it is important to obtain data at small values of h∞, so that the gel point can be estimated more accurately. It is also important to ensure that φ0 < φg. Aside from the trivial case where material is loaded at a value of φ0 well above even the value of φ∞ corresponding to the particle pressure at the base, meaning that py(φ0) > pS :z=0, consider an intermediate case in which pS :z=0 > py(φ0) > 0. The bottom portion of the column will consolidate to its equilibrium solidosity, while the top portion of the column will remain at φ0. Now suppose that the same amount of solid material, ωtotal, is loaded into a second column at a solidosity below the gel point, so that py(φ0) = 0. This would result in a final height greater than that for the larger φ0. However the method relies on h∞ being a function of ωtotal only, and not of h0. Thus data corresponding to φ 0 > φ g c a n n o t b e u s e d in this type of analysis. (The B-SAMS batch settling analysis software uses an algorithm with a similar limitation; for settling experiments in the present work, φ0 ( φg.)

If py(φ) is modelled as the power-law function given by equation 2-49, then the final sediment height can be predicted as obtained by USHER [1063]. At equilibrium u = v = 0, and so equation 2-66 reduces to ∇pS = φ Δρ g .

[2-100]

Now assuming φ varies with z only and choosing appropriate integration limits gives h∞

−1 h∞ = dz = Δρ g 0



p y ( φ0 )

dpS . φ Δρ g



φ0 h0

[2-101]

Thus h∞ =

1−1/ n  1 ξ   Δρ g φ0 h0  + 1 − 1  1   Δρ g φg 1 − n   ξ  

[2-102]

for φ0 ≤ φg, and


131

D. I. VERRELLI

n−1 n 1−1/ n     φ0   1 ξ   φ0  ξ   Δρ g φ0 h0   − 1 + + 1 −   h∞ = 1   φg   Δρ g φ0   φg  ξ  Δρ g φg 1 − n         

[2-103]

for φ0 > φg.

2▪4▪5▪3(g)

Long-time behaviour

USHER, SCALES & WHITE [1061] derived a long-time solution of equation 2-84 to stated firstorder accuracy by considering a small perturbation of the equilibrium (infinite time) solution. The latter formulation is more tractable, as the time derivative drops out. A first-order approximation to the perturbed equilibrium differential equation is solved subject to leading-order approximations of the boundary conditions and continuity equation in terms of the perturbation variables [see 1061]. The solution to this system of approximate equations is given as a series of exponentials [1061] h − h∞ ≈ Φ [ f1 exp(− e1 t ) + f 2 exp(− e 2 t ) + f 3 exp(− e 3 t ) + ] ,

[2-104]

which is presented here in a form emphasising the similarity to the long-time filtration asymptote given by equation 2-124 (p. 147). Φ ≡ (dpy/dφ)/(Δρ g φg) evaluated at φ → φg+ *. The coefficients fi are numerical solutions to an eigenvalue sub-problem [1061].

The

(positive) coefficients ei are proportional to the eigenvalues, defined such that ei ≤ ei+1, and apparently with the property ei / ei+1 [1061]; further details can be found in the reference  h0 −2 [1061]. [1061]. It is also implied that e1 ∝

There is no explicit time shift shown (cf. tc in equation 2-124), but the equation could be further rearranged into such a format, considering that the equation is deemed to be mathematically consistent from the time at which the suspension becomes (or is) fully networked [1061].

*

Notice that ΔpS = ∫Δh φ Δρ g dh within the network. The derivative at φg is defined for functional forms such as equation 2-50. If a functional form with unbounded derivative at φg were used (examples can be found in the references cited following equation 2-49), the precise definition of Φ is not crucial, because in practice Φ is treated as an adjustable parameter.

132



Given the strongly increasing trend in the ei, a good approximation is afforded by retaining only the first term of equation 2-104, namely [1061]:

  h − h∞ ≈ exp ln (Φ f1 ) − e1 t  ,       constant

[2-105a]

or, following the form of equation 2-125b (p. 147): t ≈ E1 ‒ E2 ln(h ‒ E3) .

[2-105b]

The model predicts e x p o n e n t i a l decay of the height (and indeed the settling rate) at long times. Notice that the model predicts that the settling rate will be a linear function of height, h ∝ h . For comparison, the geomechanics models which give a true logarithmic asymptote (see §R2▪2▪3▪2(a)) correspond to h ∝ exp( h − h∗ ) with h < h ∗ and decreasing.

It has been claimed that empirical data supports the above model of asymptotically exponential behaviour [1061]. However closer inspection reveals a number of concerns: see Appendix S3. Logarithmic and power-law fits appear to be as good or better, depending upon the system. One of the most persuasive grounds for rejecting the universal existence of an exponential decay of h (t) once the system is fully networked is that the analysis presented by USHER, SCALES & WHITE [1061] takes no explicit regard of the form of py(φ) and R(φ) over the region φg to φ∞ :z=0.

2▪4▪5▪4

Batch centrifugation

Batch centrifugation is typically modelled as if it were simply batch gravity settling with an amplified ‘gravitational’ acceleration acting.

To a large degree this is a reasonable

assumption. The main complications arise from two points of difference between batch centrifugation and batch gravity settling: 1.

The sample tube cannot be considered an inertial frame of reference (it is a rotating frame of reference).

2.

The centrifuge must spin up and spin down, at the start and end of a test.


133

D. I. VERRELLI

2▪4▪5▪4(a)

Comprehensive analysis The most important assumptions of a model are not in the equations, but what’s not in them; not in the documentation, but unstated [...]. — STERMAN (2002) [970]

The rotation of the tube means that when the settling is analysed a s i f the tube were an inertial frame of reference it is necessary to consider a number of ‘fictitious’ forces. The most obvious is the centrifugal force, acting outward from the axis of rotation, however CORIOLIS forces also arise [201, 293, 900, 971]. CORIOLIS forces are experienced when components of the sample — e.g. particles — move with respect to the tube [see 201];

otherwise the

situation reduces to solid-body rotation. The CORIOLIS force can [971]:

• lead to sediment deposition on the trailing wall and dewatering (i.e. appearance of supernatant) at the leading wall of the tube — for r > rcrit; and

• lead to sediment deposition on the leading wall of the tube — for r < rcrit; • induce convective flow in the cross-sectional area — i.e. circulation currents; • generate unstable bulk flow — for rmin < rcrit < rmax; and • change the overall rate of dewatering: o in a h o r i z o n t a l tube (i.e. perpendicular to the axis of rotation), as commonly

approximated in a bucket centrifuge, accumulation of sediment at the base of the tube is generally r e t a r d e d , although the dewatering rate may be e n h a n c e d (rmin > rcrit) or r e t a r d e d (rmin < rcrit < rmax, cf. rcrit > rmax), but o in an i n c l i n e d tube, as in a fixed-rotor centrifuge, the dewatering rate is

e n h a n c e d due to the BOYCOTT effect *. (Note that the geometry can be rendered e f f e c t i v e l y ‘inclined’ due to CORIOLIS effects [1057].)

*

Namely the phenomenon observed where the settling suspension interacts with inclined walls [971], as in a lamellar settler.

134



rmin and rmax are the distances of the top and base of the sample from the axis of rotation (see

Figure 2-5), and rcrit is a critical radius defined in equation 2-110 which marks a transition in the direction of the CORIOLIS currents [971]. Evaporation can also induce convection, but is easily avoided [993]. Although separation based on particle size and density is possible [993], as in batch settling the samples studied in the present work are expected to settle in ‘zone’ form and maintain a constant composition throughout the bed.

s r

r0

rmin

rmax

ω

h(t) h0

y

z Figure 2-5:

x

Schematic of centrifuge system, looking down on plane of rotation.

Gravity is

assumed to act in the –z direction.

STIBI & SCHAFLINGER [971] give guidance on when the CORIOLIS force will be significant, assuming low φ0. The calculations depend on the following dimensionless numbers [900, 971, 1057]: э ≡

ρagg − ρL

Ta ≈

*

ρL 2 ω dagg

18 η / ρL

relative density difference

[2-106]

(modified) TAYLOR number *

[2-107]

The RYBCZINSKI–HADAMARD formula for particle drag has been used [971]; it is also assumed that the aggregate’s kinematic viscosity is much greater than that of the fluid.


135

D. I. VERRELLI

Ro ≡

1 + Ta u0 = э Ta ω rmax 1 + 4 Ta 2

ROSSBY number

[2-108]

Ek ≡

η / ρL Ro = 2 Re ω rmax

EKMAN number

[2-109]

The TAYLOR number compares the CORIOLIS forces and the viscous drag force on a single particulate [971, 1057].

The ROSSBY number characterises the influence on the settling

velocity of fluid inertia [293] (i.e. convective [900] or advective [1057] flow) relative to the rotational CORIOLIS forces [650]. The EKMAN number compares the viscous and CORIOLIS forces acting on the mixture [293, 971, 1057]. For most centrifugal separations Ek is very small, and Ro is also often small [293, cf. 1057], and in those limits it is valid to neglect the CORIOLIS terms in the m o m e n t u m b a l a n c e [971]. However, even in that case, the CORIOLIS influence on the r e l a t i v e m o t i o n cannot be ignored if э → 0 but Ta = O(1) [971]. Experimental results of the present work indicate that э ~ 0.005. For the present system N = 1000rpm, so ω ≈ 100s‒1; Ta ~ 1.4.

dagg ~ 5×10‒4m, and the supernatant is practically water, so

Thus CORIOLIS effects remain.

The ROSSBY number is Ro ~ 0.0019, and with

rmax ≈ ⅙ m the EKMAN number is Ek ~ 4 × 10‒7. Furthermore, the depletion and accumulation of solids at the leading and trailing walls of the cell can occur where the distance from the axis of rotation is greater than a critical radius given by [971] rcrit =

D φ (1 − φ) , 4 Ta {φ (1 − φ) 4.7 }

[2-110]

in which the width (or diameter) of the cell is D (here 0.025m) and φ is the volumetric fraction of aggregates, equal to φ / φagg. The convective flow and consequential sedimentation enhancement is promoted by small D [971]. The reader may note the term in braces is familiar from the RICHARDSON–ZAKI equation [971], which suggests a convenient cancellation. In the present system φ is not well known, but even taking an upper estimate of 0.50 [cf. 900] gives rcrit ≈ 0.35 rmax ≈ 0.06m < rmin ≈ 0.09m, indicating that the motion in the tube is stable and dewatering enhancement is relevant along the entire cell. Naturally these analyses neglect any interaction between aggregates, which could hinder the formation of convection currents. 136



BÜRGER & CONCHA [201] derived a rigorous mathematical expression describing centrifugal sedimentation of a particulate suspension. It improved upon the preceding analysis by appropriately accounting for compression of the sediment [201]. In a frame of reference rotating with the sample the analysis can be expressed s c h e m a t i c a l l y as: Coriolis inertia     centrifugal  gravity      hydrodynam    ic ∗ ∗ Fr  ˆ D vi sample ∗ ∗ ∗ ˆ ∗ ∗ ∗ ∗ = − 2 ρi ρi Frsample ω (k × vi ) + ρi φi  − k + Frdevice r  ± R Δ v ∗ Roh D t∗     [2-111] Fr sample ∗ ∗ ∗ ∗ ∗ ∗ ∇ Σi − φi ∇ p − ∇ p y i +    Re      

( )

pressure

compressive yield strength

viscous

in which the superscripted asterisks denote nondimensionalised variables (implied magnitude of order one), subscript i indicates the solid or liquid phase, kˆ is a vertical (upward) unit vector, r is the radial co-ordinate, Σ is the ‘excess’ or ‘viscous’ stress (see p. 117), and the Fr are FROUDE numbers [amended from 201]. The yield stress for the liquid phase is, of course, zero. The dimensionless groups h e r e (cf. equation 2-108) are [201, cf. 1057]: Frdevice

=

ω 2 rmax g

~

ω2 10 2

[2-112]

Frsample

=

u0 2 g h0

~ u0 2

[2-113]

Frsample / Roh

u2  =  0   g h0 

 u0    ωh  0  

~

u0 ω 10

[2-114]

Frsample / Re

u2  =  0   g h0 

 ρ u0 h0     η   

~

u0 10 5

[2-115]

where the orders of magnitude (in S.I. base units) are obtained for a typical benchtop system with physical dimensions of order 10‒1m and a water-like liquid phase.


137

D. I. VERRELLI

Provided u0, the characteristic settling velocity, is ( 10‒2m/s we obtain Frsample ( 10‒4 and Frsample / Re ( 10‒7, so the inertial and viscous terms (respectively) may be neglected * [cf. 201]. This limit on u0 is a reasonable assumption for WTP sludges. (The dimensionless groups were set up on the basis of an acceleration g, and so for compatibility u0 should relate to g r a v i t y settling, e.g. u . Industrial clarifier loading rates are of order 10‒4 to 10‒3m/s [111, 116, 282, 503, 557, 754], while typical settling experiments in the present work revealed interface settling velocities of order 10‒5m/s (Figure 9-4, cf. Figure 2-6);

however, the

densification of centrifuge samples may perturb the magnitude of u0.) Additionally, more rapidly settling systems would not necessitate centrifugation in practice! Note that it is n o t reasonable to neglect viscous terms in the boundary layers [see 900].

Interface settling rate, –dh /dt [m/s]

1.E-4

1.E-5

Power fit

Linear fit

Plant alum Lab. alum Plant ferric Lab. ferric

Plant alum Lab. alum Plant ferric Lab. ferric Plant Fe fit

1.E-6

1.E-7

1.E-8 –dh /dt = 0.07097t -1.3733 R2 = 0.8992 1.E-9 1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

Cumulative centrifugation time, t [s]

Figure 2-6: Interface settling rates of c ent r ifug ed samples. (The two alternatives given for each sludge type refer to the local form of h(t) assumed in numerically estimating the derivative.)

*

BÜRGER and colleagues [200, 202, 207] had been markedly more cautious in applying the same type of justification to gravity settling; e.g. the consideration of all nondimensionalised variables as being of order unity in magnitude is explicitly flagged as an a s s u m p t i o n . The putative differences in magnitude of the discarded and retained terms were (notwithstanding) much greater in the settling analyses [200, 202, 207].

138



In order to neglect the ‘pure’ gravity term we require Frdevice T 103, say; this implies ω > 102, that is N > 103rpm. Finally, the CORIOLIS term may be neglected for Frsample / Roh ( 10‒3, say; so that ω ( 10‒2 / u0. In the case of rapidly settling suspensions with u0 ~ 10‒2m/s, this implies ω ( 1s‒1, which is incompatible with the requirement for neglecting ‘pure’ gravity.

More slowly settling

materials with u0 ~ 10‒4m/s yield ω ( 104s‒1, or N ( 105rpm. This analysis indicates that a desirable speed lies in the range 103 < N < 105rpm, where the upper limit is determined by how slowly the particles would settle under gravity. Errors of a n t i c i p a t e d o r d e r 1% can be tolerated as s m a l l [cf. 201] (as distinct from negligible), and supposing that u0 ( 10‒3m/s, then the range of speeds for expedited analysis becomes 103 ( N ( 103rpm for u0 ~ 10‒3m/s (that is, N ~ 103rpm), 103 ( N ( 104rpm for u0 ~ 10‒4m/s, and so on. In the present work N = 1000rpm was used for centrifugal settling experiments. Hence it can be a n t i c i p a t e d that gravitational and CORIOLIS effects are s m a l l during quasi-steadystate operation. To have more confidence it would be necessary to extend the mathematical analysis beyond orders of magnitude, or else to devise a series of experiments to probe dependence on the ROSSBY number, say. For the experimental data compared by BÜRGER & CONCHA [201] circulation currents in the sample may have decreased the dewatering rate by ~10 to 25%. BÜRGER & CONCHA’s [201] assertion that the mathematical analysis can be easily extended to include CORIOLIS terms by ”assuming that the flow variables depend on the radius only” is rather misleading. The difficulty is embedded in the ‘reduction’ of the s i m p l i f i e d partial differential equation from vector to scalar terms [see 201]. The cross products of equation 2-111 indicate that material moving in the +r direction — e.g. particles moving in accordance with the centrifugal force — will be diverted forward (i.e. in the +s direction); conversely, material moving in the ‒r direction (e.g. fluid) will be diverted backward (‒s direction). Already this suggests that considering one-dimensional motion in r may not be sufficient, but this is confirmed by considering what happens at the walls of the tube (and the interface with the supernatant and consolidated bed) where the fluxes set up by the CORIOLIS forces encounter boundaries and thus generate c i r c u l a t i o n currents as discussed above.


139

D. I. VERRELLI

Aside from the quasi-steady-state anomalies when the centrifuge is operating at a constant rotation rate, further complications arise when the centrifuge is accelerated at the start of a run and decelerated at the end [cf. 1057]. The most obvious additional effect is for the material to want to bank up against the trailing edge as the centrifuge accelerates and against the leading edge as it is decelerated. Furthermore, experimental trials employing centrifuges with fixed-angle rotors have shown that “rapid” deceleration results in convective mixing of the tube contents due to the CORIOLIS effect [432, 496]. Additionally, BERMAN, BRADFORD & LUNDGREN [141] showed that liquid–liquid interfacial profiles in a centrifuge vary depending upon whether the rotational rate is increasing, constant, or decreasing.

Narrow centrifuge tubes are generally avoided, where feasible, in order to avert the wall effects observed by a number of researchers, where the walls apparently supported the network leading to underestimation of φ∞ [422, 425]. Yet further complications exist if the tube diameter is significant compared to the radius of rotation; in such cases the acceleration vectors at a given (planar) cross-section through the tube cannot be assumed parallel, but rather diverge (radially), with components directed towards the tube walls [e.g. 102, 425]. (The latter problem is, in principle, avoided by using cells of “sectorial” shape [712, 993]). DE GUINGAND [435] reported that wall effects were negligible with tube diameters above 20mm for flocculated red mud; other researchers found smaller diameters acceptable.

2▪4▪5▪4(b)

Simplified one-dimensional analysis

If the negligibility of all terms suggested above is accepted, then centrifugation can be described exactly as for gravity settling (equation 2-84), viz. [cf. 201, 652] ∂φ ∂  ∗ ω 2 r  ∂  ∂φ  − −  qS ⋅ D =0 , ∂t ∂r  g  ∂r  ∂r  except that the solid flux–density function is multiplied by an

[2-116] acceleration

e n h a n c e m e n t factor (quasi-linear scaling), and the orientation of the axis r is opposite to that of z in gravity settling. This is a second order, strongly degenerate hyperbolic–parabolic partial differential equation, and requires special treatment at the type-change plane, using a jump condition and imposing an entropy weak solution [see 201, 218]. 140



When the CORIOLIS and spin-up/spin-down effects are neglected, the following analysis can be undertaken to determine the compressive yield stress. The procedure is similar to that first reported by GRACE [416] for filter cakes *, followed inter alia by MEETEN and co-workers [e.g. 737] [cf. 927], and later applied to centrifuge cakes by ZUKOSKI and co-workers [e.g. 242, 745] and GREEN [425], among others [605]. (The hindered settling function is obtained by iteratively predicting the h(t) profile with improved parameter estimates to match the observed profile.) The equilibrium-centrifuged bed, or cake, is sectioned into n disks of height Δri and constant diameter †, with i = 1 at the top. Experimentally this is done by decanting (i.e. syringing) off the supernatant (i.e. centrate) and successively scraping off layers of the cake ‡. The (volume mean) solidosity of the layers, CφiD, is determined in the usual way by oven-drying at 100°C (cf. §2▪1▪1, §4▪3▪1).

However, the top section is liable to incorporate a portion of pure

centrate, and this may be corrected by a volume balance §. Define distances from the axis of rotation of the centrifuge: r i at the centre of section i, and ri at the bottom of section i. (The sample is assumed to swing horizontally out due to the ‘bucket’ arrangement of the device.)

*

TERZAGHI (1923) [1011, 1012], and perhaps others, employed a related technique where porosity was determined as a function of height by dissection, and this c o u l d have been related to a yield stress from knowledge of the relationship between applied stress and equilibrium porosity.

†

This is measured directly from the tube, but also systematically estimated for each section from the measured total mass and Δri. The second-smallest of these estimates (excluding the two at the bottom of the tube) is used as an ad hoc average.

‡

MEETEN’s [737] technique included an enhancement whereby the cake was progressively exposed for sectioning by a plunger-type mechanism (also explored by GREEN and others), but in the present work a square-ended palette knife was used in combination with a clamp to physically constrain the depth sampled. An advantage of the former technique is that soft ‘cakes’ can be more easily sectioned [737].

§

The VS,1 is first approximated from the total-solids mass and specified ρS. Given Δr1, the total volume of the section is known, and so an alternative estimate of the liquid phase volume can be made. The measured ysupernatant is used to estimate mDS,1 and hence correct VS,1 and VL,1. The e x c e s s mass of p u r e centrate is then estimated by subtracting (mS,1 + ρL VL,1) from the measured total section mass. If the excess mass of pure centrate is positive, then xsample,1 is instead calculated from the foregoing (mDS,1 + mS,1)/(mS,1 + ρL VL,1), whence φ1 — if negative (and small), then no correction is made.


141

D. I. VERRELLI

The particle pressure, pS, immediately beneath a given section i — that is, at ri — is [102]: ri



pS (ri ) = Δ ρ ω 2 r φ . dr .

[2-117a]

r0

pS (ri ) ≈ Δ ρ ω 2

i

r

j

Δ rj φ j .

[2-117b]

j =1

The product Δρ Δrj CφjD is the ‘buoyant’ mass of particles in section j per cross-sectional area, which is being rotated at ω radians per second through an arc of (arithmetic mean) radius rj — the angular acceleration is thus ω2 rj . Of most interest is py(φ). Note that pS = py, because the system has been centrifuged to equilibrium.

However the foregoing essentially produces py evaluated at ri, but CφiD

evaluated at r i [745]. py at r i is estimated by simple averaging: pS (ri ) + pS (ri −1 ) 2  ri Δ ri φi ≈ Δ ρ ω2  + 2 

p y (ri ) ≈

. rj Δ rj φ j  

i −1

 j =i

[2-118]

GREEN [425] also discussed analysis of such discrete data.

A further option is to fit an analytic function φ(r) — using the ( r i , CφiD) data — which can be integrated exactly according to equation 2-117a to yield an analytical form for py(r). A suitable, generic function is [cf. 423, 745] φ(r) = a + b ln(r) + c [ln(r)]2 .

[2-119]

(Other forms may be derived by supposing that py(φ) takes one of the forms given on p. 109, and then substituting into equation 2-117a and differentiating with respect to r. This process yields a differential equation dφ/dr which must be solved to obtain φ(r).)

A useful check on the experimental error is to confirm φ0 h0 = Cφ∞D h∞ ≈ ∑ CφiD Δri (by conservation of solid-phase volume).

An alternative technique, analogous to the multiple test batch settling analysis, was described by GREEN, EBERL & LANDMAN [423] for estimating py(φ).

142


Both this and the


foregoing cake-sectioning technique have been found to yield results consistent with filtration measurements [422, 425, 745]. GREEN [422, 425] and MILLER, MELANT & ZUKOSKI [745] preferred the cake-sectioning technique due to the ability to reliably obtain characterisations with acceptable accuracy fairly rapidly and from a straightforward analysis. The principal disadvantage is the operator time required for the actual sectioning [422, 425].

2▪4▪5▪5

Permeation

In the case of a fluid permeating through a uniform packed bed of particles, the fluid force balance (equation 2-65, p. 117) simplifies to φ R Δu = (1 ‒ φ) ∇pL ,

[2-120a]

if the load of the applied pressure is much greater than the self-weight, with Δu ≡ u ‒ v [cf. 425]. Given the bed is considered fixed, and permeation is occurring in one dimension, this can be further simplified to: φ Δp vR , =− Δz 1− φ

[2-120b]

where Δp is the pressure applied to the fluid, and Δz is the bed thickness [cf. 425, 627]. v is the fluid velocity; recall from §2▪3▪1 that dV /dt = ‒qL = ‒(1 ‒ φ) v [contrary to 425]. Hence φ dV Δp R . = Δz (1 − φ) 2 dt

[2-120c]

Equation 2-120 can be used to obtain R from experimental measurements, which have been shown to be consistent with those obtained by cake-forming filtration experiments [e.g. 425].

Comparison of equation 2-120 and equation 2-18 (p. 75), which describes DARCY’s law, yields [604, 1027, 1028] *

*

This differs by a factor of (1 ‒ φ) from earlier formulations [e.g. 425, 1063] that used a non-standard substitution of v for qL. Equation 2-16 suggests that in principle such formulations could be justified for a n o n - s t a n d a r d definition of KD. However, the earlier formulations were inappropriately used [e.g. 425, 1063] to derive versions of equation 2-121 that are unambiguously wrong. STICKLAND et alii [975, 976] derived essentially the correct relationship between R and “hydraulic conductivity” (identical to KD 1856, and equal to ρL g KD / ηL for spatially invariant ρL g — see §2▪3▪1).


143

D. I. VERRELLI

R=

(1 − φ) 2 ηL , φ KD

[2-121]

with KD the permeability. Equation 2-121 shows that the definitions of KD and R conceal a peculiarity. Suppose two beds are constructed from different materials to have identical thicknesses (Δz) and permeabilities (KD) but different solidosities (φ): permeation experiments would show the exact same permeation rate (dV /dt) for a given pressure drop (Δp), but analyses would yield a lower value of R for the more concentrated sample. Consider too the hypothetical scenario where the permeability of a given sample decreases as it is dewatered to greater φ — as expected — yet if h y p o t h e t i c a l l y the permeability (KD, KD 1856 or K D∗ — see §2▪3▪1) does not decrease too rapidly, then R need not increase and could even decrease *.

Although suspension-filtration experiments are generally preferred to fluid-permeation experiments on the grounds of accuracy and expediency [425, 1063], permeation experiments are useful for exploring behaviour at lower solidosities or for characterising suspensions that are prone to settle rapidly during a filtration run.

In pressure permeation an initial bed is formed by gravity settling in the cell, through which supernatant is later forced under pressure. The bed first consolidates further to a new equilibrium, at which point the above equations may be used to obtain R for the a v e r a g e solidosity, CφD, of the consolidated bed [605]. (It is assumed that this will be equal to the R obtained if the entire bed were at CφD.) In practice CφD may be calculated by monitoring the height at which the piston contacts the bed as all of the supernatant is pushed through.

2▪4▪5▪6

Filtration

Many permutations of the filtration operation exist [e.g. 293, 414, 881, 1027] (cf. §R1▪4▪4). In the following discussion only pressure-controlled dead-end filtration is considered. It is

*

Typical rule-of-thumb correlations suggest this is unlikely to occur in practice:

f o r e x a m p l e with

 φ4 [1036, 1037]  R ∝  φ4 (1 ‒ φ)2; the former R ∝ (1 ‒ φ)‒n and n = 4.5 [495] (or n = 10? [652]), or with αV ∝

increases monotonically with φ for 0 ≤ φ ≤ 1, the latter for 0 ≤ φ ≤ 2/3 ~ φcp. (Cf. equations 2-16 and 2-20.)

144



usually assumed that such systems operate at constant pressure;

in practice minor

corrections may need to be made to account for the initial time to build-up pressure and the pressure drop across the membrane [881].

In filtration the applied pressure usually dominates the self-weight. Hence equation 2-67 (p. 118) reduces to [cf. 1036, 1037, 1040] ‒∇(pL + pS) = 0 .

[2-122]

The definition of the gradient operator implies that the sum (pL + pS) is s p a t i a l l y i n v a r i a n t , and equal to the a p p l i e d p r e s s u r e , Δp, which might vary with t i m e or might be c o n s t a n t [cf. 255, 628, 631, 642, 643, 764, 867, 881, 882, 883, 1026, 1036, 1037, 1039] [see also 1013, 1014]. It is easiest to explore filtration concepts in the case of a constant applied pressure. In this case a dilute suspension initially resists the pressure entirely by fluid pressure — which drops instantaneously to atmospheric pressure as it passes through the membrane, due to hydrodynamic resistance.

As a cake forms, the fluid passing through it experiences a

pressure drop before reaching the membrane, and this pressure drop is exactly counterbalanced by the local network stress. In modelling, the pressure drop through the cake is often assumed to dominate the total fluid pressure drop — i.e. ‘negligible’ membrane resistance.

Eventually, as the filtration proceeds, the material becomes networked

throughout the filtration cavity. As equilibrium is approached, v → 0 and u → 0, pL → 0 (atmospheric gauge pressure), and pS → Δp (the applied gauge pressure). As in batch settling, a slightly different sequence of events takes place if the material loaded is initially networked, i.e. φ0 ≥ φg [628].

Though almost always ignored in the development of filtration theory, it has long been recognised that significant gravity settling can occur in the suspension under certain conditions [1034]. If gravity settling is significant on the timescale of the filtration, then an analysis that assumes otherwise can be in considerable error in terms of the dynamics [628] — equilibria should be unaffected. The analysis is particularly complicated by the appearance of a clear supernatant above the settled material [see 624, 628] [cf. 983, 1006, 1027].


Although

145

D. I. VERRELLI

sedimentation can reduce the bed formation time, the general tendency is for overall filtration times to increase, because of the greater bed thickness and resistance [628, 983]. As implied earlier, gravity effects can often be ignored. When dilute materials are filtered, they generally have little resistance to filtration, and so filter very quickly. When materials are loaded nearer their gel points, the filtration may proceed more slowly, however the settling would also be reduced, and moreover the sample would quickly network, even if the subsequent consolidation required an extended time. Gravity effects can become important when a thin, compact cake develops as a near-impermeable ‘skin’ at the membrane’s face, thereby greatly slowing the filtration kinetics, or when filtering very coarse particulates [cf. 624, 1027]. In the present work gravity effects were only of concern for the freeze–thaw conditioned and polymer-conditioned sludges.

Interactions between the particulate cake and the cell wall (see §3▪5▪3▪4(b), §9▪2, §9▪4▪2) may be important, but are neglected in the analysis below.

With the above assumptions, the general governing differential equation for filtration can be written as [cf. 626] ∂φ = ∇ ⋅ [D ∇φ − φ Q], ∂t

[2-123a]

where Q represents the local suspension flux. This may be written in other forms using the solid-phase continuity equation (equation 2-68) [626]. For one-dimensional filtration equation 2-123a simplifies to [629]: ∂φ ∂  ∂φ ∂h  D = − φ  .  ∂t ∂z  ∂z ∂t 

[2-123b]

Recognising φ dh/dt as the solid-phase flux density function, qS∗ , this is mathematically i d e n t i c a l to equation 2-84 (p. 121), which described s e t t l i n g . Comparable equations were derived by SMILES and co-workers (1970, 1973, 1988, et cetera) [see 626, 629, 642].

Modelling filtration according to the equations of LANDMAN & WHITE is numerically and computationally challenging.

LANDMAN, SIRAKOFF & WHITE [625] described suitable

algorithms [cf. 624]. 146



Useful simplifications have also been described, which lead to approximate solutions [e.g. 629]. One such simplification is suggested by a series of changes of variable in equation 2-123b, which enable l i n e a r i s a t i o n of the transformed differential equation if the product φ 2 D can be taken as ( p i e c e w i s e ) c o n s t a n t [629]. A suitable approximation is a step function that jumps from 0 to φ∞2 D∞ in such a way that the function yields the correct value of ∫ φ2D .d(φ‒1) integrated from φ0‒1 to φ∞‒1 [cf. 629]. These choices ensure that the approximate solution has the correct asymptotic behaviour as t → 0 (provided φ0 < φg *) and as t → ∞, and also the correct ‘diffusion’ kinetics quantified by the “mean action time” [629]. A peculiarity of this analysis is that short-time solutions are modelled as cake formation processes, irrespective of the true ratio φ0 / φg [629]. The long-time solution is obtained as an infinite series, which can be written [cf. 629, 1063]



  − (t − t c )   − 9(t − t c )   − 25(t − t c )   + f1 exp  + f 2 exp  +  , [2-124] E2 E2  E2      

V∞ − V ≈ Φ  f 0 exp 

in which a number of constants are wrapped into summary parameters — Φ, E2 and the coefficients fi — for clarity. It is important to note that |fi+1| < |fi| [629]; also, Φ ∝ h0 [1063]; further details can be found in the references. tc represents the (nominal) time of transition from cake formation to cake consolidation. V∞ is the specific filtrate volume at equilibrium. Taking only the first term gives the asymptotic result:

lim t →∞

    t t  V∞ − V ≈ exp c + ln (Φ f 0 ) − ,  E2 E2        constant = E1 / E2

[2-125a]

or, in the notation of USHER [1063] and others [e.g. 605]: t ≈ E1 ‒ E2 ln(E3 ‒ V ) as t → ∞ .

[2-125b]

E3 clearly is just E3 ≡ V∞ = h0 ‒ h∞ = h0 (1 ‒ φ0/φ∞) ,

[2-126]

given that V = h0 ‒ h.

*

An alternative that was not explored by LANDMAN & WHITE [629] in their paper is to set the low-end value of the φ2 D step-function approximation to φ02 D (φ0) instead of 0.


147

D. I. VERRELLI

E2 is defined by 2

2 D (φ∞) ≡  (h0 − E3 ) ÷ E2 = π



( h∞ ) 2 . (π / 2) 2 E2

[2-127]

E1 is the constant indicated in equation 2-125a; it depends partly upon D (φ) in the interval φ0 to φ∞ [see 629, 1063], but the details are irrelevant to the present work, where it is treated as a statistical fitting parameter. All of the Ei are constant, given a constant applied pressure [cf. 1063]. A discussion of the problem when two terms are retained in equation 2-124 is presented in §S4. The above equations are very similar to the approximate formulæ for long-time settling, viz. equations 2-104 and 2-105 (p. 132). They can also be compared to the soil creep correlations (§R2▪2▪3) and the macrorheological models (§R2▪3▪2). E1 and E2 may be estimated by ordinary least-squares regression of t against ln(E3 ‒ V ), while E3 could potentially be obtained (if unknown) by iterating to obtain the straightest line [1063]. An alternative, novel methodology (not used in the present work) would be to differentiate equation 2-125b, viz.  dt  ln   ≈ ln( E2 ) − ln( E3 − V ) as t → ∞ ,  dV 

[2-128]

and vary E3 to ensure that regression of ln(dt/dV ) against ln(E3 ‒ V ) yields a slope of precisely ‒1. This procedure is analytically and statistically appealing, but at the same time suffers the disadvantage of requiring numerical differentiation of the experimental data, which will certainly be subject to noise. A further alternative is to differentiate equation 2-125a, viz. t  dV  E1 ln  − ln( E2 ) − ≈ E2 E2  dt   

as t → ∞ ,

[2-129]

constant

which should allow simple estimation of E2 and E1 by linear regression. As E3 is ordinarily required to obtain R(φ∞) (see below) it could be estimated directly from equation 2-125b.

148



Filtration permits more direct probing of dewatering characteristics than methods relying on self-weight: the compressive yield stress is a direct experimental output, and the hindered settling function can be calculated analytically using the approximate expression [626]: R(φ∞ ) ≈ 2

 1 1    (1 − φ∞ )2 −  dV 2   φ0 φ∞   d  dt  c.f.   d(Δp)

[2-130]

derived from equation 2-136, where V is the filtrate volume per unit filter area.

The

derivative dV 2/dt is evaluated during c a k e f o r m a t i o n — with negligible membrane resistance — and is approximately c o n s t a n t for a given (constant) applied pressure, Δp. The approximation arises from the commonly-made assumption that particle velocity in the cake is negligible, which introduces an error of order ±1% for typical systems, although larger errors would be encountered for large φ0 [626, 631] [cf. 1034, 1039, 1040]. Although, strictly, cake formation occurs only for φ0 < φg, in practice a ‘dense-cake’ region builds up from the membrane even within initially-networked suspensions, and so samples with φ0 > φg can still be analysed using equation 2-130 [425, 608, 972] *. In practice the derivative of Δp with respect to dV 2/dt :c.f. is found by evaluating its reciprocal based on the curve-fit: dV 2 dt

[

= ξ ( Δp ) n

](

1 − π Δp )

,

[2-131]

c.f.

where ξ, n and π are fitting parameters;

often π can be taken as 0 [cf. 608].

It is

straightforward to show that for this correlation

 dV 2   d  dt    (1 − π Δp ) π  n π c.f.    ln ξ (Δp)n  ⋅ ξ (Δp)n , + =  1 − 2  d(Δp) Δp  Δp (Δp)  

[

] [

]

[2-132]

the reciprocal of which can then be used in equation 2-130.

R can be related to the average solid-volume-specific cake resistance, CαVD [cf. 1040]: αV =

*

(

R

ηL 1 − φ

)

2

,

[2-133a]

A key feature is the near-linearity of the solidosity profiles in the growing ‘dense-cake’ region [shown without discussion in 972].


149

D. I. VERRELLI

where φ is an ad hoc average of the material solidosity (representative of the cake) [cf. 628, 631, 1059] (see also equation 2-43, p. 102). φ ≈ 43 φ∞ + 41 max{φ0 , φg }

[2-133b]

appears to be a reasonable approximation [cf. 628, 631]. An alternative derivation links equations 2-40a and 2-41c with equation 2-120b (remembering that dV /dt = ‒qL = ‒(1 ‒ φ) v) to yield [cf. 604] αV =

R ηL (1 − φ ) 2

[2-134]

for the local properties.

Similarly, the ‘specific resistance to filtration’ (SRF), αSRF, defined in equation 2-31 (p. 90) can be related to R as: αSRF =

φ R . φ − φ0 ρS ηL (1 − φ ) 2

[2-135]

The SRF is effectively based on the implication that the suspension solidosity is zero, so that the (pre-formed) cake is not growing: αSRF ~ αm for φ0 / φ [934, 1039, 1040].

The solids diffusivity can be calculated using the derivative py′(φ) directly, as in the definition (equation 2-63), which requires φ∞, or by three other avenues. The f i r s t alternative is obtained as the penultimate step in the derivation of equation 2-130 (which follows from the definition of D (φ), equation 2-63). The approximation is [606, 626]:

 dV 2   d −1   t d 1  1  c.f.   1   , − D (φ∞ ) ≈ φ  dφ∞ 2  0 φ∞ 

[2-136]

where again dV 2/dt is evaluated during cake formation, and the expected i n h e r e n t error is of order ±1%. This alternative also requires φ∞, and the numerical differentiation may not be as accurate as direct estimation from the definition [cf. 627]. The s e c o n d alternative arises from the limiting theoretical kinetics of cake compression as t → ∞. This involves fitting the parameters Ei in equation 2-125b. This allows estimation of the solids diffusivity using the definition of parameter E2 [606, 1063], viz. equation 2-127. R(φ∞) can be calculated in turn from the definition of D (φ∞) (equation 2-63).

150



In the t h i r d alternative a point estimate of D (φ∞) is iteratively improved [626]. The method is computationally more cumbersome, no more accurate than the foregoing techniques [see 626], and has not been widely implemented.

Nevertheless, it does avoid numerical

differentiation, which may be advantageous for noisy experimental data [cf. 626]. Details are in LANDMAN, STANKOVICH & WHITE’s paper [626].

2▪4▪6

Other continuum models

CONCHA & BÜRGER [274] have presented their own interpretation of phenomenological dewatering theory.

HARRIS,

SOMASUNDARAN

&

JENSEN

[450]

presented

a

set

of

“semi-empirical”

“phenomenological models” which were little more than fairly well fitting curves over short sections of the h(t) profile, providing negligible insight into the process.

LEE & WANG [642] reviewed the classes of typical dewatering models applied to filtration; these can be conveniently categorised according to the assumptions they rely on, aside from their conceptual approach (e.g. EULERian ‘spatial’ co-ordinates versus LAGRANGian ‘material’ co-ordinates) [see also 643, 1026, 1028]. In addition to the ‘conventional’ DARCY-style models and ‘diffusional’ LANDMAN–WHITEstyle models presented above, the third main category they identified was ‘multi-phase modelling’: details can be found in that reference [642] and the publications cited therein — largely due to WILLIS, TOSUN and co-workers. (TIEN [1027] includes the models of LANDMAN & WHITE and TOSUN in the single category of “continuum” or “multiphase flow” theory.) For a number of (simple) cases the various models produce equivalent results [642, 643, cf. 1026], provided that appropriate input parameter data is used.

2▪4▪7

Fundamental mechanistic theory

An alternative approach to empirical curve fitting or phenomenological theory is to consider the dewatering process on a microscopic scale and thence deduce the bulk material behaviour. (This is the converse of the philosophy adopted in this study, where results 2▪4 : Dewatering analysis

151

D. I. VERRELLI

obtained through application of phenomenological theory have been used to either affirm or oppose proposed microstructural mechanisms.) LEE & WANG [642] compared this approach to more traditional continuum-modelling approaches [see also 643, 1026]. The fundamental approach includes study of aggregate structure and fractal dimension (§R1▪5), and is well represented by the following quote from TAMBO & WATANABE [997]: In order to rationally design and operate chemical coagulation process followed by solid– liquid separation operations such as sedimentation and filtration, the physical properties of flocs such as their [effective] density and strength are the most important factors.

The i n h e r e n t disadvantage of a fundamental microscopic approach is the difficulty in making the link from the microscopic structure and behaviour to the bulk properties. (Of course, the converse also applies [83]!) The p r a c t i c a l disadvantage of microscopic modelling of particle mechanics [cf. 83] is seen in the following statement of LEE & WANG [642] referring to the application of filtration: Theoretically, information regarding the entire process can be obtained if the interactions between particles and medium are properly considered, including the compaction of cake [...].

However, for a simulated cake with, say, 10,000 particles, more than 60,000

differential equations are required to be simultaneously solved. If other factors are incorporated, such as [if] the particles exhibit an irregular shape or a highly porous interior such as in a floc, previous literature does not provide adequate information for [...] successful modeling [...].

Obviously, current research considers a number of simplifications to enable practical generation of numerical outputs. Existing formulations are unable to correctly predict dewatering behaviour based on modelling of interactions on the primary-particle level [e.g. 745].

An important branch of this research deals with the aggregation and fracture of aggregates in the presence or absence of an imposed shear field [e.g. 472]. A related approach is the simulation of individual particles as cellular automata [cf. 165, 906].

2▪4▪7▪1

Micromechanical dependence of yield stress on d0

In ‘model’ gels formed from aggregates of monodisperse primary particles the compressive yield stress has been found empirically to vary with the i n v e r s e s q u a r e o f p a r t i c l e 152



s i z e , that is py ∝ d0‒2, (in the range 1kPa < py < 10MPa) [745] — analogous to the behaviour of the shear yield stress, τy [605], and indeed the shear viscosity and shear modulus [371] *. (Alternative correlations suggesting py ∝ d‒3 [e.g. 241] or τy ∝ d0‒1 [897] are not as well supported by empirical evidence [but see 1069].) However, the gel point does not appear to be sensitive to particle size [745]. The ratio py / τy tends to vary in the range ≤10 † to 100 ‡ for the systems reported on in the literature [242, 243, 422, 425, 435, 447, 605, 609, 737, 927, 1098]. The proportionality py ∝ d0‒2 is consistent with certain theoretical developments relating the compressive [753, 845] and tensile [151, 875] s t r e n g t h s of a model a g g r e g a t e to d0‒2 §. (Although “numerous experimental results have shown that there is no simple correlation between tensile and compressive strength” [151].)

The proportionality arises from the

density of interparticle ‘bonds’ per (projected) s u r f a c e a r e a , under application of an arbitrary stress (e.g. uniaxial [875] or isotropic [753]). The agreement between the theoretical and empirical results is surprising considering that the theoretical developments insist upon several simplifications of the problem, including the random distribution of primary particles in an aggregate — whereas more realistic a g g r e g a t e models yield a f r a c t a l

*

FRANKS & JAILANI [371] proposed an explanation for this in which the shear yield stress was proportional to the product of bond strength and bond density: bond strength varies directly with particle diameter in the case of DLVO-type interactions [including the limit where VAN DER WAALS forces dominate], while the bond density was given as an inverse cube relation [cf. 860] — although this assumes n o n - f r a c t a l behaviour. The simplicity of this explanation promotes the universal applicability of the inverse square power, as indicated experimentally.

†

The low end of the range may be less than 10, as the data is based on apparent overestimation of py [see 738]. [Cf. 425, 558.]

‡

Even larger values of the ratio have been suggested [211, 928]; there may be a tendency for the ratio to increase as close packing is approached [e.g. 422, 425, 435, 609, 927], although SHIN & DICK [928] estimated the opposite trend for a lime–softening WTP sludge.

§

If the interparticle bonding force is a (power-law) function of particle size, then the stated proportionality can differ significantly [e.g. 616]. KENDALL [561] also demonstrated that RUMPF’s theory does not correctly predict the tensile failure of agglomerates that contain physical defects, which can initiate cracks: the analysis is apparently less relevant to compression — perhaps because compression tends to ‘homogenise’ the agglomerate structure, so that initial yielding (before ‘ultimate’ failure) may close up cracks [cf. 151], destroy large aggregate structures, et cetera.


153

D. I. VERRELLI

structure * (§R1▪5). Fractal scaling has been applied in a limited way to obtain the (initial) “dominant structural correlation length”, which essentially corresponds to dagg, presented as directly proportional to d0 [386]. Cf. §R1▪4▪4▪3(b).

Early discussion in the literature speculated about the need for partial cementation of primary particles to be overcome, and on a possible resistance to particles “sliding over each other” (i.e. friction) [375]. Recent microscale experiments by FURST & PANTINA (2007) [386] indicate that aggregate interparticle ‘bonds’ may fail by exceeding a critical bending moment of the ‘bond’, Mc, which is proportional to the contact area (Mc ∝ dbond2). This is consistent with the critical moment arising from a static friction mechanism (rather than rolling friction, for which (Mc ∝ dbond3) [386]. Assuming that externally applied (normal) force is negligible compared to the surface adhesion force †, the ‘bond’ contact area is in turn related to the (primary) particle size as dbond ∝ d02/3 (for equal-sized particles ‡) [386, 532, 814]. The correlation and theoretical derivations are summarised by [386]:

*

In a limited sense the large-scale structure of a particulate b e d may more nearly approximate random packing, viz. with respect to the erstwhile aggregates [cf. 386, 844, 845, 967]. And perhaps with respect to smaller and smaller clusters as deformation proceeds. However, this argument suggests a scaling as a function of dagg, or dclus, n o t d0. The desired model could only be recovered if dagg and dclus both scaled with d0, which is a petitio principii. Alternatively, the co-ordination number [151, 217, 733] may have more influence on the strength.

†

This assumption is likely to hold for submicron particles (or radii of curvature) for the solids found in the present work, except possibly at the highest compressive stresses (i.e. pressures) [532] — the latter especially considering that the ‘superficial’ applied stress will not be distributed uniformly across the (solid) material at a given cross-section. When applied forces are dominant, the contact area will be independent of the particle size, but will scale with the one-third power of the external force [532].

‡

Where the particles sizes are very different, the scaling is expected to follow the diameter of the smaller particle [cf. 532]. The compressibility of bidisperse mixtures of particles seems to scale roughly with the surface area fraction of each component [860]. Aggregates from these mixtures also tend to have large resistances to dewatering [860]; presumably this is due to the reduction in pore size — i.e. the interstitial lengthscale.

154



d −2 F ∝ d0 −1  0 −3 tensile ∝ d0 −1 d M τy ∝  0 −3 c −5 / 3 d0 M c ∝ d0  d0 − 2 

for tensile failure for bending failure with rolling friction mechanism

 for bending failure with static friction mechanism experiment 

.[2-137]

(Note that here bending failure, rather than tensile failure, is more pertinent to compressive loads, as it is expected that the bonds will fail as interparticle contacts slip (or roll).)

Although earlier correlations were fitted to τy ∝ d0‒2, FURST & PANTINA [386] demonstrated that the same data is just as well fitted by a correlation τy ∝ d0‒5/3. Given the empirical similarity of the correlations of τy and py with d0, the small difference between exponents ‒5/3 and ‒2 in view of experimental uncertainty, and the common failure through shear of materials under a uniaxial external load (see §9▪4▪2), it is plausible that also py ∝ d0‒5/3. VAN DE VEN & HUNTER [1069] reported a correlation τy ∝ d0‒1 for aggregate breakup in a shear field. They modelled this as a tensile failure process [1069], which is consistent with the foregoing discussion.

At low solidosity the main route by which primary particle size (and shape) influences dewatering is through its effect on the strength of aggregation [416] (cf. the equation for VAN DER

WAALS interaction potential: §S17▪1). It is only at higher solidosity that any aggregate

structures are likely to have been disrupted and that the primary particles can g e n e r a l l y be assumed to ‘directly’ control dewatering [416].

2▪4▪8

Stochastic analysis

One final branch of dewatering theory is s t o c h a s t i c m o d e l l i n g . This approach has received less attention than other methods described, but is nonetheless important and conveys certain advantages in analysing settling and thickening problems. TORY [see 1049] presents a concise review, and an outline is provided in §S5.


155

3.

EXPERIMENTAL METHODS Studies have indicated that natural variations in characteristics of a particular sludge are significant and that it is important to utilise laboratory data on sludge characteristics and/or pilot trials when assessing an appropriate dewatering method (Young, 1968). — OGILVIE (1997) [797, citing 1139]

[...] there is no such thing as a typical WTP. There is likewise no such thing as a typical water plant residual. — CORNWELL (2006) [282]

3▪1

Treatment parameters

The primary motivation for this study is to determine the impact of changes in typical WTP coagulation, flocculation and sludge processing conditions. Considerable diversity exists in the operation of different WTP’s, and conditions also fluctuate — to a lesser extent — over time at each individual WTP. One study option was to source plant sludge samples from a multitude of WTP’s. This was not considered practical for logistical reasons. Furthermore, it would be difficult to isolate the influence of particular operational variables. By generating sludge in the laboratory from real ‘raw water’ an optimum compromise was reached, in which individual process parameters could be varied while the remaining parameters were fixed (or at least well characterised). Moreover, this approach permitted the investigation of ‘limiting’ conditions that would not be feasible on real WTP’s.

157

D. I. VERRELLI

Dose [mg(Al)/L]

1000

Lab. alum coagulation Lab. alum coloured (dMIEX) Lab. alum aged Lab. alum sheared Lab. alum flocculation Lab. alum conditioned Plant alum Winneke Plant alum Happy Valley Plant alum Happy Valley PAC Plant alum freeze–thaw

100

10

1 4.0

5.0

6.0

7.0

8.0

9.0

10.0

pH [–] Figure 3-1: Range of alum sludges characterised. The settled sludge that was “conditioned” with polymer was also characterised after exposure to the shear only (same pH and dose).

The main sludge generation parameters investigated were: • Coagulant type (aluminium, iron, or magnesium salt) • Coagulant dose • Coagulation pH • Raw water ‘quality’ (chiefly colour and DOC) • Coagulation shear conditions • Addition of flocculant (polymer) • Addition of powdered activated carbon (‘PAC’)

158

Chapter 3 : Experimental Methods


Dose [mg(Fe)/L]

1000

Lab. ferric coagulation Lab. ferric aged Plant ferric Macarthur Plant ferric aged Plant ferric freeze–thaw

100

10

1 4.0

5.0

6.0

7.0

8.0

9.0

10.0

pH [–] Figure 3-2: Range of ferric sludges characterised.

A number of other parameters were also varied relating to the settled sludge: • Shearing • Polymer conditioning • Freeze–thaw conditioning • Ageing

3▪1 : Treatment parameters

159

D. I. VERRELLI

1000

100

Dose [mg/L]

10

1

0.1

0.01

Lab. Al

Lab Fe

Plant Al

Plant Fe

Al solubility

Fe solubility

0.001 4.0

6.0

8.0

10.0

12.0

pH [–] Figure 3-3:

Location of alum and ferric sludge generation conditions with respect to the

aluminium and iron(III) solubility curves. “Plant Al” includes the pilot plant sludges.

Results obtained from the laboratory-generated sludge were compared with plant and pilot plant samples to confirm both the magnitude of the dewaterability parameters (py and R) and any major trends. Somewhat ironically, certain plant and pilot plant samples covered conditions that could not quite be duplicated in the laboratory for practical reasons. The prime examples of this were both due to the necessity to treat a large volume of raw water (of order 102L) to generate a sufficient quantity of sludge to characterise: namely the ‘practical minimum’ coagulant dose and the ‘quality’ of the raw water.

160



The foregoing charts provide a useful overview of the range of sludges characterised (Figure 3-1 and Figure 3-2) and their relationship to the relevant solubility curves (Figure 3-3, cf.

§R1▪2▪3). A single magnesium sludge was also characterised that is not shown on these charts (see §5▪11).

3▪2 3▪2▪1

Experimental materials Purified water

Chemicals were diluted or made up with purified water obtained from an Elix 3 unit (Millipore, U.S.A.), which comprises three main treatment steps: • pre-filtration and activated carbon adsorption • deionisation • reverse osmosis.

3▪2▪2

Raw water

Raw water was sourced from Sugarloaf Reservoir, through the Winneke Water Treatment Plant, Victoria, Australia. Sugarloaf Reservoir is a 96GL raw water storage about 30km north east of Melbourne, completed in 1981 [45]. Water is taken from the Yarra River (at Yering Gorge) and Maroondah Reservoir (via the Maroondah Aqueduct) [45]. Although almost all of Melbourne’s water comes from protected catchments, the water entering Sugarloaf Reservoir is an exception [51]. Since river water has been introduced, the colour of the incoming raw water has increased to 60mg/L Pt units, compared to the previous average of around 25mg/L Pt units.

Abstraction from Sugarloaf Reservoir is from 30m above the bottom. Water is treated in Winneke Water Treatment Plant (commissioned November 1980 [51]), and supplied to the northern, western, and inner suburbs [45], comprising about 10% up to 20% (in peak summer

3▪2 : Experimental materials

161

D. I. VERRELLI

periods) of total demand for Melbourne [51] *. Current operation is high throughput in winter and low throughput in summer, which is the reverse of previous operation.

Key water quality variables are given for each sludge sample in the relevant section. An indication of the ranges of these variables is given in Table 3-1.

Table 3-1: Water quality variables for Winneke raw water as sampled or as received. Statistics are weighted by the actual number of sludges characterised for the given raw water.

Parameter

Minimum

Median

Maximum

Standard deviation

True colour

[mg/L Pt units]

4

11

42

7.4

A254nm

[10/m]

0.31

0.73

1.83

0.30

Turbidity

[NTU]

0.6

1.5

7.0

1.4

[mg/kg]

50

65

85

14

Dissolved solids a Note

a

Measurements of total solids are included, as suspended solids were negligible.

The turbidity readings do not seem to be as useful as the other measures. For example, they did not obviously correlate with the dissolved solids.

A more detailed chemical analysis of a Winneke raw water sample is presented in Table 3-2. The sample was raw water collected 2003-09-22, which was both the most highly coloured and most turbid sample collected. Analysis was carried out by analytical chemist ERNEST H. GUTSA using a PerkinElmer (U.S.A.) inductively-coupled plasma discharge optical emission spectrometer (ICP-OES). In several cases elemental species were below the detection limit. The other samples of raw water collected are expected to contain concentrations less than or equal to those presented here.

*

Output on 04 August 2003 was of order 360ML/d, supplying around 30% of Melbourne’s drinking water demand.

162



Table 3-2: Analysis of Winneke raw water. Outstanding values in bold type.

Concentration detected

ADWG(2004) [34] guideline value a

[mg/L]

[mg/L]

Aluminium

0.846

(0.2mg/L acid-soluble) b

Antimony

< 0.01

0.003

Arsenic

< 0.01

0.007

Barium

< 0.01

0.7

0.03

4

< 0.01

0.002

Calcium

3.22

(200mg/L as CaCO3)

Chrome

< 0.01

(0.05mg/L chromium, as Cr(VI))

Cobalt

< 0.01

N/A

Copper

0.018

1

Iron

0.376

0.3

Lead

< 0.01

0.01

Magnesium

2.9

(200mg/L as CaCO3)

Manganese

< 0.01

0.1

Mercury

< 0.01

0.001

Nickel

< 0.01

0.02

Phosphorus

< 0.01

N/A

Potassium

1.32

(as TDS)

Selenium

< 0.01

0.01

Silicon

3.31

N/A

Silver

< 0.01

0.1

12.8

180

< 0.01

N/A

1.43

(0.05mg/L as HS, 250mg/L as SO42‒)

< 0.01

3

Elemental species

Boron Cadmium

Sodium Strontium Sulfur Zinc Notes: b

a

Lower of ADWG health and æsthetic guideline values quoted, where both are defined.

“[Æsthetic g]uideline value based on post-flocculation problems; <0.1mg/L desirable. Lower levels needed for

renal dialysis.” [34] The N.Z. Standards [43] list an æsthetic Guideline Value of 0.1mg/L for “aluminium” to avoid “complaints [that] may arise due to depositions or discoloration”.


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D. I. VERRELLI

Table 3-2 shows that only the values for aluminium and iron are outstanding. In fact, the

guideline values quoted are essentially æsthetic guideline values (no general health guideline values are given) — the detected concentrations are not concerning. It is worth emphasising that the analysis was performed on raw water (i.e. prior to any processing, aside from residence in the reservoir), while the Australian Drinking Water Guidelines [34] pertain to drinking water (i.e. treated water). These do not differ greatly from the WHO guidelines [59], or other well-known guidelines [cf. 43].

3▪2▪3

Coagulants

The coagulants used to generate the characterised sludge samples in the laboratory were [cf. 28, 557]: • Aluminium sulfate (as Al2(SO4)3·18H2O) — “alum” — diluted to 1 and 10g(Al)/L. • Ferric chloride (as FeCl3·6H2O), at 2 and 20mg(Fe)/L. • Magnesium sulfate (as MgSO4·7H2O), at 10g(Mg)/L. All were of analytical grade. All solutions were made up with purified water. It is assumed that the coagulation process will not be sensitive to the concentration of stock solution [e.g. 300].

It may be noted that the Fe concentrations are double the mass concentrations of aluminium: that is because the relative molar mass of iron is approximately double that of aluminium, so this maintains a similar molar concentration.

Iron and its (oxy)hydroxides are also

considerably denser solid phases than aluminium and its (oxy)hydroxides (see §4▪1▪2).

3▪2▪3▪1

Magnesium

In the case of magnesium a number of other solutions were made up in preliminary experimental work (‘jar testing’): • Magnesium sulfate (MgSO4·7H2O), at 0.2g(Mg)/L in purified water. • Light basic magnesium carbonate (3MgCO3·Mg(OH)2·3H2O) o at 0.1mg(Mg)/L in purified water, 164



o at 10mg(Mg)/L in 0.001M hydrochloric acid (HCl), and o at 7.35mg(Mg)/L in 1.0M hydrochloric acid (HCl).

Acid was added to the light basic magnesium carbonate solutions in order to aid dissolution. Full dissolution of this material was achieved only in the 1.0M acid solution. Table 3-3 allows comparison of the effectiveness of the various formulations.

Table 3-3:

Preliminary ‘jar testing’ coagulation experiments with various magnesium

formulations.

Formulation Magnesium phase used

3MgCO3·Mg(OH)2·3H2O

Dilution with

MgSO4·7H2O

0 and 0.001M HCl

1.0M HCl

Purified water

2.0 to 80

4.6 to 46

2.0 to 80

11.0 to 11.1

11.0 to 11.1

11.0 to 11.1

Coagulation conditions Dose

[mg(Mg)/L]

pH

[–]

Raw water properties True colour

[mg/L Pt units]

20

A254nm

[10/m]

0.98

Turbidity

[NTU]

2.4

[mS/m]

9.5

Conductivity

Supernatant properties True colour

[mg/L Pt units]

4 to 7

2 to 10

2 to 6

A254nm

[10/m]

0.31 to 0.45

0.27 to 0.67

0.20 to 0.39

Turbidity

[NTU]

0.8 to 2.6

2.1 to 3.5

1.0 to 1.4

[mS/m]

2.7 to 2.9

3.9 to 9.4

2.5 to 7.9

Conductivity

The data in Table 3-3 indicates that the near-neutral magnesium carbonate formulation performed poorly as a coagulant. For this formulation much of the magnesium species were already present as a solid phase when dosed into the raw water. Acidifying the magnesium carbonate helped dissolve the magnesium, so that ions were available to attach to raw water organic matter and precipitate. The treatment effectiveness


165

D. I. VERRELLI

was still somewhat inferior to the magnesium sulfate formulation.

Furthermore, the

efficiency of using a highly acidified formulation is expected to be low, as considerably higher doses of alkali are required to attain the desired coagulation pH (approximately 11.0) and bring about precipitation. Although pioneering work on magnesium coagulants emphasised the use of various magnesium carbonate species, based on the foregoing preliminary work it was decided to generate the sludge using magnesium sulfate. This is expected to also be more directly comparable with the action of aluminium sulfate than a magnesium carbonate coagulant would be.

3▪2▪4

Alkali

Analytical grade sodium hydroxide (NaOH) was diluted with appropriate quantities of deionised water to produce solutions of concentration 0.2 and 1.0M. In the initial jar testing procedure this base was added to the raw water first, followed by the coagulant (i.e. aluminium sulfate). However, based on industrial practice [e.g. 436] [cf. 229], the order of addition was reversed, such that the sodium hydroxide truly acted to ‘correct’ the low pH reached following addition of coagulant [see also 300, 503].

The volume of coagulant and alkali added to each tank typically yielded a volume change of order 1% [cf. 557], which was assumed negligible.

3▪2▪4▪1

Hydrolysis ratio

The hydrolysis ratio * is deemed to be the molar ratio [OH‒]added / [Al], or [OH‒]added / [Fe] et cetera, depending upon the coagulant. Dedicated experimental investigations relying on this parameter would be conducted using purified water. Given that raw water is here the medium, additional effects due to alkalinity (buffering capacity) [see 219], ionisation of CO2

*

LIVAGE [675] describes [OH‒] / [Al] as the hydroxylation ratio (of the solution), and defines the hydrolysis ratio with respect to the actual extent of the deprotonation of the co-ordinated H2O species (of the metal ions) [see also 674] [cf. 677].

166



[219, 662], hardness, and natural metal content could potentially come into play; these are ignored in the present work [cf. 767]. This may be justified to some extent by the natural softness, low alkalinity and low metal content (cf. Table 3-2) of Melbourne’s raw water. To provide an overview, Figure 3-4 presents the experimental hydrolysis ratios — as defined — for alum coagulation in the present work. Contours have been interpolated * from the experimental data points. An indicative boundary between fast and slow coagulation, 2.7 [146, 148, 500, 978, 1100] [cf. 182, 184, 279, 573, 1008] [see also 389, 466, 538], is highlighted.

100

2.7

2.5

3.0 3.5

Dose [mg(Al)/L]

2.0 4.0 1.5

10 4.5

1.0

5.0

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 3-4: Experimental hydrolysis ratios for alum coagulation, [OH–]added / [Al]. The solubility envelope is indicated by the dashed lines.

*

Technical details are given in §5▪5.


167

D. I. VERRELLI

3▪2▪5

Polymers

Two commercial flocculants were obtained from Ciba Specialty Chemicals (Australia): • Zetag 7623 — a cationic random copolymer of 2-propenamide (‘acrylamide’, CH2=CH– CONH2) and a quaternary ammonium salt * [134]; approximately 10% charged, and with a “very high” molecular mass. • Magnafloc 338 — an anionic random copolymer of 2-propenamide and sodium 2propenoate (‘sodium acrylate’, CH2=CH–COO‒ Na+) [134];

approximately 10%

charged, and with an estimated molecular mass of 15 to 20×106g/mol [134].

Their preparation is described in §7▪3▪1 and §7▪4▪1▪1.

3▪2▪6 3▪2▪6▪1

Plant and pilot plant sludges Winneke

A number of WTP sludge samples were also collected at Winneke WTP. The raw water source for this plant was detailed in §3▪2▪2.

This plant runs a conventional a l u m

coagulation process. Incoming water is aerated prior to coagulation with alum solution of specific gravity ~1.3, made up at 48%m of Al2(SO4)3·14.3H2O [522]. Rapid mixing of the alum is attained through rapid flow of water over a weir and through a channel at right angles.

The alum dose on 2003-08-04 was recorded as 14.6±0.7mg(alum)/L ≈ 1.31±0.06mg(Al)/L, giving an associated pH change from 6.7 to 5.5 [522]. Samples collected on later dates tended to have somewhat higher doses but were not recorded as becoming as acidic.

The clarifiers are square, raked basins of depth approximately 6m at the sides and 8m at the centre. Flocculant Magnafloc LT-22 is added to the coagulated water at this point. LT-22 is a

*

N,N,N-trimethyl-2-[(1-oxo-2-propenyl)oxy]-ethanaminium chloride (‘acryloyloxyethyltrimethylammonium chloride’, CH2–CO–O–CH2–CH2–N+(CH3)2 Cl‒) [134, cf. 171].

168



long-chain, cationic polymer *. The LT refers to ‘low toxicity’, chiefly low concentrations of acrylates. Typical doses are 0.02 to 0.04mg/L [522], e.g. ~0.02mg/L on 2003-08-04 [522]. The clarifiers are run with a layer of sludge at the bottom, a ‘sludge blanket’ of about 0.5m depth [cf. 1032]. The rake operates just above the bottom of the basin, and rotates in union with a mixer that distributes the incoming water. There is an optimum speed to ensure sufficient mixing without breaking the flocs.

Overflow from the clarifiers makes its way to dual media gravity filter beds. These are backwashed relatively frequently: every 24h. Clean backwash and the initial filtered water divert is sent back to the head of the reservoir.

Due to the periodic nature of desludging operations, sludge flow is directed initially to a sludge surge chamber. There is facility to thicken the sludge in a thickener, however this is bypassed, as sludge currently goes straight to sewer (see §1▪5▪3).

3▪2▪6▪2

Macarthur

Macarthur Water Filtration Plant (WFP) supplies drinking water to over 230 thousand people in the Campbelltown area in the south west of Sydney, N.S.W., Australia [46]. Macarthur WFP is located about 20km south of the Campbelltown CBD [717], and is operated by United Utilities Australia under contract for Sydney Water [cf. 47]. The average flow in 1998 was 100ML/d, with a design flow 280ML/d [717].

Water is sourced from four dams in the Upper Nepean hydrological catchment, Cataract, Cordeaux, Avon, and Nepean, with the latter three arriving via the Nepean Tunnel [50, 717]. This system may also be (indirectly) supplied by other sources, such as Wingecarribee [50]. The catchment covers 900km2 of mostly native bushland (around 90%) and is essentially closed [717]. A “snap shot” value of 3.3mg/L for dissolved organic carbon in the raw water was measured in early 2003 [252].

*

Copolymer of acrylamide and a quaternary acrylate salt.


169

D. I. VERRELLI

The treatment process is close to conventional. The two key distinguishing features are the coagulant (cf. §R1▪2) and the coagulation pH. F e r r i c c h l o r i d e is used as a coagulant, and the flocculation/coagulation pH is typically between 8.5 and 9.0. The high pH is specified to control manganese levels [cf. 578]. Hence the raw water is first pre-limed [717], which also boosts the raw water alkalinity. The previous configuration was to dose ferric followed by polymer. After external advice, this was swapped to the current configuration, viz. dosing of polymer followed by dosing of ferric. Any change appears to be marginal [254]. A polyDADMAC, Nalco 3265 (Nalco), is dosed at the head of the plant at about 0.80mg/L (as on 2005-03-23) to 2.75mg/L (as on 2005-09-21). Previously an “equivalent” product from another supplier was used (Magnafloc LT-35, Ciba Specialty Chemicals); this reportedly yielded higher supernatant quality and thinner sludge [254]. 0.02mg/L polyacrylamide (Magnafloc LT-20) is also dosed.

The typical ferric dose up to 2005-03-21 was 10 to 15mg/L (of 42% liquid) ≈ 0.87 to 1.30mg(Fe)/L. The range historically has been from 5 to 15mg/L (of 42% liquid) ≈ 0.43 to 1.30mg(Fe)/L. As with Winneke WTP, the actual doses of the samples collected were higher than this range — of order 2mg(Fe)/L.

A small amount of flocculant Magnafloc LT-20 (supplied by Ciba Specialty Chemicals) [or Nalco equivalent] is usually dosed into the thickener:

typically < 0.05mg/L (0.02mg/L).

However, on the sample collection dates no sludge conditioner was added.

Sludge is sent to eight drying beds, applied at a depth of 1.0 to 1.5m. Sludge dries by a combined mechanism of drainage and (in warm, dry weather) evaporation. It does not appear to ‘re-wet’ following rainfall events. The beds are filled on rotation in a 3 to 4 week cycle, and the sludge is thus allowed to dry for a period of approximately 8 months, which has been found to be “more than enough time” [254]. Underdrain from the beds is recycled back into the plant.

170



3▪2▪6▪3

Happy Valley

Four a l u m sludge samples were obtained from a pilot plant at Happy Valley (South Australia) operated by United Water International Pty. Ltd..

The Happy Valley Water Filtration Plant (WFP) is operated by United Water International on behalf of SA Water. Happy Valley WFP is located approximately 14km south of Adelaide, S.A., Australia, and is “by far” the largest of the six Adelaide WFP’s, with a capacity of 850ML/d [58], although it normally runs at flowrates of 200 to 500ML/d [60]. (The annual supply is of order 70GL [57].) Happy Valley WFP supplies drinking water to around 450 thousand people from Port Adelaide in the north, to Noarlunga in the south, and to Glen Osmond and Blackwood in the east [60]. This makes up around 40% of the Adelaide metropolitan region [30].

Water is sourced from Happy Valley Reservoir, which is an SA Water asset, of 11.6GL capacity [66].

The reservoir water originates primarily from the River Murray and is

supplemented by the Mt. Bold catchment [60], drawn from the Onkaparinga River [66]. Unlike Melbourne or Sydney, Adelaide raw water cannot be described as being derived from protected catchments.

The River Murray is “notoriously turbid” (at least in the more

downstream reaches, where Adelaide lies) — the influent to Happy Valley WFP averages 8 to 12NTU * [64] — and “many parts of Adelaide’s densely populated natural catchments have polluted waterways” [67]. Happy Valley raw water is also relatively highly coloured (a median of 61 Hazen units), with corresponding DOC (averaging 8 to 9mg/L [cf. 252, 778]) [64]. (The local catchment raw water tends to be more highly coloured than River Murray water [57].) The specific ultraviolet absorbance (SUVA254nm, see §R1▪1▪4▪2) is typically about 3.1L/mg.m [778].

Happy Valley WFP runs a sludge dewatering centrifuge along with a number of filter presses [57]. Sludge is pressed to a cake of 20% solids, and then transported to approved

*

LEHMANN & PALMER (1995) gave the median turbidity as 5NTU and median colour as 35 Hazen units [797].


171

D. I. VERRELLI

landfill sites [60]. A sludge drying stockpile has been constructed to allow efficient drying prior to disposal while containing run-off and leachate [57].

A pilot plant is operated in conjunction with the Australian Water Quality Centre (AWQC), which is a participant in the Cooperative Research Centre for Water Quality and Treatment (CRC-WQT), along with SA Water and United Water International. Samples settled for approximately one hour before collection.

The first three samples varied significantly only in their coagulant dose. These are described in §5▪6▪2.

The final sample was nominally algal;

significant proportion of PAC had been added.

however it was established that a

Details of the PAC-dosed sludge are

provided in §8▪3▪3.

3▪3

Sludge generation

This study aims to characterise the sludges arising from drinking water treatment, with special reference to their dewaterability. As such there are two main aspects that may be expected to control sludge properties, namely the conditions under which they were generated, and any subsequent handling or ‘conditioning’. It is important to have a reasonable understanding of the manner in which the sludges are produced industrially. Following on from this, sludge production in the laboratory should follow a comparable route. A key requirement for achieving this is accurate knowledge and control of the characteristic velocity gradient (§R1▪4▪1▪1), which will be the focus of the following discussion.

3▪3▪1

Industrial practice

Generation of WTP sludges was outlined in §1▪2, and pertinent background material is critically reviewed in Appendix R1. It is important to realise that there is no ‘normal’ industrial practice, as design and operation of each site is tailored to the local situation. Overviews of relevant plant and pilot plant configurations were presented in §3▪2▪6.

172



Two distinguishing features of industrial sludge generation are that it is a nominally continuous process, and is often complicated by ancillary operations.

Such operations

include the addition of various chemicals, such as in pre-oxidation, that are ‘extraneous’ to the purposes of the present discussion — although they could still ultimately affect the sludge properties. Sludge from a number of different sources is commonly combined on site.

A conventional WTP will generate sludge through sweep or enhanced coagulation, involving the addition of a coagulant and an alkali in close succession at the head of the plant. Polymers are often added shortly after in order to build larger or stronger flocs; further polymer may be added downstream for ‘conditioning’. A multitude of variations on this configuration exist, including sequential dosing of coagulant [e.g. 253, 272], or doublestep coagulation [272, 360];

such permutations are beyond the scope of the present

discussion. Throughout the coagulation–flocculation process the prevailing shear field is crucial to favourable treatment, as alluded to in §R1▪4 and §R1▪5. Once formed the aggregates go on a journey through the plant, from the clarifier to the thickener and so on, as they dewater to form the ‘sludge’. Shear is important here too (cf. §7).

3▪3▪2

Scaling by velocity gradient

Given that the sludges characterised in this study were predominantly generated in the laboratory, it was desired to find a means of selecting small-scale conditions that would correspond to full-scale operation.

The parameter of greatest concern was the mixing

intensity.

While agreeing with its application to flocculation (‘slow mixing’) AMIRTHARAJAH stated [754]: [...] the velocity gradient, or G-value, concept is a gross, simplistic, and totally inadequate parameter for design of rapid mixers.

3▪3 : Sludge generation

173

D. I. VERRELLI

According to this thinking, for rapid mixing the only basic design parameter is t i m e of mixing or dispersion [754]. Coagulants should be dispersed within fractions of a second, although industrial plants typically have mean residence times of seconds or even minutes in the ‘rapid mix’ chamber [754]. For the present work the rapid mixing and slow mixing stages were scaled in the same way, namely the mixing speed was adjusted to keep G constant while the time was unchanged. Based on real-time pH measurements (see Figure 3-8) it appears that the time for chemical dispersion is no more than 10s (cf. Table 3-5).

With regard to the slow mix speed, there are some concerns about dependence upon the ‘speed for just suspension’ [cf. 28, 199] condition: • the condition of maintaining particles in suspension is distinct from the suspending of settled particles [293]; • the speed will vary for different particle sizes, densities, aspect ratios, et cetera; • matching the criterion is subjective, and so degrades reproducibility; and • it cannot be used where vision is impaired, such as with opaque vessel walls [293].

3▪3▪2▪1

‘Standard’ tank configuration

Two key objectives in mixing are to achieve effective and efficient mixing, and to allow dimensional scaling. With these two motivations in mind, HOLLAND & CHAPMAN [485] presented their “Standard Tank Configuration”, which is a relatively simple design, readily implemented, which provides good, well-characterised mixing. As the power input, velocity field and characteristic velocity gradient are well-characterised, the configuration can readily be scaled to larger (or smaller) designs.

The set-up presented by HOLLAND & CHAPMAN [485] as the “Standard Tank Configuration” is actually not regularly referred to in the literature. However, although experimenters in the field do not adhere dogmatically to the proposed configuration, the configuration described does constitute an ‘average’ design, which may be recommended for general application [e.g. 144] [cf. 199]. 174



Table 3-4: Specifications for HOLLAND & CHAPMAN’s [485] ‘standard’ tank configuration.

Parameter

Arrangement

Vessel type

Upright, flat-bottomed, cylindrical tank

Tank dimensions a

Diameter

DT, the reference datum

Liquid level

Hl = DT

Height

HT > Hl (= DT)

Number of baffles b

nb = 4

Baffle width (radial dimension) c

Wb = DT / 10

Baffle height

Hb > Hl (= DT)

Clearance of baffle from wall of tank d

0

Agitator type

6-blade, disk-mounted flat-blade turbine, or i.e. RUSHTON turbine impeller

Impeller orientation

Top-entry, aligned with centreline of vessel

Impeller diameter e

Da = DT / 3

Clearance of impeller from bottom of tank f

Ha = Da (= DT / 3)

Impeller blade width (axial dimension)

q = Da / 5 (= DT / 15)

Impeller blade length (radial dimension)

r = Da / 4 (= DT / 12)

Length of each impeller blade that is s = r / 2 (= Da / 8 = DT / 24)

mounted on the central disk Hence, the diameter of the central disk

Ddisk = Da ‒ 2 s (= DT / 3 ‒ DT / 12 = DT / 4)

Impeller thickness (blade & disk) g

[Minimum for mechanical strength]

Alternative general recommendations: a

0.75 DT ≤ HT ≤ 1.5 DT for top-entering impellers [293]. Hl ≤ 1.25 DT to avoid the need for multiple agitators [485].

b

4 ≤ nb ≤ 8 for salt solutions [683]. nb = 2 may be adequate [see 784].

c

0.10 DT ≤ Wb ≤ 0.20 DT [683]. DT / 12 ≤ Wb ≤ DT / 10 [293].

d

For suspensions DT / 50 is usual; up to DT / 20 is acceptable [784]. DT / 10 (= Wb) is typical [485] (cf. stators).

e

0.3 DT ≤ Da ≤ 0.6 DT [293]. Da ≥ 0.35 DT [557]. Da = 0.5 DT [774, 785].

f

Ha ≈ DT / 2 (= Da [774, 785]; = 1.5 Da [613, 980]). Ha = 0.18 DT for gas dispersion applications [199]. Often an

alternative definition for Ha is used, referenced to the centre of the impeller [e.g. 144, 199, 743, 784, 980] [cf. 962]. g

Da / 67 (= DT / 200 = Ddisk / 45) at a thickness of 1.5mm [808]. Da / 33 (= DT / 100) at 1 to 3mm, and same for baffles

[743]. Da / 32 (= DT / 93 = Ddisk / 19) at 3.2mm [980].


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D. I. VERRELLI

Wb

r

DT

s TOP VIEW

Wb

q

Da

Hl

Ha

SIDE VIEW

Figure 3-5: Schematic of HOLLAND & CHAPMAN’s [485] ‘standard’ tank configuration.

Other specialised mixing designs will be more appropriate than the ‘standard’ tank configuration in certain specific applications, including the mixing of liquids with [485] : • a “high” solids content; • a “high” viscosity; or • a shear-sensitive character.

Details of the ‘standard’ tank configuration are provided in Table 3-4, and it is depicted diagrammatically in Figure 3-5.

176



Further detailed design issues to be considered are chemical feed and baffle–wall clearance.

The effect of introducing reagent to a stirred vessel is sensitive to the location of the feed point [293]. Hence, this must be controlled to allow reproducibility. It has been suggested that if powders are to be added, then they should be fed to the “shoulder” of a vortex created by stirring the water, to avoid collection of the powder on the surface [28]. In the present work chemicals were added roughly midway between the impeller shaft and the wall of the vessel, although powders were not added and the tank was baffled (suppressing vortex formation). The fully-baffled case is preferred, as vortex formation can induce mechanical vibration, reduce top-to-bottom mixing, and promote air entrainment [808].

Although the ‘standard’ tank configuration has baffles abutting the vessel wall, it is common practice for viscous fluids and for fluids containing particles that the baffles be positioned away from the wall [485, 784], to avoid the formation of ‘dead’ zones which mix poorly and where particles may accumulate. Some consideration may have to be given to the extent to which a small clearance between the baffle and the vessel wall, as described, would act as a high shear orifice, ‘pinching’ the flow and possibly damaging flocs. From the point of view of practicality, both metal frameworks, which leave some wall clearance, and ‘cement’ (i.e. glue) have been used to install baffles into bench-top jar testing units by different researchers [485, 623]. In the present work a small gap, on the order of the thickness of the baffles, existed. There were no indications of undue particle accumulation or other problems.


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D. I. VERRELLI

3▪3▪3

Jar test rig (optimal dose selection) The jar test is a valuable tool for empirically resolving the many complexities of coagulation for a given situation. — JOHNSON & AMIRTHARAJAH (1983) [533]

The utility of the jar test is well established. However it does not provide adequate insight into floc character.

Indeed, there are considerable

dangers in using jar test data to draw wider conclusions about the coagulation process in the absence of other information. — BACHE et alia (1999) [113]

A custom-built, six-gang ‘jar test rig’ was used for small-scale preliminary investigations, typically to establish optimal dose and pH conditions and to estimate sludge production under given conditions [see e.g. 503]. A qualitative analysis of sludge properties was also possible.

3▪3▪3▪1

Mechanical construction and operation

Despite the existence of at least one standard [viz. 28] relating to jar testing for drinking water treatment studies, in practice a multitude of variations exist [283, 518]. These may be guided at the national, test-rig manufacturer, water utility, site, or even operator level. The jar testing procedure that is employed will depend upon what full-scale unit operations the results will be applied to, as it is intended to mimic the actual coagulation and flocculation operation. This means that comparisons between rigs may not be valid — although normally jar testing is undertaken for site-specific investigations only.

The jar testing procedure adopted is based primarily on ASTM D 2035 [28] as follows:

178



1.

Measure the initial temperature, pH and conductivity of the sample, and set aside portions for analyses of TSS and turbidity (unfiltered), TDS and true colour (filtered), et cetera.

2.

Commence the ‘rapid mix’ stage.

3.

Add the various chemicals in the desired order. a.

Coagulant

b.

Alkali (after 1 minute)

c.

Flocculant, if desired (after a further 30 seconds)

Maintain rapid mixing for 2 minutes after first chemical dosed. Record the pH at 10 second intervals. 4.

Reduce the speed of mixing for the ‘slow mix’ stage:

fast enough that the

aggregates remain uniformly suspended. Maintain for 20 minutes. a.

Record the time at which the first aggregates were observed.

b.

Periodically record the size of the aggregates.

Record the pH at 1 minute intervals. 5.

Once the slow mix stage is complete, observe the settling for about 20 minutes. (If the agitator will not impede settling, it may be left in place;

otherwise,

carefully withdraw it.) The rate can be indicated by either the thickness of the supernatant layer at a given time or the time taken for the turbid interface to drop to the bed at the base of the beaker. 6.

Record the final temperature, pH and conductivity of the sample, and set aside portions for analyses of turbidity (unfiltered), true colour (filtered) et cetera. The portions were withdrawn slowly using a wide-mouthed syringe from 5cm below the water surface after 5 minutes settling, or from 10cm below the water surface after 10 minutes settling.

7.

After settling overnight, remove a portion of supernatant for TSS and TDS analyses.

8.

Decant the settled sludge into smaller pots (~100 to 200mL). Allow to settle further overnight, then record final settled volume.

9.

Decant settled sludge from pots and dry in oven to measure approximate dry sludge mass generated.


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D. I. VERRELLI

In the present work a design based on the ‘standard’ tank configuration described in §3▪3▪2▪1 was adopted to enable scaling according to the velocity gradient. This was embodied in 1.6L samples of raw water held in baffled 2.0L round glass beakers (127mm diameter) mixed with centred RUSHTON turbine impellers mounted overhead. Four baffles were also installed. Parts were fabricated from 1.45mm-thick stainless steel.

The rapid mix speed was

approximately 300rpm and the slow mix speed 50rpm, which equate to characteristic velocity gradients of 241 and 12s‒1 respectively. Further details are presented in Table 3-5. Square jars were avoided as their more complex geometry would impede shear characterisation and hence scaling. Likewise, off-centre mounting of the impeller [as in 28] was avoided, as it would increase the required mixing time [784], promote erratic vortexing [293] and diminish reproducibility. Supernatant sampling as at point 6 of the procedure (p. 179) was specified based on a nominal clarification rate of 1cm/min, as in §S6▪1.

A survey of alternative physical configurations and operating protocols is presented in Appendix S6▪1.

3▪3▪3▪2

Identifying the optimum

Jar testing can be used to assess and optimise a multitude of treatment parameters [115], typically relating to the extent and rate of clarification [333] [cf. 191]. The general aims of coagulation in water treatment were given by EDZWALD & TOBIASON [335] as: 1) to maximize particle and turbidity removals by downstream solid–liquid separation, 2) to maximize TOC and DBP precursor removals, 3) to minimize residual coagulant, 4) to minimize sludge production, and 5) to minimize operating costs.

The optimum conditions for achieving each of these aims are frequently contradictory [e.g. 272, 339]. According to PAPAVASILOPOULOS & BACHE [815]: The precise nature of the optimum dosage is difficult to define because it tends to be linked to specific analytical techniques and their interpretation.

180



That is, optimum doses are operationally defined. A selection of implementations described in the literature is collected in Appendix S6▪2.

In the present work supernatant true colour was found to be the most useful routine measure of treatment efficacy, due to the low raw water turbidity.

The optimum was

assessed as the condition at which further variation of the manipulated variable did not yield a significant decrease in true colour. As the values are used in the present work only qualitatively, a precise mathematical definition is not necessary.

3▪3▪4

Tank

Experience with jar testing (§3▪3▪3) of 1 to 2L of raw water demonstrated that considerable volumes of raw water would need to be treated in order to generate sufficient sludge to permit complete dewaterability characterisation. The reason for this is that, on a mass basis, the raw water is relatively ‘clean’ (total dissolved solids fluctuated around 0.07±0.02mg/L for the Winneke WTP water, cf. Table 3-1; suspended solids were negligible), and the highest coagulant doses used in this study correspond to precipitate loadings of order 0.3g/L (cf. §4▪1▪1). However the characterisation proceeds to a quite concentrated phase in pressure filtration and centrifugation, such that 3g of dry solid material constitutes a bare minimum, and 5g is a more reasonable target. This generally provides sufficient material for at least gravity batch settling and the formation of two filter cakes of thickness 3mm or more (at 300kPa). (A priori estimates of the required raw water volume made based on literature reports were very unreliable, due largely to the uncertainty attached to the concentrations at which sludge volumes were reported.)

Taking into consideration the need to physically and manually manipulate the vessel chosen, and having regard for existing vessels available, a stainless steel tank of approximate capacity 53.5L was initially selected for further work on the larger scale (see Figure 3-6). The internal tank diameter was approximately 405mm. This tank was fitted with baffles in accordance with the ‘standard’ tank configuration, and a RUSHTON turbine impeller of


181

D. I. VERRELLI

corresponding dimensions was also fabricated from 3.0mm-thick stainless steel (see §3▪3▪2▪1). The impeller was constructed without a hub [cf. 199, 485, 980].

Figure 3-6: Large (53.5L) mixing vessel based on ‘standard’ tank configuration.

In order to further expedite the sludge generation process, seven straight-sided, flatbottomed plastic tanks were subsequently procured to replace the existing tank. Ancillaries were manufactured to enable nearly parallel processing in six of the tanks, with the seventh acting as a dedicated decanting/settling vessel. See Figure 3-7. The newer coagulation vessels were filled to a volume of approximately 48.4L, based on their slightly smaller diameter of 395mm. The existing baffles and RUSHTON turbine impeller were used, and the impeller speed settings were not changed (see Table 3-5) — at this size the effect of the volume change on mixing computations is marginal (of order 5%) [see also 199].

182



As explained in §R1▪4▪4▪2, holding the characteristic velocity gradient, G, constant (or, equivalently, the mean specific energy dissipation rate, ε ) is the most appropriate way to scale coagulation and flocculation processes.

Figure 3-7: Large-scale coagulation equipment. The tanks in the foreground are of 60L nominal volume (filled to 48.4L) each. The carboys in the background are of 20L nominal volume (filled to ~21.5L) each.

Table 3-5 shows a comparison of the various characteristics of the three vessels operating at

both the ‘fast’ and ‘slow’ mixing speeds. It is clear that while the characteristic velocity gradient has been maintained at approximately the same value for a given condition, other indicative variables, such as the REYNOLDS number, Re, change significantly. This is an unavoidable drawback of practical scale-up. It can also be seen that generally the aggregation mechanism is predicted to be p e r i k i n e t i c until the aggregates exceed 1μm in size. Thus only the larger features of aggregate structure are expected to be affected by G.


183

D. I. VERRELLI

Table 3-5: Scale-up of vessel mixing parameters. All used a RUSHTON turbine impeller.

Parameter

Rapid mixing stage Beaker

Density, ρL [kg/m3]

Slow mixing stage

Old tank New tank

Beaker

Old tank New tank

1000

1000

1000

1000

1000

1000

300

135

135

50

20

20

[1/s]

5

2.25

2.25

0.833

0.333

0.333

[mm]

127

405

395

127

405

395

Agitator diameter, Da [mm]

42.3

135

135

42.3

135

135

1

1

1

1

1

1

Stirring rate, N

[rpm]

Vessel diameter, DT

Liquid viscosity, ηL

[mPa.s]

REYNOLDS number, Re

[–]

8,946

41,006

41,006

1,491

6,075

6,075

(FROUDE number)y, Fry

[–] a

1

1

1

1

1

1

[–]

5.5

6.1

6.1

3

5.2

5.2

[W]

0.093

3.1

3.1

0.00024

0.0086

0.0086

[L]

1.6

53.5

48.4

1.6

53.5

48.4

dissipation rate, ε [mW/kg]

58.2

58.2

64.4

0.147

0.161

0.178

[1/s]

241

241

254

12.1

12.7

13.4

[m/s]

0.66

0.95

0.95

0.11

0.14

0.14

[s]

4

10

9

25

65

59

dKolmogorov c

[μm]

64

64

63

(287)

281

274

d / Pé 1/3 at 293K d

[μm]

0.19

0.19

0.19

0.52

0.51

0.50

Power number, Po Power, P Volume, V Mean specific energy

Characteristic velocity gradient, G Tip speed, vtip Mean circulation time b

Notes a

It has been assumed that the effect of the FROUDE number is negligible (as in the fully baffled case [485]).

b

Indicative value calculated from V / (Da3 N) — see §R1▪4▪4▪1, p. 723.

c

Only values for turbulent flow are physically meaningful.

d

For Pé = 1, require d e q u a l to this value; For Pé = 1000, require d t e n t i m e s l a r g e r than this value.

The aggregates generated were allowed to settle overnight to form a thin sediment. This sludge was decanted to a smaller vessel, and again allowed to settle; if necessary, this was repeated once or twice more. For the lowest coagulant doses, up to 11 batches (532L) were 184



combined in order to collect sufficient settled sludge (minimum 500mL, approximately 5g of dry solids) for characterisation.

3▪3▪5

Reproducibility

Good reproducibility was obtained, as indicated by repeatable supernatant quality for given treatment conditions — in both jar testing and tank testing — and agreement in the dewatering properties of replicate sludge samples, as presented in §3▪5▪4.

3▪3▪6

pH

Measurement of pH was carried out using Sensorex (U.S.A.) S200C combination pH probes with a Radiometer (Copenhagen) PHM92 meter; this was calibrated periodically. The pH varies significantly during the course of treatment: initially near-neutral, it falls to ~4 upon coagulant addition, and then is raised again when alkali is added. pH values were manually recorded every 10s for the 2min rapid mixing stage, every 1min during the following 20min of slow mixing, and finally each 5min during the 5 to 10min of settling. The value reported as “coagulation pH” was an indicative average for the slow mixing period, once it had more or less stabilised [cf. 300, 331, 1017]. The variation during this period was generally within ±0.1. The transient pH profiles are illustrated in Figure 3-8 for five different coagulations at 80mg(Fe)/L. The slightly discordant early behaviour of the pH 6.2 batch is likely to be an artefact of the alkali dosing location relative to the pH probe.


185

D. I. VERRELLI

9.00

8.00

pH [–]

7.00

6.00 Nominal pH

5.00

7.3 6.2 6.1 6.0 5.6

4.00

3.00 0:00

5:00

10:00

15:00

±0.1 ±0.1 ±0.1 ±0.1 ±0.1

20:00

Time, t [min:s] Figure 3-8: Transient pH profiles for five consecutive ferric treatments at 80mg(Fe)/L carried out on Winneke raw water collected 2004-09-15.

3▪4

Treatment characterisation

In order to verify the practicality of a given set of water treatment parameters (dose, pH, et cetera), the quality of the supernatant was in each case given a basic assessment, comprising the measurements described in the following.

3▪4▪1

Absorbance

The light absorbance spectra of raw and treated waters are of interest for two main reasons, being the direct measurement of visible colouration and the indirect (i.e. surrogate) measurement of the NOM concentration. Principles of light absorbance are summarised in Appendix S7▪1.

186



3▪4▪1▪1

Procedure

Measurements were made on a Varian Australia Cary 1E dual-beam UV–visible spectrophotometer. Changeover of lamp source was made at 350nm. Matched 100mm silica (quartz) glass cuvettes were used to enhance precision [cf. 334]. Absorbance scans were carried out from 750nm to 200nm in 1nm steps, with SBW = 2nm (at λ = 656.1nm [421]), at a rather slow rate of 0.5s/interval. This rate was chosen to maximise the number of sensor readings (15 [cf. 421]) averaged at each wavelength to make up the reported measurements. The “baseline” characteristics of the instrument and cuvettes may be obtained by running a scan with reference material (i.e. purified water) in both cuvettes.

Any (significant)

difference may be accounted for when reporting sample absorbances from subsequent runs. Samples were filtered with a 0.45μm syringe filter — typically a Sartorius Minisart 16555K unit with a 26.0mm diameter surfactant-free cellulose acetate (SFCA) membrane — prior to analysis [cf. 290, 334]. (Filtration efficacy can be verified from the absorbance scan, as only particulates tend to yield significant absorbance at wavelengths above ~700nm [290].) A detailed discussion is presented in §S9▪2.

The general procedure for making a series of measurements on the instrument is as follows: 1.

Allow ~1h for the lamps to warm up. Samples are at room temperature [334].

2.

Rinse and fill both cuvettes with the reference substance — a.

zero the instrument (at 750nm), insert the cuvettes, and create a baseline * or

b. 3.

recall a saved baseline, insert the cuvettes, and run a scan for verification.

Empty ‘sample’ cuvette; rinse out twice with sample [334] and fill with fresh sample; replace in holder; scan. Repeat for next sample.

*

The baseline (100% transmission) was applied to raw transmission values, such that ⇔

Treported = Traw / Tbaseline

Areported = Araw − Abaseline .

Another option is to correct for both 0% transmission (i.e. 100% absorbance) and 100% transmission:

Treported =

Traw − T0% Tbaseline − T0%

.

See §S7▪1 for an explanation of the terms.

3▪4 : Treatment characterisation

187

D. I. VERRELLI

It is important that the cuvettes be clean, so that surface contamination does not corrupt the observed spectra.

Various cleaning regimens apply, depending upon the degree of

contamination, involving (in order of increasing rigour) [451, 474]: 1.

purified water;

2.

ethanol or acetone; methanol or propan-2-ol;

3.

concentrated acid or hot surfactant solution;

4.

concentrated alkali.

Sonication may also be performed.

In practice it was found that contamination was minimised by rinsing the cuvettes well with purified water after use.

Additionally, the reference and sample cuvettes were never

interchanged.

3▪4▪1▪2

Spectra

It is often advisable to obtain full absorbance spectra in order to ensure that no unexpected features (e.g. peaks, noise) are present, and to characterise the region around wavelengths of interest (e.g. peak width). Correlations can also be determined, as shown in §S7▪1.

3▪4▪1▪3

Single wavelengths

Where the interest is on the a m o u n t of organic colour-causing components present, rather than the colour itself, ultraviolet (UV) absorbance measurements are often made.

It is

“generally accepted” that this UV absorbance is caused “primarily” by aromatic structures [553]. There are a few organic compounds that do not absorb light at 254nm [252, 553, 647]. The colour-causing components — humates, lignins, iron and manganese salts, et cetera — have higher absorbances at lower wavelengths [290], so absorbance measurements made at lower wavelengths are more sensitive to the presence of these components. For this reason a wavelength of < 400nm is used for UV absorbance measurements. Wavelengths lower than 200nm are generally unsuitable due to problems with absorption by the sample cell [318]. 188



While some species other than NOM will absorb ultraviolet light, “[m]any natural waters and waters processed in drinking water treatment plants have been shown to be free of these interferences” [334].

Such interferences can, in any case, generally be identified by

performing an absorbance scan [334]. The wavelength most commonly used in practice is 253.7nm (often rounded to 254nm) [334, 553, 597, 647, 657], which is an expedient value derived from the peak emission from a mercury lamp [334, 553, 662]. It also has the benefit of having low/no interference from inorganic compounds [553].

Another commonly used wavelength is 280nm, which

correlates well with NOM aromaticity [553, 554] and apparent molecular mass [647]. LI, BENJAMIN & KORSHIN [657] found that the decreases in absorbance upon chlorination were consistently greatest at 272±4nm, which they suggested as a convenient surrogate parameter for estimating trihalomethane (THM) production. See also §S7▪2.

Ultraviolet absorbance of the water was measured spectrophotometrically on filtered samples at a wavelength of 254nm, as per the convention. Typical values of A254nm are as given in Table 3-6.

Absorbances at 400 and 460nm were also separately recorded as

intermediaries in true colour estimation (see §3▪4▪2▪1(a)).

The measurements are carried out at room temperature (subject to slight increase within the sample chamber) at the original sample pH. The U.S. Standard Methods [334] advise that (as for true colour) the pH value should ideally not be below 4 or above 10, and state that the sample pH may be adjusted “for specific applications and correlations”.

However the U.S. drinking water regulations (40CFR

§141.131) [56], in the context of SUVA254nm calculation (see §R1▪1▪4▪2), direct that, “The pH of UV254 samples may not be adjusted”. Similarly, U.S. EPA Method 415.3 [846] proscribes acidification. 95% of respondents to a 2002 survey did not adjust sample pH [555].


189

D. I. VERRELLI

Table 3-6: Typical values of A254nm [289].

Water sample

A254nm [1/m]

Natural raw water Treated, filtered water

3▪4▪2

2.5 to 12.5 5 to 8

Microfiltered water

2.5 to 40

Reverse-osmosis water

1 to 2.5

True colour

Aside from æsthetic considerations, colour has also been identified as a useful index of dissolved humic matter due to the difficulty in fractionating and directly quantifying the presence of humic substance in water [291, 487]. However, the relation is not perfect [291]: DOC correlates well with water color [...]. However, DOC is a measure of many different carbon compounds, several of which are not humic substances and do not impart color to water. Humic substances typically account for 40 [to] 80% of the total DOC in lake water [...].

The a p p a r e n t c o l o u r of a sample may include contributions from both suspended solids and dissolved materials. The term ‘ t r u e c o l o u r ’ is intended to mean that part of the colour due only to dissolved components (usually predominantly organic [854, 979]). In the present work only true colour was measured and reported. Particulates were removed prior to analysis by passing through a 0.45μm syringe filter — typically a Sartorius Minisart 16555K unit with a 26.0mm diameter surfactant-free cellulose acetate (SFCA) membrane — in accordance with ISO 7887 : 1994 [4]. A detailed discussion is presented in §S9▪2.

The conventional definition relates to comparison of the sample ‘by eye’ to a set of standards. ISO 7887 [4] describes the platinum–cobalt standard colour measurement method as: Determination of the intensity of the yellowish brown colour of a sample by visual comparison against a series of matching solutions.

This traditional procedure for determination of true colour is described in Appendix S8▪1. 190



CROWTHER & EVANS [290] described the platinum–cobalt standards as being “brilliant yellow with a touch of blue,” in contrast to natural water samples, which tended to be “faded yellows with tints of red and brown.”

The U.S. Standard Methods [334] recognise that the platinum–cobalt standard method is not always the most appropriate method: Waters of highly unusual color, such as those that may occur by mixture with certain industrial wastes, may have hues so far removed from those of the platinum–cobalt standards that comparison by the standard method is difficult or impossible.

In such cases spectrophotometric or tristimulus filter methods are to be used, although they do not allow comparison with platinum–cobalt method results. However, visual comparison is applicable especially to potable waters, where colouration is due primarily to the presence of natural organic matter (NOM) [334]. The waters studied in the present work derived from surface catchments and had a predominantly ‘natural’ yellow colouration due to humic substances, and so issues related to groundwaters or service water [see 477] can be neglected.

3▪4▪2▪1

Spectrophotometric determination

As early as 1955 SKOPINTSEV & KRYLOVA found a linear relationship existed between colour and absorbance (although none was found between these and total organic content) [157].

The U.S. Standard Methods [334] recognises four main i n s t r u m e n t a l methods for measuring true colour: • “Multi-wavelength” spectrophotometry; • Tristimulus filter spectrophotometry; • ADMI (American Dye Manufacturers Institute) ‘weighted-ordinate’ spectrophotometry — produces a single-value measure of colour, independent of hue or chroma. • Single-wavelength spectrophotometry. Key features of these methods are summarised in Table 3-7.


191

D. I. VERRELLI

Table 3-7: Options for instrumental colour measurement according to the U.S. Standard Methods [334].

Multi-wavelength

Tristimulus

ADMI

Single-wavelength

Standard

Standard

Standard

Proposed

Cuvette length

≥10mm

10mm

10mm

25 to 100mm

Wavelengths

10 or 30

Many

Many

1 (450 to 465nm)

–

–

Platinum–cobalt

Platinum–cobalt

Manual

Instrument a /

Software / manual

Manual

~True colour

~True colour

Status

Calibration Computation

manual Output as

Dominant

Dominant

wavelength, hue,

wavelength, hue,

luminance, purity luminance, purity et cetera Note

a

Requires a spectrophotometer that can output ‘tristimulus values’ (see §S8▪3▪1); previously, physical

filters were used [cf. 4, 270].

Both the ADMI and single-wavelength methods produce single-value measures of colour, directly comparable to conventional measures of true colour.

The ADMI method

furthermore produces a result that is nominally independent of hue or chroma [334], yet it appears rarely to be used: this is probably due to the need for specialised knowledge and equipment, or to the relative invariance of hue in most real water samples. The multi-wavelength and tristimulus methods described are essentially equivalent, except that the latter is presumably more accurate supposing that more wavelengths are used. See also §S8▪3▪2, along with the discussion on p. 193.

A single-wavelength method is of interest due to its simplicity, and compatibility with conventional measurements by visual comparison. It is expected to yield reasonable results provided sample hue does not significantly diverge from that of the platinum–cobalt standards. See also §S8▪2.

More precise standard colourimetric analyses are described in §S8▪3. perceptually-uniform colour space [260] is suited for such analyses. 192


The CIELUV


A small trial conducted in the present work (§S8▪3▪3) found that the ‘saturation’ parameter in this system best represented perceived ‘colouredness’, with the complementary parameters to complete the description being the hue (mapped to an angle) and lightness. BENNETT & DRIKAS [139] reported better agreement between colour ‘purity’ than with ‘luminance’ for platinum–cobalt standards and water of the same perceived true colour.

3▪4▪2▪1(a)

Estimation from single-wavelength absorbance

In the present work true colour was determined by finding a platinum–cobalt standard (with d e f i n e d colour) of equal absorbance at a wavelength of 460nm. This requires no ‘subjective’ operator assessments (i.e. comparisons) that must be averaged over many readings.

However, it relies on the selection of a wavelength (or

band/combination of wavelengths) that is sufficiently representative of the colour as perceived by the human eye. A justification is presented below. Multiple-wavelength correlations were avoided for the unnecessary complexity that would hinder usage in the field and comparison with conventional measures. Nevertheless the actual instrument set-up was identical to that for the absorbance scans described in §3▪4▪1▪1. Identification of 460nm as the most appropriate wavelength was based on a comprehensive survey of the literature, summarised in Appendix S8▪2▪1. Absorbance at 400nm was also recorded for comparison with industry measurements.

Measurements on platinum–cobalt colour standards of various dilutions (as in Figure S8-2, excluding the stock solution) yielded the following linear correlations: A400nm = 8.830×10‒3 C + 5.101×10‒4 ;

R2 = 0.9998

[3-1]

A460nm = 2.665×10‒3 C + 2.611×10‒4 ;

R2 = 0.9998

[3-2]

with Aλ in [10/m] and C in [mg/L Pt units]. Evidently the intercept ought to be zero, but the results here are sufficiently close. Equation 3-2 was inverted to predict true colour from A460nm. Using the 460nm wavelength, the absorptivity is 0.0267m‒1.(mg/L Pt units)‒1.

Excellent

linearity was obtained in the given range (cf. §S7▪3).


193

D. I. VERRELLI

If correlations are developed based on the operator-assessed colour of real samples (cf. §S8▪2▪1), then the correlations between Aλ and C can vary between sites, because of differing characteristics of the raw water. Examples of such variation are presented in Appendix S8▪2▪2. The underlying mechanisms suggest seasonal variation would also be possible on a given site (cf. §R1▪1▪5). In contrast, equation 3-2 was developed based on the absorbance of the standard. Site or seasonal variations may suggest a different optimum wavelength for the correlation, but equation 3-2 is certainly adequate for the purposes of the present work.

3▪4▪3

Turbidity

Turbidity is an aggregate optical property indicating the presence of suspended particles by the scattering of light [e.g. 1000]. The contribution to scattering by particles of size less than 0.02μm is expected to be negligible [922], although the particle shape will also affect results [796]. Suspended particles in drinking water may be of size up to about 10μm [922].

3▪4▪3▪1

Measurement

The ISO standard on measuring turbidity in water, ISO 7027 [15], describes four techniques: 1.

Transparency testing tube comparison.

2.

Transparency testing disk comparison.

3.

Diffuse radiation measurement [Formazin Nephelometric Units, FNU], in which light scattered by the sample is measured at 90° from the incident.

4.

Radiant flux measurement in [Formazin Attenuation Units, FAU].

The first two techniques are semi-quantitative. The second pair of techniques are quantitative measures using optical turbidimeters calibrated against standard formazin (poly(tetraformal triazine) [888]) solutions. So-called “secondary standards” are available for calibration, however these are suitable more for determining when a turbidimeter should be recalibrated against (primary) formazin standards [24].

194



Regulatory bodies generally specify values in FNU or NTU (Nephelometric Turbidity Units), the latter being associated with the U.S. EPA Method 180.1 [334, 594, 791]. The two units are often taken as identical [24], despite differences in the prescribed wavelength of the incident light and in the turbidimeter design tolerances specified [e.g. 92]. The U.S. turbidimeter design standards have been unfavourably compared to the international standards for having excessively large tolerances that may allow significant errors in reported values [922].

The differences mentioned above, among others, mean that readings from different machines cannot necessarily be directly compared [see 92]. Indeed it has been recommended that the mechanism of measurement should be immediately identifiable from the reporting units [746]: the present set-up (see below) corresponds to units of “NTRU” [see 91, 92]. For brevity, units of NTU are retained throughout the present text. Considering the additional variations due to apparent refractive index (real or complex, i.e. absorbing), particle size, and particle shape, even “interregional or interseasonal” measurements may not be directly comparable [922].

3▪4▪3▪2

Experimental

The turbidity of the supernatant and raw water was estimated by use of a Hach (U.S.A.) 2100AN turbidimeter. This model is equipped with three silicon photodiode detectors to avoid measurement interferences due to either significant true colour [887] or extremely high turbidity [see also 92]. The turbidimeter is fitted with a broad-band filter with “spectral peak response between 400 and 600nm” conforming to “U.S. EPA Method 180.1” [594], enhancing sensitivity to small particles [887]. Sensitivity peaks for particles whose (geometric volumemean) diameter is ~2.5 times the measuring wavelength [399]. Machine accuracy at the low end was verified by measurements on deionised (filtered) water, and calibration against fresh stabilised standards * was performed.

*

StablCal (Hach, U.S.A.) formazin standards, supplied in 6 vials: <0.1, 20, 200, 1000, 4000, and 7500NTU. (According to the U.S. Standard Methods [334] u s e r - p r e p a r e d formazin is the sole p r i m a r y standard — yet it should only be prepared “as a last resort”; commercial standards are accepted in practice [92, 887].)


195

D. I. VERRELLI

One inherent source of inaccuracy is that the sub-samples are measured in a sample cell, where the sample is assumed to be quiescent, rather than in a flow cell [e.g. 92] — which would require a much larger quantity of material to test, and is less convenient. Other potential sources of error are in the sampling (which could break up agglomerates, or be unrepresentative) and in the sub-sampling (due to possible settling, agglomeration or adsorption of particles after sampling but prior to measurement) [see also 92].

Samples were taken from 5cm below the water surface by means of a wide-mouthed syringe after 5 minutes of settling, and from 10cm after 10 minutes of settling. To improve homogeneity, while avoiding bubble formation [cf. 5], the sample was carefully poured down the side of the cell and mixed by slowly inverting several times [92, 887].

Experimentally it was found that laboratory turbidity measurements were less useful than true colour. Difficulties included: • Interpretation (or specification) as the properties of the supernatant ‘after clarification’, or merely after a certain arbitrary time has elapsed. • Obtaining a representative sample. • Absence of a flow-through cell attachment, that would (hopefully) avoid particle settling, bubble entrainment, and aggregate rupture.

Accuracy at this level was

important due to the naturally low turbidity of the raw waters.

3▪4▪4

Dissolved organic carbon (DOC)

There are several ways of quantifying the amount of organic carbon present in water [334]. Assimilable organic carbon (AOC) is the “microbially unstable fraction of organic carbon” and “has been suggested to be the main nutrient for microbial regrowth in distribution networks” [744] [also 647, 797]. While these components may be important, they are not routinely measured, as the procedure is somewhat more complicated than for TOC or DOC and there is currently no standard methodology defined [744]. For water treatment plants, total organic carbon (TOC) and dissolved organic carbon (DOC) are of the greatest practical importance [334]. The dissolved portion is most commonly

196



defined as that passing through a 0.45μm filter [334, 846, 1102]. The DOC usually makes up most of the TOC, typically constituting 83 to 98% in freshwaters [555] (or 90 to 99% [335], or >90% [647]). However particulate organic carbon (POC) [see 647] can dominate in certain cases, such as after runoff events [555]. In the present work samples were passed through a syringe filter prior to analysis: typically Pall Acrodisc units with 0.45μm polyethersulfone (PES) membranes. A detailed discussion is presented in §S9▪3.

The expected error in DOC measurements of typical raw and treated water samples is on the order of 10%, or less for easily oxidised (‘non-refractory’) materials such as typical calibration standards [84]. A critical step in minimising error is to ensure the efficient separation of inorganic from organic carbon [84, 846].

AIKEN, KAPLAN & WEISHAAR [84] claim that

inorganic carbon levels of 50mg(C)/L and above are common in many rivers and lakes. However such levels were not observed in this study. Inorganic carbon can be removed by converting it to carbon dioxide at pH ≤ 2 and purging [334]. This will also remove purgeable organic carbon, but “in many surface and ground waters” the purgeable component of TOC is negligible [334].

The principle of analysis is conversion of carbon to carbon dioxide, which can then be measured. The conversion is commonly achieved by high-temperature oxidation in the presence of a catalyst * (‘HTCO’), or at lower temperatures using persulfate and ultraviolet radiation [334]. The carbon dioxide formed is then analysed using either a non-dispersive infrared (NDIR) detector or by coulometric titration, or conductimetrically after absorption into high-purity water through a selective membrane [334]. NDIR is the most direct [1102]. HTCO is preferred for high levels of TOC that would otherwise require dilution (e.g. > 50mg(C)/L), for samples containing “chemically refractory” contributions to TOC, and for samples containing high levels of particulate organic carbon (POC) [334, 1102]. However, HTCO is less well suited to low levels of TOC (e.g. < 1mg(C)/L) [12, 334]. Other interferences

*

For example cobalt oxide, platinum group metals, or barium chromate [334].


197

D. I. VERRELLI

are fusion of dissolved salts if operating above ~950°C (also degrades catalyst activity rapidly) or failure to decompose some carbonates if at ~680°C [334]. WANGERSKY [1102] reviews the advantages and disadvantages of different methods of DOC determination in more detail.

He summarises, “the HTCO method comes closer to

measuring the DOC than do any of the wet oxidation methods,” which yield only a lower limit [1102]. AIKEN, KAPLAN & WEISHAAR [84] also found that instruments using HTCO tended to yield more accurate measurements.

DOC levels in certain samples (e.g. those containing biologically labile matter) can change significantly over hours and months [1102]. Yet in practice organic carbon may not be measured straightaway. Samples were immediately filtered into (rinsed) capped plastic containers with minimal headspace and stored in a cool, dark space.

Standards were

produced and kept in baked glass bottles.

It is recommended that after every tenth analysis a quality control check is carried out on a control sample [1102] and on a blank [334]. Alternatively, a known addition (‘spike’) of TOC to a sample may be made to test recovery from an unknown matrix [334].

Standards covering this measurement include:

ISO 8245:1999;

BS EN 1484:1997;

U.S.

Standard Method 5310 [334]; and ASTM D 2579 – 93 [12] *.

Organic carbon was measured on a Shimadzu (Japan) TOC-VCSH analyser, in two steps, as the difference between dissolved carbon (DC) and dissolved inorganic carbon (DIC). This device operates using high-temperature, catalysed oxidation (680°C in the presence of platinum) with analysis by an NDIR detector. Acidification is achieved by addition of phosphoric acid (H3PO4), which is most suitable for a HTCO device [555]. The carrier gas is ‘zero-grade’ air (as suggested by U.S. EPA Method 415.3 [846]). The system is rinsed with purified water between measurements to minimise any ‘memory effect’ [846].

*

ASTM D 2579 was “withdrawn” in 2002, but its replacement is still under development as Work Item WK13962 (initiated 2007-01-24). Alternative active standards include D 4129; D 4839; D 5173 (on-line); D 5904; D 5997 (on-line); and D 6317 (low levels).

198



Each measurement involved a 50μL injection of the sample, with no autodilution. Two washes were carried out between measurements. Carrier gas flowrate was held at the same value (115mL/min [cf. 12]) for measurements as for calibration *. Samples were repeatedly analysed until concordant results were obtained, defined as satisfying a maximum standard deviation criterion of 0.1mg(C)/L and a coefficient of variation (i.e. relative standard deviation) criterion of 0.5%. At least 3 measurements were made per sample, and often 5 or more. The NDIR absorbance scans were reviewed and individual measurements were excluded from the final averaging if discordant features were identified.

Organic carbon stock solution was made up of approximately 2.1254g anhydrous potassium hydrogen phthalate (KHC8H4O4) in 1000mL purified water to yield 1.00mg(C)/L. Inorganic carbon stock solution was made up of approximately 4.4122g anhydrous sodium carbonate (Na2CO3, dried at 285°C) and 3.497g anhydrous sodium hydrogen carbonate (NaHCO3) in 1000mL purified water to yield 1.00mg(C)/L. The calibration correlates integrated peak area (rather than peak height [see 1102]) with carbon concentration. The TOC of the blank is accounted for by translating the calibration curve so that it passes through the origin (slope is unchanged).

Readings were validated by testing two samples containing predominantly DOC (KHC8H4O4 at about 18.5mg(C)/L and raw water spiked with dialysed MIEX eluate at about 9.1mg(C)/L) and one containing predominantly DIC (Na2CO3 and NaHCO3 at about 19mg(C)/L) on an O.I. Analytical 1010 analyser † using a heated persulfate oxidation mechanism with NDIR detector.

Nominally pure water recorded DOC values ranging from 0.0 to 0.5mg(C)/L. See §S9▪3 for further details.

*

At the design flowrate of 150mL/min there was a significant decrease (15 to 20%) in the detector readings.

†

Thanks to Dr. JAMES TARDIO (RMIT, Melbourne).


199

D. I. VERRELLI

3▪4▪5

Total solids and dissolved solids

Total dissolved solids (TDS) constitute the nominally dissolved species in water that are left behind upon drying of a specimen [34]. The dissolved species can be defined as those substances able to pass through (say) a 0.45μm filter *, which may include “[clay] particles, colloidal iron and manganese oxides, and silica” [34]. Typically a Sartorius Minisart 16555K syringe filter was used, as for true colour; see also §S9▪2. The sample volume was typically of order 75mL. TDS may also be related to the electrical conductivity (see following) using an appropriate factor [34]. The Australian guideline value, based on æsthetics, is 500mg/L [34].

Total solids (TS) were measured by the same simple gravimetric method.

The sample

volume was typically of order 300mL. Although some standards [cf. 334] specify different temperatures for TS (~104°C) and TDS (180°C), in the present work the oven was set to 100°C in both cases [cf. 1139]. Hence total suspended solids (TSS) can be taken as equal to TS ‒ TDS.

For the present samples — both raw and treated water — the estimated TDS tended to be fractionally greater than the TS.

The reason for these unphysical results could not be

established; however the discrepancies were small enough to be neglected, and the TDS and TS taken as equal. That is, the raw and treated water sampled contained practically no particulate matter (as defined) — consistent with the turbidity results.

3▪4▪6

Conductivity

Conductivity of raw and treated water was monitored using a Radiometer Analytical (France) IONcheck 65. An in-built feature was used to correct all of the conductivities to 25°C values.

*

The U.S. Standard Methods [334] list a number of alternative filters, comprising glass-fibre depth filters (free of organic binder) of nominal pore size 1.0 to 1.5μm.

200



Conductivity of the raw water was found to be consistently in the range 10±2mS/m *. For the range of conditions explored in the laboratory, the conductivity of the treated water increased with increasing chemical dose, i.e. increasing coagulant dose or pH.

At low

coagulant doses supernatant conductivity remained at about 10mS/m; at high doses — 80mg/L of the cation † — conductivities were in the range 57 to 60mS/m (ferric), 83mS/m (magnesium), and 90 to 110mS/m (alum, and alum with dMIEX — cf. §6▪2▪1). Recall that aluminium has the narrowest solubility envelope (cf. §R1▪2▪3 and Figure 3-3), and also the lowest relative atomic mass per elementary charge (9.00 for Al3+, 12.15 for Mg2+, 18.62 for Fe3+). In Europe a guideline maximum of 40mS/m has been promulgated [34]. Ultra-pure water has a (minimum) conductivity of around 6.4μS/m at 25°C [387].

Empirically it has been found that the conductivity can often provide an estimate of the TDS [34], TDS [mg/L] ~ conductivity [mS/m] / 5,

[3-3]

and of the ionic strength, I [M] ≈ conductivity [mS/m] / Б,

[3-4]

in which Б is an empirical constant variously given as magnitude 5450 (at 20°C) [387] and 6250 [334]. (This suggests that in the present work the ionic strength varied between about 0.0017M and 0.018M.) Recall that the ionic strength is defined as [387] I≡

1 2

C z i

i

2

,

[3-5]

i

in which Ci is the molar concentration of species i in the bulk, and zi its valence.

*

The 2004-02-13 ‘raw’ tapwater sample reported in §3▪5▪4 had a conductivity of 13mS/m.

†

At the highest doses 100mS/m (at 160mg(Fe)/L) and 123mS/m (at 92mg(Al)/L) were recorded.


201

D. I. VERRELLI

3▪5

Sludge characterisation — compressional rheology

Sludge dewaterability — including aggregate settling — is a strong function of the solidosity, φ. The determination of φ is described in detail in §2▪1▪1 (cf. §4▪3▪1). The solidosity can be calculated based on the initial condition, as loaded. It can also be backcalculated from measurements on the final dewatered cake or bed, given CφD h = φ0 h0. Generally both estimations were made. For batch settling an average of the two was normally used. In filtration the final value was used for ‘compressibility’ runs, as these tests seek to correlate Δp with φ∞ (independent of φ0), and the final-solids measurement tends to be more reliable [745]. For stepped-pressure ‘permeability’ filtration runs the initial value was used, given the possibility for errors in h0 due to drainage of a portion of liquor through the membrane while loading and before lowering the piston [cf. 598].

3▪5▪1

Batch settling

Batch settling tests were carried out in graduated glass measuring cylinders of suitable size (typically 250, 500, or 1000mL). For the WTP sludges characterised, the settling behaviour is independent of diameter in this range (36 to 61mm) — see §9▪2▪1. Normally it was desired that the sample should settle to about 25 to 50% of its original height, and so material was more often taken from the top of the bed of collected sludge, to avoid the more highly concentrated, somewhat compressed material at the bottom. Sometimes additional supernatant was intentionally added. The measuring cylinder was covered and gently inverted before commencing the test. A video cassette recorder (VCR) with long-play (LP) capability was employed to capture batch settling behaviour overnight. Use of a single 300 minute Video Home System (VHS) video tape allows 10 hours of footage to be recorded. In later work a digital video camera (DCR-TRV50, Sony, Japan) was used in ‘time lapse’ mode (e.g. record for 1s at 60s intervals *).

*

The camera cycle times were found to be approximately 5% in error, and so times were validated (or corrected) by including a stopwatch in the frame.

202



These facilities eliminated several problems that arose from attempting to fit smooth functions to the h(t) settling profiles where important data had previously not been able to be obtained.

3▪5▪1▪1

Temporal data (single test)

Characterisation of each sample at low values of φ was carried out through batch settling test under gravity until the system attains steady-state (negligible movement over an interval of one week or more), and analysing the fall of the interface as a function of time. The ‘B-SAMS’ version 2.0 (The University of Melbourne, May 2005) * software package was used to extract estimates of py(φ) and R(φ) from the transient settling data, following the practical solution procedure outlined in §2▪4▪5▪3(c). This produced a large array of data points — for clarity only the terminal points from settling analysis are explicitly shown in the R(φ) results that follow. (The lower terminal point is determined by the solidosity at which the cylinder is loaded, and the upper point is based on the estimated gel point.) This technique is less robust than the filtration data analysis, and some settling tests will yield more data than other settling tests. Points obtained from centrifugation (§3▪5▪2) or filtration (§3▪5▪3) are always shown individually.

3▪5▪1▪1(a)

Reproducibility

Multiple batch settling tests (cf. §3▪5▪1▪2, §S10) were carried out for an alum plant sludge sourced from Winneke on 2005-04-05.

Each was analysed individually to provide an

indication of the reproducibility of the routine characterisation procedure.

*

P527 B – SAMS (Batch Settling Test Analysis and Modelling Software) — ROSS G.

DE

KRETSER, SHANE P.

USHER, DANIEL R. LESTER, ANNA Q. Y. CAI, and DEEPAK AGARWAL.

3▪5 : Sludge characterisation — compressional rheology

203

D. I. VERRELLI

Compressive yield stress, p y [kPa]

1.E+3 1.E+2 1.E+1

φ_0 φ_0 φ_0 φ_0 φ_0 φ_0 φ_0

= = = = = = =

0.00205 0.00207 0.00205 0.00207 0.00206 0.00102 0.00052

, , , , , , ,

h_0 h_0 h_0 h_0 h_0 h_0 h_0

= = = = = = =

0.230m 0.231m 0.230m 0.231m 0.247m 0.225m 0.248m

1.E+0 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 0.001

0.01

0.1

Solidosity, φ [–]

Figure 3-9:

Compressive yield stress curves computed from seven batch settling tests.

Centrifugation and filtration data also shown.

Hindered settling function, R [Pa.s/m2]

1.E+15 1.E+14 1.E+13 1.E+12 1.E+11

Interpolation

1.E+10 1.E+09 1.E+08 1.E+07 0.001

φ_0 φ_0 φ_0 φ_0 φ_0 φ_0 φ_0

= = = = = = =

0.00205 0.00207 0.00205 0.00207 0.00206 0.00102 0.00052

, , , , , , ,

h_0 h_0 h_0 h_0 h_0 h_0 h_0

0.01

= = = = = = =

0.230m 0.231m 0.230m 0.231m 0.247m 0.225m 0.248m

0.1


Figure 3-10:

Hindered settling function curves computed from seven batch settling tests.

Filtration data also shown.

204



Figure 3-9 shows that the variation in estimated gel point is not large. The one curve that

deviates most strongly from the rest corresponds to the test run under the most dilute conditions. Figure 3-10 shows that the data obtained from the different runs are all highly consistent in

the range where measured data overlap. The main discrepancies arise where the data do not overlap.

The highest solidosity for which an estimate of R could be generated varied

between batch settling runs;

curves between these respective upper limits and the

(invariant) filtration data were generated by simple interpolation, hence the difference.

These results confirm that consistent results may generally be obtained through the standard batch settling characterisation procedure employed here. However, the potentially serious implications of interpolation are established in Appendix S10. Because of this uncertainty, interpolations have been omitted from all R(φ) plots in the main part of this thesis. The analysis of c o m b i n e d multiple-test batch settling data is discussed in the following sub-section (see also §S10). Potential interferences due to wall effects and ambient light are considered in §9▪2 and §9▪3▪1▪2. A final source of error is the variation in ambient temperature: see §3▪5▪3▪4(a).

3▪5▪1▪2

Equilibrium data (multiple test)

The usual procedure for obtaining the function py(φ) at low values of φ, has been to input data from individual batch settling experiments into the B-SAMS settling analysis software application. A further method is available that utilises data from multiple batch settling experiments, the theory for which was presented in §2▪4▪5▪3(f).

For the present work it is especially of interest for validation to compare the results of this analysis with single-test estimates. The multiple batch settling technique was carried out on three samples. The estimated gel points were in good to fair agreement with those obtained by single test analysis. These results are summarised in Table 3-8. 3▪5 : Sludge characterisation — compressional rheology

205

D. I. VERRELLI

Table 3-8: Single test and multiple test batch settling estimates of φg.

Sample

High-pH lab.

Moderate-pH lab.

Plant

Winneke

Winneke

Winneke

2004-05-21

2006-06-09

2005-04-05

[mg(Al)/L]

80

80

1.9

[–]

8.6

5.9

6.1

4

4

7

Raw water source and date Dose pH Number of tests a Single test φg

[–]

0.0012±0.0003

0.0021±0.0002

0.0046±0.0003

Multiple test φg

[–]

0.0008±0.0001

0.0021±0.0001

0.0048

Note

a

Includes duplicate tests (i.e. identical values of h0 and φ0), and tests with φ0 > φg.

Table 3-8 shows that the latter two samples yielded good agreement, within the range of

experimental error. The first sample shows mediocre agreement: although the explicit and implicit errors are not much greater than for the other two samples on an absolute basis, they are large on a relative basis due to the small value of φg (say 0.0009). This suggests that gel point determination may be more problematic for more voluminous samples with lower gel points. A more detailed discussion of the multiple-test batch settling analysis technique and comparison to single test estimates is presented in Appendix S10 for the high-pH laboratory sludge.

3▪5▪1▪3

Accuracy

A rigorous analysis of the multiple batch settling analysis technique and comparison to single test estimates is presented in Appendix S10 for the high-pH laboratory sludge of Table 3-8. Some key findings are summarised here.

206



It is possible to generate s e v e r a l a l t e r n a t i v e interpolated curves when fitting the dewatering functions py(φ) and R(φ) which seem eminently p l a u s i b l e . These can lead to entirely d i f f e r e n t h ( t ) p r e d i c t i o n s , however (see also §S10▪3), and also to entirely different characteristics of the solids diffusivity, D (φ) (cf. §5▪9▪3). Optimising the py(φ) and R(φ) curves so as to generate accurate h(t) predictions leads to different functions depending on the settling test chosen for the optimisation. Aside from putative shifting (i.e. translation) of the curves to higher or lower φ, consideration of the residual discrepancies suggested that long-time settling may be dominated by creep. This long-time data is most difficult to (re-)predict.

Other difficulties stem from

characterisations based on settling tests with φ0 > φg, and in trying to obtain concordant results for different φ0 values generally. The latter issue raises the question of whether the effective gel point of the material is truly constant (and the trends in the outputs from BSAMS are methodological artefacts), or whether the experimental procedure causes φg to become a function of φ0. The multiple-test batch settling analyses offered the advantage of not requiring significant shifts in φ (‘post-processing’) in order to obtain good agreement between re-predicted settling data and the original raw data. It also requires, however, a greater volume of sample, more bench-space, and more experimental attention (e.g. measuring φ0 and φ∞, monitoring h).

3▪5▪2

Batch centrifugation

The main centrifuge used in this work was a model CT4-22 (Jouan, France) equipped with the M4 swing-out (‘bucket’) rotor. This took containers of 500mL and 50mL capacity, the latter held in bucket inserts. The nominal length of the ‘arm’ (comprising rotor and bucket) is 172mm, which is used to determine the nominal rotational acceleration of the device. A model Sigma 3K10 centrifuge (B. Braun Melsungen, Germany) was also used for prethickening. This took ~200mL containers.


207

D. I. VERRELLI

3▪5▪2▪1

Pre-thickening

In the initial period of this work, problems were encountered in filtration due to the loading of samples at low solidosities (i.e. low φ0). This resulted in insufficient cake resistances in the ‘permeability’ runs, and excessively thin cakes for both stepped-pressure runs. The obvious remedy for this was to pre-thicken the samples prior to filtration. Thus centrifugation was applied at accelerations between 17g and 190g m/s2, and up to 540g m/s2 in one exceptional case *. This is consistent with the procedure adopted by AZIZ et alii [106]. It is believed that the action of centrifugation did not cause major changes to the sludge properties, as care was taken to ensure the network pressures would remain below the lowest filtration pressure (typically 5kPa), and there was no evident correlation in the results to the application or not of pre-thickening by centrifugation. Supporting data are presented in Figure 3-18 and Figure 3-19.

Pre-thickening by centrifugation was generally not carried out from early 2005 onwards. Even before this some compressibility runs and many permeability runs relied instead on prior settling and use of a final step-down in pressure (see §3▪5▪3▪3(a)). It was found possible to attain sufficiently high solidosities by permitting the samples to settle for a period of a couple of days, and then decanting the uppermost level of supernatant and sludge before sub-sampling the somewhat thicker layers below for the filtration runs. It is believed that this procedure is the most ‘conservative’ in terms of avoiding undue mechanical action; however, it may not be suited for samples that age rapidly.

The samples analysed for solid phase density were also centrifuged, as described in §4▪3▪1▪1.

3▪5▪2▪2

Accelerated settling

Aside from merely serving as a preparatory tool, centrifuges can provide useful dewatering data in their own right — not surprising considering that centrifugation is an important dewatering unit operation in the field. However the analysis of sludge centrifugation is simplest for the batch operation with a swing-out rotor, compared to industrial designs such *

208

Alum sludge generated from tapwater 2004-02-13: 84mg(Al)/L, pH 6.1.



as continuous ‘decanter’ (or ‘scroll’ or ‘solid bowl’) centrifuges [976] et cetera [293]. The theory is essentially that of gravity batch settling with allowance for spatial variation in ‘gravity’ (i.e. the hypothetical centrifugal acceleration), except for certain complications arising from CORIOLIS effects. This is discussed in §2▪4▪5▪4.

Samples were loaded into heavy-duty polycarbonate tubes of approximately 40mL capacity. The internal diameter was measured as 25.9mm (at the top), although mass balance calculations suggested a slightly lower figure (toward the base); they were 88 to 89mm tall. Care was taken to ensure that the internal bases of the tubes used were flat; this was conveniently achieved by adding liquid polymer mixture to the base of the upright tubes, which dried flat and level provided the tubes were held vertical. DE GUINGAND [435] recommended a 15min ‘rest’ period prior to centrifugation to enable the material to ‘stabilise’ after loading into the tube.

Although this direction was not

intentionally followed, a comparable period did elapse in the present work.

The procedure followed that outlined in §2▪4▪5▪4(b) in which the bed height is monitored over the course of the run to obtain h(t) data and the equilibrium cake is dissected into disks for which the solidosity of each is measured according to §2▪1▪1, following the protocols of §4▪3▪1. (In practice the process of scraping material out of the tube may unrecognisably deform each disk, but that is unimportant.) The primary motivation for these tests is to characterise dewaterability at solidosities intermediate to that of filtration and gravity settling. Other experimental considerations imply upper and lower limits too, as in Table 3-9.


209

D. I. VERRELLI

Table 3-9: Considerations in specifying centrifugation speed.

Encouraging a lower acceleration:

Encouraging a higher acceleration:

• availability of high-solidosity filtration

• availability of low-solidosity gravity batch

data;

settling data;

• ensuring the bed settling rate was not too fast to observe;

• ensuring the bed settling rate was not too slow to reach equilibrium in a practical

• minimisation of the time ramping up and

time;

down the rotation rate between bed height • the need for significant dewatering, so that bed settling height changes are less subject

observations; • the need to have sufficient cake to dissect into numerous sections (i.e. constraint on

to error; • the need to form a cake firm enough to dissect; and

data resolution); and • the mechanical strength of equipment.

• the need for the tubes to swing-out horizontally, so that forces and interfaces are perpendicular.

It was found that for WTP sludges acceleration of gravity-settled * samples at 1000rpm in the CT4-22 was suitable. While the nominal acceleration was then 190g m/s2 †, the true local acceleration was as low as 107g m/s2 at the top of the unsettled bed, (150 to 166)g m/s2 at the top of the final cake, and (186 to 187)g m/s2 at the flat bottom of the tube. Final bed heights of 27 to 34mm were obtained (h0 ~ 70mm), which were dissected into 8 to 10 sections. Each section was typically 2.0 to 3.0mm thick, although some at the base or top of the bed were thicker. As shown in the following section the solid-phase stresses acting through each section ranged from 101 to 103Pa.

Greater flexibility of acceleration rate can be achieved through the use of a centrifuge equipped with a viewing port and stroboscopic light [e.g. 435] or similar [992, 993], or with *

This occurred in beakers with moderate bed heights, so the (homogenised) solidosity should have been slightly above the respective gel point.

†

210

This is the value displayed on the instrument panel; in fact, calculation shows that it should be 192g m/s2.



an in-built light source (visual or otherwise) and camera [e.g. 713, 714] [cf. 712] or transmission sensor [e.g. the LUMiFuge device (L.U.M., Berlin) used currently by STUDER and WALL].

3▪5▪2▪2(a)

Results

The batch centrifugation of four sludges was carried out, covering the four combinations of alum and ferric, and laboratory and plant. Sample properties are presented in Table 3-10.

Table 3-10: Generation conditions for sludge samples used in batch centrifugation.

Sample

Alum lab.

Alum plant

Ferric lab.

Ferric plant

Raw water source

Winneke

Winneke

Winneke

Macarthur

2004-06-02

2005-04-05

2004-09-15

2005-03-23

12

–

9

8

0.83

–

0.57

–

and date True colour [mg/L Pt units] A254nm

[10/m]

Dose

[mg(M)/L]

80

1.9

80

1.5

[–]

4.8

6.1

6.1

9.0

No

Yes

No

Yes

pH Polymer added

As batch centrifugation was not routinely undertaken in this study, the results are presented in parallel with the results obtained following analysis of filtration and gravity settling data only.

The compressive yield stress data is shown in Figure 3-11 (alum) and Figure 3-12 (ferric). Aside from the ferric plant data, the agreement of the centrifugation data with the basic curve fit is reasonable, and the revised fits that include centrifugation data do not differ greatly from the original py(φ) curves.

Two trends may be identified.

First, the

centrifugation data tends to fall below (or to the right) of the original py(φ) curves; alternatively, the region of the original py(φ) curves that interpolates between the filtration


211

D. I. VERRELLI

and gravity settling data is overestimated. Second, associated with the first trend, refitting the py(φ) curves yields lower estimates of the gel point.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 80mg(Al)/L, pH 4.8 lab. As above: refitted p_y 1.9mg(Al)/L, pH 6.1 plant As above: refitted p_y As above: refitted p_y & model R

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 3-11: Compressive yield stress determined first without centrifugation data, and then with centrifugation data, for a laboratory and a plant alum sludge.

There is no clear reason for the behaviour of the ferric plant sludge. It diverges from the original estimate of the py(φ) curve with increasing solidosity; the centrifugation data is fit by a power-law function of much lower exponent (~2.8, R2 = 0.997), or ‘steepness’, than the other three sets (3.9 to 4.6, R2 ≈ 0.986).

The data from centrifugation and filtration are

incompatible, yet no other indications of experimental fault were evident. Two alternative explanations are proposed: either the sub-samples analysed by the two techniques were 212



significantly different, or else the different physics of the centrifugation experiment actually measures a slightly different mechanism to the filtration experiment.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 80mg(Fe)/L, pH 6.1 lab. As above: refitted p_y 1.9mg(Fe)/L, pH 6.1 plant As above: refitted p_y

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 3-12: Compressive yield stress determined first without centrifugation data, and then with centrifugation data, for a laboratory and a plant ferric sludge.

Different sub-sample properties could arise due to factors such as shear upon loading, inhomogeneity of the original sample, or ageing effects. It is assumed in the underlying theory that dewatering by filtration or centrifugation can be modelled using the same principles in the ideal case. However, in the context of practical experimentation, addition considerations arise, such as: wall effects; vibration of a sample as it spins around the centrifuge; ‘cyclic’ effects as the centrifuged samples were removed


213

D. I. VERRELLI

periodically for measurement (perhaps including elastic re-expansion of the cake — see §9▪4); and equilibrium tolerances — given the lesser resistances to dewatering encountered in centrifugation, it may be that a closer approach to equilibrium was attained. Previous experimental work [e.g. 422, 745] has not reported significant differences. Such ‘solidosity-shifting’ of the py(φ) curves estimated from different experiments is also apparent in the R(φ) curves optimised as in Figure 3-13. Additional discussion can be found in §S10.

The corresponding R(φ) curves obtained purely from gravity settling and filtration information are plotted in Figure 3-13 (alum) and Figure 3-14 (ferric). The curves obtained when centrifugation data is used to obtain py(φ) are also presented. However the difference between the two types of estimate is not obvious: the data at low solidosity has been truncated, so that a longer and (by default) lower interpolated curve between the settling and filtration data results. This change is due to the reduced estimate of φg. This adjustment highlights the usefulness of data collection in the region of intermediate solidosity, such as by centrifugation.

Without it, it is difficult to evaluate the best

interpolation over this middle region of the R(φ) curve.

While no algorithm has been developed to back-calculate R(φ) data d i r e c t l y from batch centrifugation h(t) profiles, as is presently done for gravity settling h(t) profiles, it is possible to i t e r a t i v e l y improve on the R(φ) estimates. This method proceeds in the following sequence: 1.

Estimate the py(φ) curve using all available data.

2.

Obtain an initial hindered settling function curve, R1(φ), based on the py(φ) curve — typically by combining gravity settling data and filtration data, and using a simple interpolation.

3.

Use py(φ) and Ri(φ) to generate a prediction of the interface height decrease in centrifugation, hi(t). i = 1, 2, 3, ....

4.

Compare hi(t) with the raw data, h(t).

5.

If hi(t) and h(t) are in acceptable agreement, then take Ri(φ) as R(φ). Otherwise, generate a new estimate, Ri+1(φ), by making appropriate adjustments to Ri(φ) at

214



intermediate solidosity, and return to step 3 using Ri+1(φ). (The estimated py(φ) curve may also be adjusted, if required.)

2

Hindered settling function, R [Pa.s/m ]

1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 80mg(Al)/L, pH 4.8 lab. As above: refitted p_y 1.9mg(Al)/L, pH 6.1 plant As above: refitted p_y As above: refitted p_y & model R Interpolation

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 3-13: Hindered settling function computed with and without centrifugation data for a laboratory and a plant alum sludge. Revised fits using centrifugation data were obtained firstly by simply adjusting py(φ) as in Figure 3-11. For the plant sample, the estimates were iteratively revised by optimising the predicted centrifugation h(t) profile as in Figure 3-15.

The algorithm described here is conceptually simple, but time-consuming. This technique was applied to only one of the four samples, namely the plant alum sludge. (An equivalent technique was also occasionally applied to gravity settling data (§S10) and filtration data (§7▪4▪4▪3(b), §7▪4▪4▪3(c)) in order to validate the B-SAMS results.)


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D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09

80mg(Fe)/L, pH 6.1 lab. As above: refitted p_y 1.9mg(Fe)/L, pH 6.1 plant As above: refitted p_y

1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 3-14: Hindered settling function computed with and without centrifugation data. Revised fits using centrifugation data were obtained only by adjusting py(φ) as in Figure 3-11.

It may be noted that batch centrifugation was carried out twice for this sample, one week apart, with highly concordant compressive yield stress data. However, h(t) settling profiles can only be analysed one-at-a-time, and here only analysis of the second profile is presented. The first test yielded surprisingly good results, considering it was a preliminary run. Its mass balance discrepancy was larger (of order 5%, compared to 1.5% for the second test). There was also more apparent elastic re-expansion of the cake, while the samples were removed from the centrifuge for prolonged periods. Nevertheless, the R(φ) curve obtained

216



by optimising the predicted h(t) profile for the second test also provides the best prediction for the first centrifugation test. An additional level of sophistication would be to attempt to adjust R(φ) to optimise all settling profiles. Alternatively, additional settling profiles can be used as validation.

A prediction of centrifuge settling based on naïve use of the py(φ) and R(φ) estimates computed without centrifugation data is presented in Figure 3-15.

This is shown for

comparison purposes only: ordinarily no prediction would be made until the py(φ) curve had been adjusted to agree with the centrifugation data, and the reason for this is obvious from the extremely poor agreement between the prediction and the observed profile (note that the time scale is logarithmic).

Consideration of py(φ) data obtained from centrifugation resulted in a similar, but slightly lower, R(φ) curve, as seen in Figure 3-13. The predicted centrifugation h(t) profile for this combination of estimates is also shown in Figure 3-15. The agreement with the observed settling profile is still poor.

This is not entirely surprising:

although the py(φ) curve

incorporates centrifugation data, so that the predicted equilibrium extent of settling is much improved, the R(φ) curve is still essentially reliant on a simple interpolation over the range of solidosities relevant to centrifugation here. It is seen that the revised h(t) prediction corresponds to much slower settling than observed. This implies that some or all of the interpolated R(φ) data was overestimated — that is, the resistance to dewatering was overestimated.

Finally, after eight iterations a new interpolation with lower values of R at intermediate φ was obtained (plotted in Figure 3-13), which results in an h(t) prediction that matches the raw data (Figure 3-15).

It should be acknowledged that a small degree of further

optimisation may be possible, although the benefits would likely be marginal. It should also be recognised that in some cases there may not be a unique ‘optimised’ R(φ) curve. Nevertheless, there can only be one true curve, based on the material properties, and only this one true curve should be able to predict settling profiles across a range of tests.


217

D. I. VERRELLI

It is seen that the ‘optimised’ R(φ) curve has a generally similar shape to the original curve, but with progressively lower values as φ decreases. An alternative perspective is that the lower end of the ‘optimised’ portion of the R(φ) curve has been ‘ s h i f t e d ’ to higher solidosities; this appears to reflect the same s h i f t i n g in the py(φ) data upon inclusion of centrifugation data (see Figure 3-11).

Certainly the ‘optimised’ R(φ) curve as presented seems suspicious, given the mismatch (or discontinuity) at the low end. This is further tested by generating gravity settling profile predictions for each of the three combinations of py(φ) and R(φ) considered above. These are shown in Figure 3-16. All of the predictions match the experimental h(t) profile * well until close to complete settling. The nearer the settled bed is to equilibrium, the higher the solidosity, and so the greater the influence of the adjustments made at intermediate solidosity based on the centrifuge data. It would appear that the adjustments have resulted in inferior gravity settling profile predictions. However, it is difficult to be conclusive about this effect in the tail end of the gravity settling profile, due to concerns about long-time effects such as creep (cf. §9▪3▪2, §R2▪1, §R2▪2, §R2▪3).

In Appendix S10 it is shown that B-SAMS routinely shifts the dewatering parameter curves to higher solidosity as φ0 for the test is increased.

Evidently the centrifugation data

corresponds to quite high initial solidosities, and so the offset in predicted py(φ) and R(φ) noted here between settling and centrifugation data is consistent with that trend.

*

In fact, seven batch gravity settling tests were carried out in parallel for this sample, under a range of initial conditions. Five of those were quite similar, and it suffices for the purposes of the present work to choose one representative test.

218



0.09 0.08

Interface height, h [m]

0.07 0.06 0.05 0.04 0.03 0.02 0.01

Raw centrifuge settling data Default fit (no centrifuge data) p_y refit with centrifuge data ...and R from optimising centrifuge prediction

0.00 1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

Time, t [s] Figure 3-15: Predicted centrifugation h(t) profiles. The prediction for the py(φ) and R(φ) curves obtained without centrifugation data is for comparison only. The first ‘improved’ fit was obtained using the adjusted py(φ) curve from Figure 3-11, and this was optimised to yield the second ‘improved’ prediction by iteratively adjusting R(φ) to yield the curve shown in Figure 3-13.


219

D. I. VERRELLI

0.30

Interface height, h [m]

0.25

0.20

0.15

0.10

0.05

Raw gravity settling data Default fit (no centrifuge data) p_y refit with centrifuge data ...and R from optimising centrifuge prediction

0.00 1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

1E+7

Time, t [s] Figure 3-16: Predicted gravity settling h(t) profiles. The first prediction uses py(φ) and R(φ) curves obtained without centrifugation data.

The second prediction was obtained using the

adjusted py(φ) curve from Figure 3-11. The final prediction was obtained by iteratively adjusting R(φ) (see Figure 3-13) to optimise the predicted centrifugation h(t) profile (see Figure 3-15).

Reproducibility

The py(φ) centrifuge data for the plant alum sludge was generated from duplicate runs, subsampled from the same batch (see Figure 3-11). The two runs had somewhat different initial and final heights and solidosities, were sectioned into layers of different thicknesses, and the total number of sections was also different.

220



It almost goes without saying that the reproducibility of the py(φ) data in this case was excellent, as it is nearly impossible to distinguish the two separate data sets in the plot (they are plotted using the same symbols). It should be noted that other researchers (L. J. STUDER and R. C. WALL), working with biologically-active sludges, have encountered greater variability in their results.

3▪5▪2▪2(b)

Implications

Batch centrifugation data provides a useful check to the interpolated py(φ) and R(φ) data lying between gravity settling and filtration results, and good reproducibility was demonstrated. The data obtained from the method should be able to be used to improve estimates of py(φ) and R(φ), which would improve any predictions (e.g. full-scale) made using these parameters. Unfortunately there are a couple of disadvantages to this technique, which may be summed up as laboriousness and incomparability. The method currently requires a time-consuming process of ‘manual’ iteration to implement in full, and thus is not practical as a routine procedure. (An automated version of the algorithm is being developed by S. P. USHER.)

Furthermore, the results seem to be

incompatible with filtration data in some cases, and possibly also with gravity settling data. The shapes of the py(φ) and R(φ) curves are similar, and it is expected that trends in these curves from one sample to another will be qualitatively unaffected. However, this does mean that dewatering parameter estimates that include centrifuge data cannot safely be compared with those that do not.

It is important to establish the reasons for the lack of consistency between estimates obtained from the various methods, and this is a recommended avenue for further research in future. There is an indication that gravity settling analysis (coded into the B-SAMS software application) may be permitting the generation of R(φ) data beyond the values of φ where it is valid. That is, the analysis algorithm may be allowing settling data to be fit over too long a period. (WTP sludge samples settling under gravity exhibit unusual behaviour at ‘long’ times that may not be explainable by the LANDMAN–WHITE-type model employed.)


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D. I. VERRELLI

A final useful conclusion of this work is the significant effect that apparently small changes in py(φ) and R(φ) curves can have on practical dewatering behaviour. The py(φ) and R(φ) plots are generally given with logarithmic vertical scale, so significant changes may not immediately be seen as such.

Reviewing the changes in the parameters here and the

resulting changes in centrifugation profile is enlightening.

3▪5▪3

Dead-end filtration

Dead-end filtration characterisation was carried out in accordance with the methods published by USHER, DE KRETSER, and co-workers [608, 1059]. Some modifications and enhancements have been made, as described in §3▪5▪3▪3. The rig design is shown schematically in Figure 3-17.

Linear encoder

P

Compressed AIR S

Double-acting, double-rod pneumatic cylinder

40mm Bleed valve ~120mm

P.C.

Pressure transducer

O ring Membrane Sintered disk (SS) Perforated plate (SS)

Sample Bolt

Base plate Frame

Receiving dish

Drain valve

Figure 3-17: Schematic of laboratory filtration rig. Valves shown in positions for filtration. Only one rig was fitted with a drain valve. P.C. = personal computer loaded with Press-o-matic.

222



The incremental linear encoder (Gurley Precision Instruments, U.S.A.) has a claimed precision of 10μm, accuracy of ±10μm/m, and hysteresis of 0.5μm [cf. 608]. The pressure applied to the sample is controlled in a cascade configuration by adjusting the cylinder pressure in order to modulate the transducer pressure [608]. The instantaneous piston pressure is generally controlled within ±1kPa after ramping up (or down), and commonly within ±0.5kPa; this magnitude of error is typical also of the mean applied pressure. This being the case, the minimum applied pressure is limited to about 5kPa. The filtration rig control software, Press-o-matic (written by R. G. DE KRETSER), makes an internal on-the-fly (approximate) correction for the hydrostatic head of fluid, such that the control system ultimately seeks to match the total stress at the membrane to the set pressure. An outstanding feature of the rig is the ability to correctly determine the stress at the upper surface of the sample. Many other designs incorporating a piston do not exclude wall friction effects [e.g. 416, 585, 598, 682] [cf. 984], or do not distinguish between sample–wall and piston–wall friction [e.g. 195, 316, 646, 661, 1010, 1033, 1144]. (Devices applying pressure through a fluid, especially compressed air, often have other operational problems.)

The principle of the analysis is to measure dV 2/dt in cake formation and φ∞ at equilibrium for a number of applied pressures, Δp, with the initial solidosity, φ0, held constant. py(φ∞) is then obtained directly by equating with Δp [241, 1059]. R(φ∞) is found by fitting dV 2/dt :c.f. as a function of Δp, and then differentiating this function, as described in §2▪4▪5▪6. R(φ∞) is thus found from equation 2-130.

3▪5▪3▪1

Stepped pressure analysis

Characterisation of the samples at higher values of φ was carried out using a dead-end filtration rig (Figure 3-17) with stepwise incrementing of the pressure in two separate runs according to the method described by DE KRETSER, USHER and co-workers [608, 1059]. The ‘compressibility’ run allows the cake to dewater to equilibrium at each pressure before stepping to the next [608].

Given that py(φ∞) is a material property, the foregoing

compression should not affect the equilibrium state of subsequent dewatering at higher pressures. (This was earlier validated by DE GUINGAND [435] for centrifugation.) Thus, this single run generates multiple pairs of (Δp, φ∞) data. 3▪5 : Sludge characterisation — compressional rheology

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D. I. VERRELLI

The ‘permeability’ run operates such that stable measurements of dt/dV 2 can be made while the filter cake is forming.

This is achieved by incrementing the pressure as soon as a

reasonably constant value of dt/dV 2, or ‘plateau’, is reached — long before equilibrium [608]. In this way multiple pairs of (Δp, dV 2/dt :c.f.) data are obtained. With the multiple-pressure permeability runs there is a trade-off between waiting for ‘perfectly’ linear V 2(t) behaviour before stepping to the next pressure and accepting significant curvature. In practice an acceptable compromise is usually reached, although there are occasional difficulties — if the tolerances are set too tight, the permeability run can effectively become another compressibility run. (The less rigorous single-run stepping protocol of MURASE et alia [764] may suffice for materials that exhibit small relative increases in solidosity upon compression in the pressure interval of interest, but cannot be relied upon for the present samples.)

Solids diffusivities are generally not reported here, but were routinely computed from stepped-pressure filtration data according to equations 2-63 and 2-136: typical outputs are presented in §5▪9▪3. Solids diffusivities were also occasionally estimated as intermediate results, according to equation 2-127, to permit calculation of R for samples where reliable data could not be obtained from ‘permeability’ filtration runs: see §7▪4▪3, §7▪4▪6. (The latter data, extracted from ‘compressibility’ runs, imply that only a s i n g l e steppedpressure run is required to fully characterise a sample at high solidosity. The experimental time saving is offset by the reduced p r e c i s i o n of end-point extrapolation, as demonstrated in §7▪4▪4.)

3▪5▪3▪1(a)

Reproducibility

Figure 3-18 and Figure 3-19 illustrate the reproducibility of measurements obtained by

stepped-pressure filtration characterisation for a given sludge. It can be seen that repeated measurements conducted some days or weeks apart on each of the four alum sludges presented here exhibit good agreement. The paired curves generally show the same trends, and the differences between repeated runs are relatively small.

A few possible reasons for the discrepancies can be conceived of. 224



There does not appear to be any consistent trend indicative of ‘inherent’ changes in the sludges due to ageing between runs. (The parameter pairs are listed chronologically in the chart legends.) This is in line with the findings of §8▪1 with regard to much longer ageing periods. It has been mentioned (§3▪5▪2▪1) that pre-thickening of samples was originally practised, but later abandoned in order to minimise sample handling and alterations to sample shear history. As alluded to, no consistent tendencies due to the centrifugation can be identified. Finally, every analysis depends heavily upon accurate determination of the solidosity. Concordant results were usually attainable, which generates confidence in their accuracy. Regardless of this, the choice between solidosities based on loaded or unloaded material has been systematised (described on p. 202), and evidently this is advantageous: even where a massive discrepancy between φ0 estimates of ~61% was obtained, ultimately the R(φ0) estimates differ by a much smaller — practically negligible — amount.

(Despite this

reassurance, dewaterability parameter estimates arising from data manifesting such large discrepancies could not be used without verification from a repeat characterisation, as here.)

In §3▪5▪4 the consistency in dewaterability assessment for s i m i l a r sludges (generated separately) is demonstrated across the full range of solidosity.


225

D. I. VERRELLI


300 20050405 20050405 20040705 20040705

79 79 80 80

6.3 6.3 5.8 5.8

65rpm 65rpm c dMIEX c dMIEX c

100

50

10 5 1

0.01

0.1 Solidosity, φ [–]


300 20040213 20040213 20040705 20040705

84 84 80 80

6.1 6.1 4.8 4.8

TW c TW c dMIEX c dMIEX c, 18%

100

50

10 5 1

0.01


Figure 3-18: Duplicate compressive yield stress measurements from stepped-pressure filtration. Samples are identified by raw water date, alum dose [mg(Al)/L], pH, and other characteristics. In the final column “c” represents samples pre-thickened by centrifugation, and percentages indicate mismatch in solidosity estimates based on measurements of loaded and unloaded material.

226


2



3.E+14 20050405 20050405 20040705 20040705

79 79 80 80

6.3 6.3 5.8 5.8

65rpm 9% 65rpm c dMIEX 16% dMIEX c

1.E+14

3.E+13 1.E+13 0.01

0.1

2



3.E+14 20040213 20040213 20040705 20040705

84 84 80 80

6.1 6.1 4.8 4.8

TW TW c, 61% dMIEX dMIEX c

1.E+14

3.E+13 1.E+13 0.01


Figure 3-19: Hindered settling function estimates from duplicate stepped-pressure permeability runs, based on av er age of py(φ) measurements. The legend lists the raw water collection date, alum dose [mg(Al)/L], pH, and other sample characteristics. “c” denotes prior centrifugation; percentages indicate mismatch in the estimates of φ0 based on loaded and unloaded material.


227

D. I. VERRELLI

3▪5▪3▪2

Permeation

A permeation run is suited to a material that is highly permeable and settles extremely rapidly (i.e. on the order of tens of seconds), such as sludges subjected to freeze–thaw conditioning (§8▪2). For these materials a routine ‘permeability’ run cannot be conducted. Permeation experiments can also be carried out on materials that settle and dewater slowly, however more time is then required to reach steady-state conditions, and for such samples the usual filtration tests would run as desired.

For such materials the chief benefit of

permeation testing is the ability to apply the technique outside of the filtration rig with only gravity and hydrodynamic forces applied, so that data for pressures between those found in settling and filtration can be obtained [e.g. 105].

In these experiments sample is loaded into the filtration rig compression cell as usual. On top of this material, additional supernatant that has been previously decanted off is carefully added. Thus the first major difference between a permeation run and a regular filtration run (including single pressure, and stepped pressure compressibility and permeability runs) is that the material loaded is not homogeneous, in the sense that it comprises a sludge at the bottom and a clear liquid on top. The second major difference lies in the way the (first) set pressure is reached. In a normal filtration run the pressure applied to the sample is gradually ramped up to the setpoint (so as not to overshoot significantly). For stepped-pressure filtration the first setpoint is typically quite low, so the time taken to reach the set pressure is typically no more than a couple of minutes. (For single pressure filtration, the setpoint is generally reached long before the material goes into the cake consolidation mode, and otherwise the pressure can be manually adjusted up by briefly bypassing the automatic control.) However, for materials that dewater very rapidly, it is not feasible to wait even one minute for the set pressure to be established, and so use is made of a new feature of the filtration rigs, namely a toggle valve on the permeate outlet — i.e. the ‘drain valve’. This is shut off initially, while the internal pressure reaches the setpoint, at which time it can be fully opened.

228



This feature also prevents the sample from rapidly draining away before the experiment has commenced. For runs with a high first pressure (e.g. 200kPa), the rate of dewatering is so rapid that the movement of the piston causes the pneumatic cylinder to move faster than air can be let in through the conventional automatic control valve. For such cases the practical solution is to open the bypass line around that control valve sufficiently to boost the air inflow to the cylinder, with control effected by the cylinder exhaust valve, which will pulse open whenever the cylinder pressure is too high. This is a rudimentary form of control which is made necessary by the fact that the rigs are generally not tuned to operate with such highly dewaterable samples. The efficacy of this mode of pressure control is indicated by Figure 3-20.

The theory allowing extraction of dewaterability information — namely R — from permeation experiments is actually simpler than regular filtration, and harks back to the experiments of DARCY with RITTER and BAUMGARTEN [295, reprinted in 502].

This is

400

350

350

300

300

250 200 150 100

250 200

Consolidating cake. Waiting for automatic pressure control.

400

Pressure [kPa(g)]

Pressure [kPa(g)]

expounded in §2▪3▪1 and §2▪4▪5▪5.

Getting up to pressure 'manually' with permeate valve closed.

150

Open valve for permeation.

100 Set pressure Sample pressure Cylinder Pressure

50

Set pressure Sample pressure Cylinder Pressure

50

0

0 0

500

1000

1500

2000

100

200

300

Time [s]

(a)

400

500

Time [s]

(b)

Figure 3-20: (a) The period from 500 to 1700 seconds shows the close control of sample pressure attainable using automatic control when the rate of dewatering is not too high. (b) the period from 340 to 370 seconds shows the level of control achievable using ‘manual’ control when the rate of dewatering is high.


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D. I. VERRELLI

3▪5▪3▪3

Improvements made to methodology

3▪5▪3▪3(a)

Rig design and operation

Experiments performed in the present work were carried out on filtration rigs like those described in the literature [608, 1059], but with a range of enhancements.

The following key modifications to the physical set-up were made: • 0.22μm polyvinylidene fluoride (PVDF) membranes were employed in place of the usual 0.65μm PVDF membranes.

This is based on sludge solids observed in the

permeate when membranes of the larger pore size were employed. • A shallow liquid seal beneath the filtration cell was created in order to eliminate the possibility of evaporation from the sample [cf. 242] — either during a run or after completion and awaiting collection. • A drain valve was installed (by R. G. DE KRETSER) to permit samples to be loaded and the applied pressure to be ramped up without any filtration occurring. o Installation of the drain valve on a long, thin length of tubing was also sufficient

to adequately reduce evaporation without the need for a (separate) liquid seal. • Shielding of the rig from direct sunlight was found to ameliorate thermal cycling (see §3▪5▪3▪4, following).

A simple innovation was introduced in the multiple-pressure permeability characterisation configuration. Simplistically, the sample, whose initial solidosity is assumed known, may be compressed until linear V 2(t) behaviour is attained.

This is the fastest method of

characterising permeability. Unfortunately, the initial solidosity is often not sufficiently well known to employ this technique. There is the additional disadvantage of cleaning up a cell of still-fluid sludge. Conventionally, the final pressure is maintained until equilibrium is reached, providing a single compressibility value as well as a firm cake whose solidosity may be analysed with reasonable accuracy. Unfortunately, the desire to run a permeability test with a more dilute sample (to avoid entering cake compression too soon) is countered by the need to avoid

230



forming excessively thin final cakes.

This is a particular problem for drinking water

treatment sludges, where the errors in the height measurement would become unacceptable. Therefore a procedure was introduced whereby the run steps through each pressure after attaining linearity, as described above, while the final cake compression is carried out at intermediate pressure. That is, there is a step d o w n in pressure. This enables a final solidosity analysis to be carried out (spatial variation of φ is allowable here, provided a representative sample is collected upon unloading), while avoiding the formation of an excessively thin cake. Some artefacts potentially due to elastic expansion of the sample upon partial relief of the pressure have not been fully explored at this date (cf. §9▪4), but are expected to be negligible.

A number of technical improvements have been made to the filtration rig control software (Press-o-matic) by R. G. DE KRETSER to further improve reliability and usability. Even without these, there are a number of user-specified settings that will affect the progression of a filtration run.

It has been found that the following settings (Table 3-11) often yield a good result. The chosen tolerances are significantly tighter than the default settings (Table 3-12). The reason for the tightening is to increase confidence that linearity has been achieved.

It is also apparent that the final permeability pressure is designed never to achieve the linearity condition (0.00% tolerance), acting only as a stage in which formation of a cake is completed. This setting would usually be made to the final pressure even if the default linearity criterion parameters were otherwise adopted.

The specified tolerances can be interpreted as follows.

The penultimate row, labelled

‘tolerated σ/μ’, gives an indication of the maximum tolerable random noise in a signal that is not drifting. The final row, labelled ‘tolerance / points’, gives an indication of the tolerated gradient, in the absence of any noise.


231

D. I. VERRELLI

Table 3-11: Typical Press-o-matic stepped pressure filtration run settings for compressibility (py) and permeability (R). Relative standard deviation, σ/μ, estimated assuming a GAUSSian statistical distribution (upper limit, α = 0.05).

Step number

1

2

3

4

5

6

7

8

Pressure (py)

[kPa]

5

10

20

50

100

200

300

Pressure (R)

[kPa]

5

10

20

50

100

200

300

75

[–]

100

100

100

100

100

100

100

100

Tolerance (R)

[%]

2.00

1.50

1.00

1.00

1.00

0.50

0.50

0.00

 Tolerated σ/μ

[%]

0.61

0.46

0.30

0.30

0.30

0.15

0.15

0.00

 Tolerance / points [%]

0.020

0.015

0.010

0.010

0.010

0.005

0.005

0.000

Points (R)

Table 3-12:

Default linearity criterion parameters for Press-o-matic stepped-pressure

permeability runs.

These apply regardless of the set pressures entered.

Relative standard

deviation, σ/μ, estimated assuming a GAUSSian statistical distribution (upper limit, α = 0.05). [cf. 608]

Step number

1

2

3

4

5

6

7

8

[–]

50

60

70

80

90

100

110

120

Tolerance (R)

[%]

3.50

2.75

2.25

2.00

1.75

1.75

1.75

1.75

 Tolerated σ/μ

[%]

1.14

0.88

0.71

0.62

0.54

0.53

0.53

0.52

 Tolerance / points [%]

0.070

0.046

0.032

0.025

0.019

0.018

0.016

0.015

Points (R)

Aside from slightly tightening the effective tolerance, increasing the number of points improves confidence that the slope has settled to an essentially constant value, rather than decreasing slowly but erratically.

The initial data-collection phase of the permeability runs is typically monitored to ensure that linearity tolerances are appropriate.

232



3▪5▪3▪3(b)

Data processing and analysis

While not strictly a component of the experimental procedure, the data processing and analysis was expedited by the refinement of a partially automated spreadsheet (based on earlier versions created by R. G. DE KRETSER and A. R. KILCULLEN) for the computation of a range of dewaterability parameters. This spreadsheet was suited for routine analysis. Of course, other spreadsheets were also developed for specific purposes, such as the error analyses described in §7▪4▪4▪2 and §S15.

3▪5▪3▪4

Key interferences

Two key factors may interfere with accurate measurement: • temperature; and • side-wall interaction. Side-wall interaction is the primary mechanism for a potential violation of the assumption of one-dimensional dewatering. Further aspects are considered in the discussions following.

3▪5▪3▪4(a)

Temperature

Ambient temperature changes have apparently led to cycling at long times. Figure 3-21 illustrates cycling that was observed in two compressibility runs. One of the runs was carried out on the older filtration rig, which (at that time) was exposed to direct sunlight. The cycling is only evident in the slope data, and then only because the run reached extraordinarily low filtration rates before stepping to the next pressure (this in turn was due to the greater amounts of solids loaded, leading to a thicker cake, with slower overall filtration kinetics). This was a rare occurrence, and did not affect the general results of the present work.


233

D. I. VERRELLI

3.0E+9 V² 1/Slope

9.0E-3

200kPa 100kPa 50kPa

8.0E-3

2

20kPa

7.0E-3

2.0E+9

10kPa

2

6.0E-3

2.5E+9 1 / Slope, dt /dV [s/m ]

Specific filtrate volume squared, V ² [m²]

1.0E-2

5kPa

5.0E-3

1.5E+9

4.0E-3 1.0E+9

3.0E-3 2.0E-3

5.0E+8

1.0E-3 0.0E+0

0.0E+0

0.0E+0

5.0E+5

1.0E+6

1.5E+6

2.0E+6

Time, t [s]

Figure 3-21: Thermal cycling in filtration. 160mg(Fe)/L sludge filtered on newer ‘aluminiumframed’ rig. Minor tick marks and graticule demarcate one-day intervals. Inverse slope calculated for 13-point centred moving sub-sets.

Although thermal expansion of the frame may be significant for changes in temperature of order 15°C (of order 100μm), the inner members compensate for most of this, so that the ‘mismatch’ is considerably smaller. This mismatch can be estimated from the differences in linear thermal expansion coefficients for the various components of the rig (stainless steel ~ 17×10‒6 K‒1;

mild steel ~ 12×10‒6 K‒1;

aluminium 23×10‒6 K‒1 [662]).

The complicated

construction makes accurate computation difficult, and temperature-dependent flexure of the cross-bar is not considered. Nevertheless, the ‘compensation’ effect indicates that this mechanism may not be the cause of the cycling seen in Figure 3-21. This suggests that the viscosity of the liquid phase is dominating the cycling behaviour. Certainly the variation in viscosity with a 15°C temperature change is significant: around 30% or more for water [917].

Melbourne’s o u t s i d e

air temperature

typically

varies about 10°C over 24h,

superimposed on a seasonal variation of about 10°C between summer and winter [77, 790]. The laboratory in which settling and filtration were conducted was equipped with basic temperature control, which was adequate to avoid extremes of ambient temperature, but still 234



affected somewhat by outside conditions. (In the centrifuge a consistent temperature setting was used that equated to just under 20°C. The temperature of laboratory coagulation was 20±5°C, with almost all within 18±3°C — this level of variation ought cause no perceptible change in aggregate properties [269] [cf. 1113].) Variation in liquid viscosity up to ~30% over the course of an experiment, or between experiments, could occur.

Due to the difficulty in correctly determining an ‘effective’

temperature for each test, the liquid viscosity was universally taken as 1mPa.s, equivalent to a temperature of 20°C. Fortunately the level of variation in the hindered settling function (which depends on viscosity) is typically many times greater. No significant artefacts arising from this assumption have been identified, and the good concordance of R(φ) between similar (or identical) samples indicates that the assumption is reasonable.

3▪5▪3▪4(b)

Violation of one-dimensional dewatering assumption

The potential for friction between the sample and the walls of the filtration chamber to occur and introduce errors into characterisation results was first recognised in early studies (from circa 1953 [416] [see also 297, 863, 1038]), but more frequently dismissed as negligible.

LU, HUANG & HWANG [682] showed that two-dimensional effects (adhesion or friction against the side walls) are significant even for large cross-sections, manifesting as losses in the transmission of the applied stress through a (filter) cake of typical order 10% and as radial variation of solidosity and particle pressure [1144]. Similarly, ZHAO et alii [1143] reported that side-wall friction can significantly decrease the axial stress transmitted through to the membrane (from the piston), and can also lead to significant radial variation in solidosity, with reduced φ at the walls. Modelling of the sludge as an elastic solid also predicted radial variation in φ even with perfectly frictionless walls at short times, given sufficiently low modulus of elasticity [1143]. BRISCOE & ROUGH [195] found qualitatively the same spatial variation of φ in alumina powder compacts. Earlier research by SHIRATO et alia [930] and TILLER, HAYNES & LU [1033] likewise demonstrates the relative magnitude of losses due to contact between the particulate cake and the cell wall in filtration. The losses were attributed to friction arising as a multiple (coefficient of friction, μ) of the lateral stress — which was itself assumed to be a multiple 3▪5 : Sludge characterisation — compressional rheology

235

D. I. VERRELLI

(stress analogue of ν, say н) of the axial stress [see also 140, 194, 195, 316, 361, 661, 682, 850, 859, 912, 918, 946, 984, 1012, 1013, 1014, 1038] [cf. 242, 1056, 1121, 1125], as in equation 9-10b — and a constant cohesion term [930, 1033]. It should be noted that the local axial stress at the relevant z plane must be used; this is often assumed uniform [1033], but in reality may vary, so that some average is required (which also yields a tractable p s e u d o -twodimensional problem) [682, cf. 1143]. Published values of н are provided in §9▪4▪2.

According to measurements by LU, HUANG & HWANG [682], the radial stresses in filtration are of order 30 to 40% of the a p p l i e d axial load (less for larger Z / D, as the l o c a l axial stress drops off further). The axial stress also varies over the cross-section, being maximal at the centre (the variation is greater further from the piston face) [682] [see also 195, 661, 1121] [cf. 984]. The sample may also experience a small lateral shear stress [984, 1121].

In practical terms it is of interest to estimate the ratio of networked-sample height, Z, to vessel diameter, D, for which wall friction is likely to be negligible. The following results have been reported to yield <10% frictional loss: • SHIRATO et alia [930] — Z / D ( 0.45 to 0.65 at respective pressures of 160 and 450kPa for 100μm kaolin. • TILLER, LU and HAYNES [1033, 1038] — Z / D ( 0.1 * for cellulose (fibrous, deformable particles of size ~5μm [416]) in acrylic and stainless steel cylinders at ~690kPa; the ratio must be smaller at lower pressures;

the allowable ratio can be doubled for very

smooth poly(difluoromethylene) cell walls, but is smaller for ~1mm sand samples. • LU, HUANG & HWANG [682] — Z / D < 0.20 for various 101μm-sized particulates compressed at 490kPa [see also 1143]. • STRIJBOS et alia [984] — Z / D ( 0.14 (lubricated cell) and Z / D ( 0.12 (unlubricated cell) for 40nm ferric oxide powder compressed at ~10MPa.

*

The authors [1033] have the ratio as 0.05, but emended curve fits of their Figure 7 data that are not forced through 0% losses at Z / D = 0 suggest that friction between the p i s t o n and the cell wall, which they did not correct for, may have caused losses of order 10% of the axial stress.

236



• DIMILIA & REED [316] — Z / D ( 0.15 (lubricated cell) and Z / D ( 0.10 (unlubricated cell) for 58μm agglomerates of alumina powder compressed at 25 to 125MPa. • BRISCOE & ROUGH [195] — Z / D ( 0.30 (lubricated cell) and Z / D ( 0.15 (unlubricated cell) for agglomerated alumina powder compressed at 70MPa [cf. 194]. • GRACE [416] — Z / D ( 0.75 for flocculated 0.4μm-sized calcium carbonate compressed at 2.4MPa; Z / D ≤ 0.6 recommended for pressures from 7kPa to 19MPa. This was construed based on local solidosity measurements obtained by cross-sectioning filter cakes [416].

Only short times (≤15min) were allowed for the process to come to

‘equilibrium’, suggesting that frictional effects may have been overstated [see 1010]. • ASTM D 2435–04 [37] — Z / D ≤ 0.4 for double-ended (œdometric) testing of soils; Z / D < 0.25 preferred. At lower pressures Z is likely to be higher, compounding the frictional losses. It should also be recognised that the trend for frictional losses to increase with Z indicates that piston–wall interactions are secondary, as these would decrease for increasing Z. The published data [682, 930, 1033] indicate that higher-solidosity cakes are less efficient at transmuting axial stress into lateral stress [not 1038] (ν < 0.5), and so frictional losses in the axial stress tend to be smaller — aside from the decrease due to reduced Z / D. A more general discussion of wall effects is presented in §9▪2.

Any deterioration in transmitted axial stress ought to be small in the present work, given the low equilibrium cake heights typically seen — (25mm for Δp = 5kPa, and (10mm for Δp = 300kPa — relative to the diameter of the cell, viz. 40mm. For stepped-pressure runs, the accuracy would increase at higher pressures where the cake height is less and also the higher solidosity tends to reduce radial stresses (so axial stress is maintained better [cf. 682]). In a ‘permeability’ run the data is generally obtained while the s a m p l e height is large, however the c a k e height is small, as the cake (or higher-density cake) has only just formed — so Z / D is relatively small, and the errors due to sidewall friction small *.

*

GREEN [424, 425] presented filtration ‘permeability’ measurements to demonstrate that wall effects are negligible for cylinder diameters of 28 to 40mm (for coagulated zirconia). This ‘validation’ does not necessarily extend to ‘compressibility’ measurements.


237

D. I. VERRELLI

A further justification for the model can be made when the compressive yield stress is significantly greater than the shear yield stress, and hence controls the process [630]. While this is true of empirical py(φ) and τy(φ) data (§2▪4▪7▪1), some uncertainty exists over whether the measured τy(φ) values are applicable, as they are almost universally * obtained in the absence of a normal (i.e. compressive) load which may strengthen a network in shear [151, 243, 753, 876, 984, 1014, 1115] [cf. 661, 912] (§9▪4▪2). An extra complication arises if the consolidation is anisotropic [see 710, 753, 1014, 1038], cf. ‘System anisotropy and osmosis’ in §2▪4▪5▪1(a).

Experimental measurements on a filter cake obtained by compressing a plant ferric sludge (Macarthur 2005-09-21) at ~450kPa showed no indication of a radial variation in φ — see Table 3-13. The filter cake was wiped clean of superficial grease and divided into two

annular portions and one core portion. The total error in CφD was estimated to be no more than 2%, or 0.005, but this includes uncertainty in ρS, ρL and ysupernatant (see §2▪1▪1, §4▪3▪1) which should be identical for each portion of the cake. Excluding this uncertainty gives error estimates of about 0.001, large enough to explain the variation in Table 3-13 given uniform φ over the cake radius.

Table 3-13: Radial variation in solidosity for a filter cake consolidated at ~450kPa.

Peripheral annulus

Inner annulus

Core

Mean radial width, CΔrD [mm]

5.2

5.0

9.8

Portion of total volume

[%]

45

31

24

[–]

0.2693

0.2707

0.2690

Mean solidosity, CφD

*

A notable exception is the ‘triaxial compression test’ common in soil mechanics [151, 267, 710, 850, 912, 946, 984, 1013, 1014, 1038]. This reduces to an ‘unconfined compression’ [1014] or ‘squeeze film’ [927] test in the limit of nil constraining stress. Simultaneous normal stresses are imposed in a few other tests [see 267, 710, 850, 876, 912, 946, 1014].

238



MEETEN [737] alluded to a similar analysis of the solidosity “across the diameter of the cake” for unspecified material(s), and likewise found no variation beyond experimental error.

An example of WTP sludge cake forms occasionally observed in the present work is presented in Figure 3-22. Featured are the non-vertical side profile and the central crevice. The diameter of the top surface matched the piston (or cylinder) diameter. The mechanism by which these features manifest has not been established.

Figure 3-22: Schematic of cake unloaded from filtration rig showing crevice in top surface and non-straight side profile. These features were present in a minority of cases.

An attempt to investigate deviations from one-dimensional dewatering by laying down coloured layers of sample was unsuccessful, because — unlike powders [e.g. 195] — it proved impractical to prepare horizontal strata in the loaded sample.

3▪5▪4

Reproducibility Experimental reproducibility of the empirical [dewatering] parameters is a continuing problem. — TILLER & YEH (1987) [1040]

Samples were identified as ‘replicates’ when their generation conditions were ‘similar’. All of the samples were generated from raw water derived from Winneke WTP (see §3▪2▪2), with one exception. In general the pH differences are < 0.5 units, and the doses are < 7% different, with one exception.


239

240

[10/m]


8.9 3.14

8.6

2.9

[–]

Hydrolysis ratio [–]

Note: Asterisked samples are taken as representative.

pH

[mg(Al)/L]

Dose 80

[mg(Al)/L]

set pH

92

0.73

0.55

~10

11

a

– 84 6.1 2.76

80 8.6 3.15

0.24

0.87

~2.5

1

2004-02-13

14

2004-05-21

2.69

6.0

79

~4

1.14

22

2006-01-05

Winneke

Tapwater

Winneke

A blend of raw water from 2004-01-08 and 2003-12-02.

2006-06-09

2004-02-11 a

9

Winneke

Winneke

∗

2.69

5.9

80

~2

0.73

11

2006-06-09

Winneke

High dose, intermediate pH ∗

High dose, high pH

–

Optimum dose at

A254nm

[mg/L Pt units]

True colour

and date

Raw water source

Sample

2.16

6.0

5.0

<3

0.31

5

2003-12-02

Winneke

2.25

6.0

5.0

≤1

0.66

10

2004-01-08

Winneke

∗

Low dose, intermediate pH

D. I. VERRELLI

Table 3-14: (a) Generation conditions for ‘replicate’ laboratory sludge samples.


Table 3-14: (b) Generation conditions for ‘replicate’ plant sludge samples.

Sample

Plant ∗

Raw water source

Winneke

Winneke

2005-07-01

2005-04-05

[mg(Al)/L]

1.9

1.9

[–]

6.2

6.1

Yes

Yes

and date Dose pH Polymer

Note: Asterisked samples are taken as representative.

The exceptions are the samples dosed at 84 and 92mg(Al)/L. These were included on the basis that at doses of this magnitude the precipitated coagulant will dominate the dewatering behaviour (see §5▪1▪1, §5▪3) — as seen, this assessment appears to be justified.

Details of the sample generation conditions appear in Table 3-14, and their compressive yield stress and hindered settling function curves appear in Figure 3-23 and Figure 3-24, respectively.

It may be seen that the agreement between the replicate runs is generally very good. This is strong evidence that: • the method of characterisation is robust and reproducible; and • the method of sludge generation is robust and reproducible.


241

D. I. VERRELLI


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 mg(Al)/L 1.E-2

Lab. Lab. Lab. Lab. Lab. Lab. Lab. Lab. Plant Plant

1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

92 80 80 84 79 80 5.0 5.0 1.9 1.9

pH 8.6 8.9 8.6 6.1 6.0 5.9 6.0 6.0 6.2 6.1

1.E-1

* * * * 1.E+0

Solidosity, φ [–] Figure 3-23:

Compressive yield stress data for replicate alum sludge samples.

Asterisked

samples are taken as representative in subsequent charts. The 84mg(Al)/L sludge has the highest gel point of those three replicates.

242



2


1.E+15

1.E+14

1.E+13

1.E+12 mg(Al)/L Lab. 92 Lab. 80 Lab. 80 Lab. 84 Lab. 79 Lab. 80 Lab. 5.0 Lab. 5.0 Plant 1.9 Plant 1.9

1.E+11

1.E+10

1.E+09 1.E-4

1.E-3

1.E-2

pH 8.6 8.9 8.6 * 6.1 6.0 * 5.9 6.0 6.0 * 6.2 6.1 *

1.E-1

1.E+0


Hindered settling function data for replicate alum sludge samples.

Asterisked

samples are taken as representative in subsequent charts.

3▪6

Sludge characterisation — shear yield stress

The shear properties of WTP sludges have been investigated by various workers, with a focus on assessing their suitability for landfill disposal [see e.g. 161, 281, 282, 880, 1098]. A number of researchers have used standard rheological techniques to estimate the rheological shear properties of WTP sludges [e.g. 447, 722]. Of especial interest is the shear yield stress, τy, which can usually [cf. 1056] be most reliably measured by inserting a four-

3▪6 : Sludge characterisation — shear yield stress

243

D. I. VERRELLI

armed ‘vane’ into a sample (other geometries are possible [127]) and observing the maximum stress, τ, at a low, constant strain rate [20, 286, 447, 779, 1014]. In comparison capillary and analytical rheometers often suffer problems of particle migration and ‘slip’ [127, 151, 527, 779, 1015], and cone (or ball [885] et cetera [151, 267]) penetration methods [282, 880] depend upon empirical correlations [151, 267, 850] and are not reliable at low solidosity or for materials that consolidate very slowly [cf. 779]. Although quite straightforward and robust compared to alternative rheological techniques, the vane test does rely on the availability of certain ‘specialised’ equipment (although more rudimentary versions are available, such as the Torvane [580]) [see also 267, 850, 912, 946, 1014]. An even simpler and cheaper alternative ‘borrowed’ from the concrete industry [e.g. 10] was promoted by PASHIAS et alia [828, 829], called the Slump Test. Data from this technique show good agreement with vane test data [268, 885] [cf. 829]. Parallel-plate compressional ‘plastometry’, ‘squeeze film’ or ‘upsetting’ devices [127, 151, 927] exploit a similar physical mechanism to slump testing [873], but again require more sophisticated equipment. The analysis is also contingent upon the degree of wall ‘slip’ [127] [cf. 927]. UHLHERR et alia (1984) [cf. 1056] proposed another test method that is physically similar to slump testing, involving the measurement of the (maximum) unyielding height of a ‘slab’ of material on a plane, or channel, inclined at an angle [285, 779]. This simple technique does not require sophisticated equipment. For some materials ‘slip’ artefacts may arise unless the surfaces are roughened [1056] [cf. 285]. In the original procedure the angle was increased until the material yielded: accuracy may be poor, especially for materials with small yield stresses [285, 779].

(‘Yielding’ can be distinguished from ‘creep’ by monitoring the

displacement of a ‘tracer’ particle embedded in the top surface of the sample [see 1056].) In a later adaptation the angle is fixed and the material yields (cf. slumps) until a stable thickness is reached [cf. 285]: in this configuration the yield stress may be underestimated due to the destructive nature of the prior flow [cf. 286, 779].

244



3▪6▪1

Conventional subaerial slump tests

The original slump test technique involved loading the sample into a conical frustum-shaped container with the broad end sitting flush on a flat surface and observing the vertical s u b s i d e n c e upon careful removal of the mould * [typified by 10]. The conical profile was presumably employed due to the expectation of more favourable disengagement of the sample from the container — perhaps through analogy to beachside experiments with sand castles [in the vein of 120 !] — and possibly also due to the cone’s greater stability — i.e. it is less inclined to lean [cf. 828], as it is ‘bottom-heavy’. However numerous disadvantages of the conical mould have been identified in comparison with a simple cylinder [cf. 10, 268, 828, 885]. Cylinder aspect ratios of approximately unity are preferred [828]. A convenient summary of the ‘conventional’ theory for estimation of τy from conical and from cylindrical slump tests was presented by CLAYTON, GRICE & BOGER [268]. Amendments to the theory have been suggested by ROUSSEL & COUSSOT [873] to account for the combination of shear and elongational flow arising in the most general analysis. Purely elongational flow is attained for asymptotically small slumps (i.e. large τy); and shear flow for large slumps [873].

Intermediate-τy behaviour tends to be better predicted by the

asymptotic shear flow model (if a combined model is not to be implemented) [873].

An obvious problem is the range of materials (or solidosities) that may be characterised, restricted to τy in the approximate range 30 to 800Pa [828]. Larger τy would result in imperceptible subsidence, unless the sample height were commensurately high [cf. 268] †. On the other hand, very small τy will result in the sample spreading over a very wide area, with an immeasurably small height of unyielded material. Moreover, in the case of WTP sludges made up of relatively fragile aggregates, the very slumping motion could even be sufficient to decrease τy to still lower values through aggregate densification (or possibly *

Depending upon the size of the mould, difficulties in loading the sample [cf. 268] could be minimised by inverting the mould before loading, and then upending it on the flat surface for characterisation. In this a removable lid would be most useful.

†

An alternative in which the sample is ‘jolted’ appears highly susceptible to operator variability [cf. 321].


245

D. I. VERRELLI

higher values through fragmentation) [cf. 722]. Furthermore, low-τy materials will stand to be more significantly affected by inertial effects and surface tension effects, whose magnitudes may be of order 101Pa [see 873].

In the case of low-yield-stress materials an adaptation has been made, whereby instead of the vertical subsidence, the radial s p r e a d of the sample at the base is measured [873], referred to as “slump flow” [321, 885].

The analytical theory for this regime has received less

attention; a model was proposed by ROUSSEL & COUSSOT [873]. It becomes inaccurate where the layer thickness approaches the size of the constituent particles or aggregates [321, 873], or as the layer diameter approaches that of a ‘puddle’ of particle-free fluid (for which τy = 0).

3▪6▪2

Proposed subaqueous slump test

A modification to the cylindrical (or conical) slump test is herein proposed, suited to lowyield-stress samples. The key feature of the proposed modification is the transfer of the slumping process to an under water environment. Borrowing from the geological sciences [e.g. 305, 851], the modified test can thus be described as a ‘subaqueous’ slump test, whereas the conventional versions are ‘subaerial’ slump tests. In the more rigorous measurement, the test would be carried out in supernatant identical to the interstitial fluid of the sample. However, provided the supernatant rheology (chiefly viscosity) is essentially that of water, tapwater may also conveniently be used as the ambient medium. Experiments suggest that diffusion of chemicals out of the sludge interstitial fluid is likely to be much slower than the kinetics of the slump test [86]. The principle of the modification is that conducting the test in a fluid medium reduces the self weight of the sample, as the relevant density becomes the buoyant density. Given that WTP sludges are predominantly made up of water, their overall densities are only slightly greater than that of water:

typical measurements in the present work were of order

1010kg/m3, depending on φ.

The corresponding buoyant density of the sludge is then

approximately 10kg/m3, i.e. two orders of magnitude lower! It should be clear that this test will be more sensitive to the density specification.

246



Further consequences of this changed environment are that capillary forces will no longer affect behaviour [see e.g. 904], surface tension becomes unimportant and inertial effects can be minimised [cf. 873]. It also becomes feasible to leave samples to slump for arbitrarily long times without fear of evaporation, if desired.

The technique has been subjected to preliminary investigation using three samples: 1.

An alum sludge conditioned with Magnafloc 338 — 80mg(Al)/L, pH 5.9; φ0 = 0.0068, φg ≈ 0.0034. py(φ0) ≈ 154Pa.

2.

An unconditioned alum sludge — 80mg(Al)/L, pH 5.9; φ0 = 0.0032, φg ≈ 0.0019. py(φ0) ≈ 14Pa.

3.

A sample of moderately concentrated calmagite solution made up in deionised water. This gave a coloured sample which otherwise behaved as pure water. — φ0 = 0. py(φ0) = 0Pa.

The sludges had been settling for several months. Material was taken from the top of the settled bed, with supernatant decanted. Further details of the alum sludges are presented in §7▪4.

As a proof of concept, the experiments were carried out on a very small scale in tap water. The cylinder used was borrowed from a CST rig (§7▪4▪1▪2), of stainless steel with inner diameter 18.0mm, and height 24.7mm. It is considered understood that routine testing would use larger cells (say 100mm). Both subaerial and subaqueous experiments were conducted on glass surfaces cleaned with ethanol.

Sludge was gently loaded into the cylinders using the thin end of a TRULLA spatula. In loading the samples, it is essential that the cylinder sit flush on the glass, to avoid material leaking out. In the subaerial experiments, surface tension tends to assist in preventing significant escape, but that is not so in subaqueous experiments. Thus, to avoid material transfer under the cylinder walls, it was found advantageous to minimise the difference in hydrostatic head (i.e. fluid level) between the inside and outside of the cylinder. This was most readily achieved by alternating between loading a portion of sludge and topping up the reservoir with tapwater.


247

D. I. VERRELLI

It was important to minimise swirling in the reservoir as tapwater was added, especially as and after the liquid level reached the top of the cylinder, to avoid disturbing the sludge.

Photographic records of the two tests for each of the three materials are presented in Appendix S11.

These observations demonstrate that for strong samples, subaerial testing is essential to ensure sufficient slump is recorded. Subaqueous testing resulted in no slump: in fact, the sample buoyant weight was so low, that the adhesion of the sludge to the inner wall of the cylinder was sufficient to lift the sample until the top water surface was reached. The sample then dropped out of the cell, but evidently was fractionally extended (by ~1mm). In contrast, weak samples behave just like water under subaerial testing, resulting in poor discriminatory power.

For such samples, only subaqueous testing is able to provide a

suitable value of the slump. By careful loading, the sample was not disturbed. The calmagite solution was seen to be readily swept out of the cylinder, and readily dispersed through convection currents induced by removal of the cylinder. As noted above, these effects are not expected to be important for sludge samples.

It has been demonstrated that this novel testing methodology provides a means of characterising the shear properties of very weak gels, without the need for expensive or sophisticated equipment. Currently analysis of the theoretical relationship between subaqueous slump and τy has not been undertaken, although it is expected to be relatively straightforward, perhaps involving simple correction factors. Also, the methodology was developed at the end of the present body of work, and thus has not been applied to any other of the sludges characterised. (This is reasonable, as τy is of lesser importance in dewatering than py.) In principle the application of this transfer to a subaqueous environment may also be beneficial for inclined-plane testing of very weak gels, however the equipment dimensions can be rather large [e.g. 285] and also ‘slip’ problems may be created.

248



3▪7

Modelling of unit operations

A number of colleagues have developed a set of computer programs to allow automated estimation of the progression of various unit operations, namely gravity batch settling, centrifuge batch settling, and various forms of filtration. These programs are files that are loaded into and run under Mathematica version 5.0+ (Wolfram Research, U.S.A.).

3▪7▪1

Gravity settling and centrifugation

Program TBS version 5.5.3 was developed by S. P. USHER and A. R. KILCULLEN, implementing an algorithm by D. R. LESTER, for the modelling of transient batch settling in either: • a constant acceleration field — as in g r a v i t y b a t c h s e t t l i n g ; or • a spatially-varying acceleration field — as in batch c e n t r i f u g a t i o n . The implementation follows closely the LANDMAN–WHITE theory described in §2▪4▪5▪3(c) and §2▪4▪5▪4(b). An explicit f i n i t e d i f f e r e n c e scheme (based on work by BÜRGER & KARLSEN) is employed [1061] to solve the differential equation (equation 2-84 or 2-116) based on the local unsupported solid-phase flux ( qS∗ ) and solids diffusivity (in the form of



φ 0

D . d φ ) as functions of the local solidosity; an implicit scheme is in development.

3▪7▪2

Filtration

Program Fill and Squeeze_Loop (version dated 2006-08-23) was primarily developed by A. D. STICKLAND, with contributions from A. R. KILCULLEN and S. P. USHER.

This program

‘typically’ utilises the s h o o t i n g m e t h o d [976] described by LANDMAN, SIRAKOFF & WHITE [625] (cf. LANDMAN & RUSSEL [624]), involving s u c c e s s i v e applications of RUNGE– KUTTA–FEHLBERG integration, to solve the governing system of coupled first-order ordinary differential equations (obtained by writing equation 2-123b, a second-order partial differential equation, as a set of first-order equations and discretising in time [cf. 495]). The program is also capable of optionally utilising a (numerical) s i m i l a r i t y s o l u t i o n approach [see 629] to predict cake formation in the special case of constant pressure, zero

3▪7 : Modelling of unit operations

249

D. I. VERRELLI

membrane resistance, and φ0 < φg [976]; the first two requirements are unlikely to be met for industrial operation. Fill and Squeeze_Loop consists of two sequential solution algorithms (regardless of the numeric technique specified), with the first corresponding to the ‘fill’ stage of a filter press, and the second to the ‘squeeze’ stage. In the fill stage a cake forms as feed material is pushed into the filter cavity — the model assumes that the cavity is initially full of material at φ0 *. For the present work it was assumed that the pressure (from the feed pump) was constant throughout the stage. In practice the pressure rises steadily at first and then stabilises to a steady value; the pressure ‘ramping’ time can be significant for WTP sludges [e.g. 976], and can be accommodated in the program. In the squeeze stage no more material is fed to the cavity. The pressure is generally larger than in the fill stage, and is applied by the inflatable diaphragm. This stage involves the onedimensional dewatering of a material with a moving boundary at (assumed) constant pressure. The starting solidosity profile is determined by the output from the fill stage. Only the shooting method technique is available here. With this program construction it is possible to model: • f i x e d - c a v i t y filtration (plate filter) — stop the program at the end of the ‘fill’ stage; • f l e x i b l e - m e m b r a n e filtration (diaphragm filter) — run both ‘fill’ and ‘squeeze’ stages; and • d e a d - e n d filtration (laboratory filter) — specify negligible ‘fill’ time. Unlike TBS, Fill and Squeeze_Loop regularly suffers from numerical convergence problems, and so requires careful attention from the user. Unusually, the default remedy is to increase the timestep (cf. §S13▪7);

in the present work the code was amended to ensure the

maximum-timestep constraint was obeyed. In future developments of such programs it may be possible to improve stability by specifying different coefficients for the RUNGE–KUTTA scheme;

*

overall execution speed

While in practice a finite time may be taken to load the cavity initially, it will have no effect on the subsequent dewatering process (provided that negligible dewatering occurs during the loading period). The loading time thus simply extends the total cycle time; this can affect operational economy.

250



might be improved by use instead of a multistep algorithm, such as a predictor–corrector scheme, but stability and convergence must also be considered [see 323].

3▪7 : Modelling of unit operations

251

4.

SOLID PHASE ASSAYS AND DENSITIES

None of the dewaterability comparisons are meaningful unless the solidosity, φ, is consistent for the various cases, which means that the solid phase density, ρS, must be known with reasonable accuracy, as φ is computed by conversion from measured mass fractions, x (see §2▪1▪1).

This importance can be demonstrated by reference to the following graphs (Figure 4-1 and Figure 4-2). It is clear that variation in ρS used in these computations can produce variations

in the calculated dewatering parameters that are significant with respect to the range of behaviours encountered — i.e. in comparison to ‘real’ variation due to the physical nature of the sludge and the manner of its generation. (STICKLAND [976] attempted to demonstrate the lack of importance of ρS, by showing that the dewatering parameters py and D (and R) would be unaffected if treated as functions of the mass fraction, x, rather than the solidosity, φ. A thought experiment shows that this does not hold. Consider a system where the solid is assumed ‘light’, but is in reality much denser than the liquid phase. Characterising py by means of a filtration test (§3▪5▪3) would lead to not only an overestimate of φ, but also an underestimate of the network pressure at the base, pS. This erroneous combination cannot be simply deconvoluted by scaling to x.)

Work was carried out to more accurately estimate the solid phase densities for the aluminium and iron sludges (plant and laboratory), along with the laboratory magnesium sludge and the PAC-loaded Happy Valley sludge. Two approaches were employed: • conducting assays to identify chemical phases present and thus obtain a representative value for the solid phase of the sludge overall using published values of ρ for these phases (§4▪2); and • direct experimental measurement of the (average) density of the solid phase (§4▪3).

253

D. I. VERRELLI

In characterising the dewaterability of the various sludges, the question arises: “Do the properties change over time?” This may be important to ensure samples do not ‘go off’ either before they are characterised or even during the characterisation itself (see also §8▪1, §9▪1 and §9▪3). On the other hand, if the dewaterability improves, such ageing may be able to be exploited. A potential component of ‘ageing’ is solid phase transformation. Conducting the assays mentioned above helps to determine the importance (or insignificance) of these mechanisms.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 Typical, at 4000 kg/m³ Typical, at 3000 kg/m³ Typical, at 2500 kg/m³ Worst lab. alum Best lab. alum

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 4-1: Effect of solid phase density, ρS, on the compressive yield stress of a sludge with typical dewatering properties. The envelope defined by the broken lines illustrates the range of behaviours encountered for drinking water sludges (with ρS = 2500kg/m3).

254

Chapter 4 : Solid Phase Assays and Densities


2


1.E+15

1.E+14

1.E+13

1.E+12

1.E+11

1.E+10

Typical, at 4000 kg/m³ Typical, at 3000 kg/m³ Typical, at 2500 kg/m³ Worst lab. alum Best lab. alum

1.E+09 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 4-2: Effect of solid phase density, ρS, on the hindered settling function of a sludge with typical dewatering properties. The envelope defined by the broken lines illustrates the range of behaviours encountered for drinking water sludges (with ρS = 2500kg/m3).

4▪1 4▪1▪1

Published data Mass balance of sludge generation

Typical volumes of WTP sludge generated industrially relative to plant throughput (or water production, or plant capacity) were described in §1▪2. The applicable solidosities or solid phase concentrations are but loosely defined by the location of their sampling on site, such as in the clarifier underflow.

4▪1 : Published data

255

D. I. VERRELLI

As the raw water quality or treatment operation varies, so too does the composition of the sludge, as illustrated by the t h e o r e t i c a l examples of RUSSELL & PECK [879] summarised in Table 4-1.

The data are compatible with experimental measurements by PAPAVASILOPOULOS & BACHE [816].

Table 4-1: Theoretical composition of WTP sludges produced under various conditions [879].

Sludge produced [mg/L] (Proportion of total [%m]) ‘Clean’ raw water:

‘Dirty’ raw water:

Turbidity ~ 10NTU;

Turbidity ~ 150NTU;

total solids ~ 15mg/L

total solids ~ 225mg/L

From aluminium sulfate dosing Hydroxide sludge

13 (46)

26 (10)

Raw water solids

15 (54)

225 (90)

Total

28 (100)

251 (100)

From ferric sulfate dosing Hydroxide sludge

43 (73)

—

Raw water solids

15 (27)

225

Total

59 (100)

—

(PARSONS & JEFFERSON [827] claimed that good quality reservoir water may yield as little as 150mg/L sludge (as dry solids), whereas poor quality river water may yield up to 600mg/L. These estimates seem rather high compared to the values found in Table 4-1; they are also very high compared to the results of the present work (see Table 3-1, discussion below, and Table 4-2).)

Clearly the two classes of materials contributing to sludge mass are the raw water constituents and the water treatment chemicals.

Of the water treatment chemicals, the most important is normally the coagulant.

256



For alum coagulation the precipitate mass can be estimated as about 3.73 times the mass of Al added, which is an empirical factor corresponding to a hypothetical Al(OH)3·1.25H2O precipitate [783]. This factor matches fairly well the value estimated from the present work, namely 4 . 0 . It is also common to see the factor given as 2.8 or 2.9 [cf. 315, 557, 797, 827, 854], which derives from the simplistic assumption that Al(OH)3 is formed.

For pure

pseudoböhmite (see §R1▪2▪5▪3 and Table 4-3) the predicted factor from stoichiometry would be slightly lower. A factor of 4.89 has also been quoted, corresponding to the hypothetical species Al(OH)3·3H2O [281, 282] [cf. 797, 879], which appears excessively hydrous. For ferric coagulation the precipitate mass can be estimated as about 1.91 times the mass of Fe added [cf. 161, 315, 557, 797, 827, 854], which corresponds to the equally simplistic assumption that Fe(OH)3 is generated. This factor matches well the value estimated from the present work, namely 2 . 0 , despite the improbability that the formula Fe(OH)3 is accurate (see e.g. §4▪2). For pure ferrihydrite (see §R1▪2▪6▪3 and Table 4-4) a slightly lower factor would be predicted.

A factor of 2.88, corresponding to formation of hypothetical

Fe(OH)3·3H2O [281, 282] [cf. 879], appears to be too high. All other insoluble additives (e.g. limestone, chalk, bentonite, polyelectrolytes) are assumed to go directly into the sludge in a one-to-one relationship [161]. Usually the mass fraction of polymer will be very low. Other chemicals (e.g. ozone, sodium hydroxide, sulfuric acid, potassium permanganate) are assumed to contribute no mass to the sludge [161].

The raw water constituents can be further classified into suspended and dissolved elements. It is impractical to consider the various species in depth, and so instead correlations have been developed relating typical sludge mass generation to either DOC, absorbance or colour, and to either TSS or turbidity [see 797]. TSS is assumed to be entirely captured in the sludge, implying a factor of unity [161, 797]. Where TSS is not measured, it can be approximated by a correlation with turbidity [161]. Turbidity [NTU] has been roughly correlated with TSS (and hence sludge mass) [mg/L] according to factors in the range 0.7 to 2.2 [161, 282, 315, 557, 783, 797, 854], but is less reliable than measuring TSS directly [797]. (If TSS is measured, then the turbidity remaining a f t e r TSS removal can be used, to avoid double counting [161], perhaps with a lower factor [cf. 797].)


257

D. I. VERRELLI

Where DOC is measured, factors ranging from 0.12 [339] to 0.13 [861] * have been reported for various Norwegian waters (with SUVA254nm in the range 4.02 [861] to 4.13 [339]). In an older study (1963), American raw waters with much higher fulvic acid levels yielded a factor around 0.29, expected to increase to 0.36 if humic acids dominated, and decrease to 0.22 if humin levels were higher [158]. OGILVIE (New Zealand, circa 1980) suggested multiplying the c h a n g e in A254nm [1/m] upon treatment by a factor of 0.6 [797]. Where instead (true) colour is measured, factors in the range 0.2 to 0.3 are recommended, although use of factors as low as 0.07 persists [161, 315, 797].

Using direct proportionality constants of 1.5 for turbidity, 0.3 for true colour, 4.0 for Al, and 2.0 for Fe, the following variation in sludge composition with coagulant dose for a typical Winneke raw water (turbidity ~ 2NTU, true colour ~ 10mg/L Pt units or DOC ~ 2mg(C)/L) may be estimated as in Table 4-2.

The total sludge generation predictions are in good agreement with results obtained in the present work.

It may be observed that on a mass basis the precipitated coagulant is

predicted to dominate most of the laboratory sludges produced, and comprise at least ⅓ of the plant sludges.

Nevertheless, the sludge dewaterability could well be affected by

components present in seemingly minor amounts. For example, the raw water constituents could alter the surface properties, affect the aggregate structure, or influence the precipitate phase formed.

*

258

This is in stark contrast to a proposal to model TOC contributions using a factor of unity [161, 557].



Table 4-2: (a) Predicted composition of alum sludges derived from typical Winneke raw water at various doses.

Component source

Alum dose [mg(Al)/L] 0.5

1

2

5

10

80

[%m]

38

30

21

12

7

1

DOC or True colour [%m]

38

30

21

12

7

1

[%m]

25

40

57

77

87

98

[mg/L]

8

10

14

26

46

326

TSS or Turbidity

Coagulant Total

(Shown to nearest percent.)

Table 4-2: (b) Predicted composition of ferric sludges derived from typical Winneke raw water at various doses.

Component source

Ferric dose [mg(Al)/L] 0.5

1

2

5

10

80

[%m]

43

38

30

19

12

2

DOC or True colour [%m]

43

38

30

19

12

2

[%m]

14

25

40

63

77

96

[mg/L]

7

8

10

16

26

166

TSS or Turbidity

Coagulant Total

(Shown to nearest percent.)

4▪1▪2

Pure component densities

Solid aluminium (oxy)hydroxide phases that might be considered include those in Table 4-3. Corresponding information for iron oxyhydroxides is given in Table 4-4. Densities of other phases arising from water treatment appear in Table 4-5, while key naturally-arising solid phases are listed in Table 4-6.


259

D. I. VERRELLI

Table 4-3: Selected solid aluminium (oxy)hydroxide phases and their densities [223, 504, 870].

Name

Formula *

Solid phase density [kg/m3]

Gibbsite

α-Al(OH)3

2420

Bayerite

γ-Al(OH)3

2530

Diaspore

α-AlOOH

3440

Böhmite

γ-AlOOH

3010

say ~ AlOOH·xH2O,

~ 2500 to 2800

Pseudoböhmite

with 0 < x < 0.5

Gibbsite is the most common polymorph of Al(OH)3 [463], and is the most stable phase at room temperature (it is favoured by a GIBBS energy difference of only about 6 to 11kJ/mol over bayerite) [118, 313], and is commonly considered the product of coagulation with alum. Böhmite is a more dehydrated phase that forms in preference to diaspore [504]. Pseudoböhmite is an aggregate of böhmite-like crystallites [121].

Work by several

researchers suggests that this phase, or something similar, may be formed upon coagulation of drinking water with aluminium sulfate.

VAN DER WOUDE & DE BRUYN [1130] observed (sub)nanometre-scale pores in the goethite crystals they formed, leading them to suggest that the effective density of these particles could be as low as ~3300kg/m3.

*

The labelling of the Al(OH)3 and AlOOH polymorphs by various researchers is not consistent. HUDSON et alia [504] recommend labelling bayerite as α-Al(OH)3, because it is the most densely packed, and the cubically packed gibbsite as γ-Al(OH)3. Bayerite is also occasionally written as β-Al(OH)3 [749, 1100]. Diaspore has also been called β-AlOOH [1]. The nomenclature used in the present work reflects popular usage.

260



Table 4-4: Key chemical and physical data of selected iron (oxy)hydroxides [279, 280, 397, 520].

Chemical

Formula (source)a

Molar Fe/O ratio [–]

Density [kg/m3]

Hæmatite

Fe2O3

0.667

5180

Goethite

FeOOH

0.500

4260

Lepidocrocite FeOOH

0.500

4090

Akaganéite

FeOOH

0.500

3560

Ferrihydrite

5Fe2O3·9H2O (A),(B)

0.417

3750 to 3960+ b

Fe5O7.5·4.5H2O (C)

0.417

"

Fe2O3·2FeOOH·2.6H2O (D)

0.417

"

Fe4.5(O, OH, H2O)12 (E) *

0.375

"

Fe1.55O1.66(OH)1.34 (F)

0.517

"

Fe1.42O1.26(OH)1.74 (F)

0.473

"

Fe2O3·1.2H2O (G)

0.476

~3800

a

Sources of ferrihydrite equations:

A

CHUKHROV et alia, 1973 [English translation: 258] †.

B

SCHWERTMANN & CORNELL, 1991.

C

TOWE & BRADLEY, 1967 [1051] ‡.

D

RUSSELL, 1979.

E

EGGLETON & FITZPATRICK, 1988.

F

STANJEK & WEIDLER, 1992 [965]. (First formula is for 6-line form, second formula is for 2-line form.)

G

VAN DER GIESSEN, 1966 [397]. The formula is equivalent to FeOOH·0.1H2O.

b

*

Theoretical predictions range between 3720 and 4140kg/m3 [520].

These researchers modelled the phase as alternating sheets of octahedral and mixed octahedral– tetrahedral iron; they concluded that the true composition lay between Fe4(OH)12 (Fe/O = 0.333) and Fe5O3(OH)9 (Fe/O = 0.417) [520].

Tetrahedral co-ordination of ferric iron has been widely disputed

[520] [see also 538, 674]. JOLIVET [538] suggested representative formulæ of Fe4.6(O, OH, H2O)12 for the 6line form, and Fe4(O, OH, H2O)12 for the 2-line form. †

CHUKHROV et alia [cf. 258] also expressed the formula as Fe5(O4H3)3. It has also been (mis)quoted as Fe6(O4H3)3 [520, 909] and as “Fe1.42O1.26(OH)1.74” [280].

‡

TOWE & BRADLEY [1051] also expressed the formula as 5Fe2O3·9H2O and “near Fe5HO8·4H2O”. The latter is commonly cited (as exact) [e.g. 279, 520], as it avoids implying the presence of a hæmatite structure [cf. 520] — although it has been also recast as 2Fe2O3·FeOOH·4H2O [677] — and it is the version appearing in the abstract. Also (mis)quoted as “Fe1.33O(OH)2” [280].


261

D. I. VERRELLI

Both hæmatite and goethite are stable phases, although goethite would seem to be thermodynamically favoured for the present system [118, 280, 306, 459, 547]. Akaganéite usually forms in chloride environments [118, 280].

Lepidocrocite can form by direct

precipitation of low molecular mass ferric species [280], although it is not usually [cf. 533] expected to form in water treatment. Rapid hydrolysis tends to produce ferrihydrite [258, 280, 520], whose stability is enhanced by the presence of various ‘contaminants’ [280, 388, 520, 583].

Although polymers are commonly added in water treatment, they tend to contribute very little to the sludge mass, and hence the density.

Table 4-5: Other solid phases arising from drinking water treatment [662].

Name

Formula


Magnesium hydroxide

Mg(OH)2

2370

CaCO3

2710

amorphous C

1800 to 2100

Calcite Powdered activated carbon Ballast sand

See Table 4-6

Table 4-6: Key chemical and physical data of naturally appearing phases.

Name Sand (silica / α quartz) Clay — kaolin NOM Rock salt Note

a

Formula


α-SiO2

2648

[662]

Al2O3·2SiO2·2H2O

2590

[662]

–

30 to 670 a

[400]

~NaCl

2180

[662]

THORSEN [1024] reported indicative densities of approximately 80kg/m3 for a collapsed cake and 7kg/m3

for fractal particles. The calculated densities are highly dependent on sample porosity, which is likely to lead to significant underestimation in some cases. For comparison, a typical peat soil — from which NOM might be derived [1016] [see also 300, 1066, 1105, 1124] — has ρS ~ 1700kg/m3 (after correcting for porosity), with the density of ‘pure’ peat apparently ~1400kg/m3, compatible with a very high cellulose (cf. lignin) content [479].

262



4▪1▪3

WTP sludge densities

4▪1▪3▪1

Bulk densities

Estimated ‘bulk’ densities of aggregates or settled sludge have occasionally been published, but the wide range of incorporated water content yields a commensurately wide range of specific gravities, so comparison and interpretation is difficult.

Specific gravities in the range 1.002 to 1.02 are typical of measurements made by settling experiments where a single aggregate is modelled as an equivalent sphere falling in the STOKES regime [111, 997] — by far the more common methodology.

Somewhat larger

estimates of 1.03 to 1.06 were obtained for large WTP flocs settling at Re > 1 [355, 1055]. Such measurements may be relevant to sedimentation and clarification [576]. The largest estimates, in the range 1.05 to 1.30, have been obtained by ‘isopycnic’ separation [331, 576, 579], a technique borrowed from the biological sciences. It was proposed that the aggregates rupture in this measurement, so that the fraction of intra-aggregate water is reduced [577].

Hence the estimates made by this method may be of more interest for

mechanical dewatering processes (e.g. centrifugation, filtration) [577].

Isopycnic separation is carried out by introducing a small portion of the sample into a ‘solution’ (or suspension) which is then ultracentrifuged. A monotonic density gradient exists in the medium either due to the original loading of the tube [e.g. 22, 577] or by migration of the ‘solute’ (either before or ‘during’ the experiment) [22, 907]. The sample particles then move (either up or down) toward a level commensurate with their density [576], at a rate that also varies with the particle diameter [22]. Hence separation on the basis of size or density can be effected [22]. Comparison to calibration beads enables the actual density to be estimated [22]. An important consideration is the osmotic pressure, Π, of the ‘solution’. High osmotic pressures dewater biological cells [cf. 22], and generate a large driving force between aggregate interstitial water and the bulk medium that favours removal of water from the aggregate (resisted by the interparticle bonds) and entry of the ‘solute’ into the aggregate pores (tempered by the diffusion rate) [cf. 576].

Many ‘solutes’ have been employed,


263

D. I. VERRELLI

including inorganic salts [907], organic molecules [576], and nanoparticles [22, 576], covering a wide range of osmolalities. 15 to 30nm silica particles coated with polyvinylpyrrolidone (PVP) [22] were typically used for the case of WTP sludge measurements [331, 576, 579]. Such preparations are of low osmolality [22, 576], and so the density measured will incorporate a significant fraction of interstitial water. Using this solute and a low background salt concentration (Π ≈ 23kPa) the alum and ferric aggregate densities were of order 1200kg/m3; significantly l o w e r estimates were obtained for coherent clumps of t h i c k e n e d sludge, due to the inclusion of interaggregate water in addition to the intra-aggregate water [576]. Preliminary measurements with 134g/100mL cæsium trifluoroacetate (Π ≈ 16.5MPa, equivalent to a 225g/L (3.8M) brine [1119]) gave much higher estimates of the aggregate density, viz. >1900kg/m3 [576]. It can be fairly assumed that the latter value is intermediate between the ‘true’ aggregate density, ρagg, and ρS.

Earlier work comprising ‘batch’ isopycnic separation with sucrose solutions yielded lower estimates of turbidity-free ferric WTP aggregate specific gravity, in the range 1.003 to 1.006, and decreasing with dagg (0.5 to 3.0mm) [621]. The measurements involved contact of a given aggregate with just one constant-density medium for “a few seconds”, which would minimise diffusional interchange [621].

4▪1▪3▪2

Solid phase densities

Several estimates of solid phase density, ρS, appear in the literature for alum and ferric sludges. (No data could be found for magnesium sludges.) These are summarised in Table 4-7. The values span a wide range: from 1400 to 3000kg/m3, assuming them all to be equally

valid for the moment. With reference to Figure 4-1 and Figure 4-2, it can be seen at once that such a range of densities would result in entirely different predictions. The next question is to consider the accuracy and the applicability of the quoted values.

264



Table 4-7: Solid phase densities, ρS [kg/m3], for alum and ferric sludges according to a range of publications.

Alum sludge

Ferric sludge

Reference

Measured

Nominal

Measured

Nominal

2800

–

–

–

[579]

(1900 to 2600) ±70

–

–

–

[494]

2114a

–

–

–

[615]

–

2650b

–

–

[106]

–

2400

–

–

[161]

–

2500c

–

–

[112]

–

2000d

–

–

[116]

–

2000

–

2000

[110]

–

2300

–

2300+

[289]

–

2500

–

2500

[315]

–

2000 to 3000e

–

–

~2500f

–

~2500f

[281]

–

2400

–

3400

[754]

2200 to 2400

2250

–

–

[797]

2260g, 2330h

–

2720i

–

[1098]

2450 to 2550

–

2860

–

[576]

–

3000

2830±100 and 2660±400j

3000

[976]

–

–

–

1400

[395]

–

–

1900 to 2400

–

[443, 448]

Notes

a

PACl sludge described in §5▪6▪3.

presumably at pH ≈ 6.0 [cf. 494].

d

b

2000 to 3000e [281, 282]

Based on density of clay [106].

50% humic material.

e

c

Average of 2320kg/m3.

VANDERMEYDEN, CORNWELL & SCHENKELBERG (1997) as “coagulant sludges” [281]. KOPPERS (1990) as “coagulant sludges” [281].

g, h, i

Mostly precipitated coagulant,

f

Data cited from

Data cited from CORNWELL &

Data cited from WANG, HULL & JAO (1991) for raw water of: (g)

high colour and low turbidity; (h & i) medium colour and turbidity.

j

The second value includes pre-lime

addition.


265

D. I. VERRELLI

The a c c u r a c y relates to the experimental methodology. In the case of the ‘nominal’ values frequently stated, the methodology is unknown. In the remaining cases two variations from the methodology adopted in the present work (§4▪3▪1) are prominent. First, none of the references seem to account for dissolved solids [see also 580], with two possible exceptions [443, 976].

Second, in at least one case [579] the drying was carried out by (ambient)

evaporation only. Both of these procedural differences would tend to result in lower estimates of ρS. Neglecting to correct for supernatant dissolved solids, specifically, can be shown to lead to density underestimation of 20 to 80kg/m3 for high-solids samples (φ ~ 0.010) depending upon the dissolved solids concentration, and much greater errors for samples that have not been partially dewatered prior to measurement, viz. 250kg/m3 (φ ≤ 0.004). A further methodological flaw may be a failure to measure the true liquid phase density (see §4▪3▪2▪1), as this was generally not described in the reported procedure — it was presumably often taken as identically 1000kg/m3, or else read from published tables for pure water as a function of temperature. Aside from this, it may be noted that e s t i m a t e d error margins are not usually given, again with two exceptions [494, 976]. Errors are likely to be high for any sludges that were not appropriately dewatered.

The a p p l i c a b i l i t y relates to the conditions under which the sludge was generated. Again this cannot be determined for the ‘nominal’ values, although they tend to imply that the same ρS applies to all sludges [cf. 289, 976]. There are two categories of parameters to consider, namely raw water quality and water treatment operation. Raw water quality is difficult to simply describe, except to indicate the relative levels of turbidity-causing particulates (assumed inorganic) and of NOM (assumed dissolved). Generally the raw waters treated in the cited studies were of low turbidity and of low to moderate [575, 579] or moderate to high [443, 494, 976] true colour. For comparison, the raw waters studied in the present work tended to be also of low turbidity, but only of low to moderate colour.

266



The primary aspects of water treatment likely to affect ρS are the coagulant type, the coagulant dose (relative to the amount of NOM or turbidity removed), and the coagulation pH. HOSSAIN & BACHE [494] carried out the most rigorous determinations of ρS, and determined that for the pure precipitated alum ρS was highest (2600kg/m3) at pH 5.5, and dropped off towards about 2400 to 2450kg/m3 at lower (4.5) or higher (7.5) values of pH. They also identified a trend with regard to the alum dose, with ρS decreasing from about 2400kg/m3 down to 1900kg/m3 as coagulant dose decreased (at pH 5.0 and 6.0) [494]. This suggests a lower density for the colloidal and dissolved matter removed from the raw water, which they determined to be 1750±40kg/m3 (by regressing ρS against coagulant dose and extrapolating) or 1540±150kg/m3 (by evaporating and drying raw water) [494]. These values are similar to the density of 1590±10kg/m3 found by KNOCKE, DISHMAN & MILLER [576] for polymer-only sludges generated from low-turbidity, high-organic-content raw water.

It is not possible to use the data given in Table 4-7 to estimate values of ρS appropriate to the present work. The foregoing also reinforces the importance of assessing ρS for the sludges to be characterised, using a method compatible with the method of measuring the solids mass fraction, x.

4▪2

Experimental determination of composition

One approach to estimating the solid phase density is to identify the various pure species present, and to measure (or estimate) the proportion in which each is present. From known densities of the pure substances the ensemble average ρS for the sludge could be calculated.

4▪2 : Experimental determination of composition

267

D. I. VERRELLI

4▪2▪1

Method

4▪2▪1▪1

Energy-dispersive spectrometry (EDS)

Energy-dispersive spectrometry (EDS) is a technique carried out on a scanning electron microscope (SEM) that is able to quantify the proportions in which elements are present. EDS was carried out on samples dried in a desiccator at ambient temperature after carboncoating under vacuum (DynaVac Mini Coater). A Philips XL30 scanning electron microscope (SEM) supplying an incident electron beam at up to 20kV was used in combination with an Oxford Instruments Isis x-ray energy dispersive system for detection and analysis. This system has a thin-atmosphere window on the detector to enable it to directly measure oxygen.

4▪2▪1▪1(a)

Samples

Four sludges were analysed by EDS, for which the details are provided in Table 4-8. The ferric chloride reagent used to generate the sludges was also analysed (as received).

Table 4-8: Ferric sludge samples characterised by EDS.

Sample

Fresh ferric lab. 9-day ferric lab.

Raw water source

Winneke

and date

Fresh plant

Aged plant

Macarthur WFP Macarthur WFP

2004-09-15

2005-03-23

2003-08-21

9

8

11

0.57

–

–

True colour [mg/L Pt units] A254nm

[10/m]

Dose

[mg(Fe)/L]

80

1.5

1.1

[–]

6.1

9.0

8.8

N/A

N/A

pH

Volume coagulated [L] Drying

1.6

48.4

Air (desiccator), Air (desiccator) Air (desiccator) Air (desiccator) 5min heat lamp

Ageing Note:

268

a

1 day

9 days

0.4 months

This sample mostly refrigerated (all other samples stored at ambient conditions).


19.4 months a


4▪2▪1▪2

X-ray diffraction (XRD)

X-ray diffraction (XRD) is a technique that produces a spectrum describing the crystalline structures present, from which the identities of the constituent compounds may be inferred. This contrasts with EDS, which can only imply the presence of a given compound based on the confirmed presence of its constituent elemental species in the appropriate proportions. XRD is the most reliable tool for distinguishing between crystalline (or paracrystalline) species such as the various iron oxides, as it provides a direct indication of long-range ordering [280].

4▪2▪1▪2(a)

Theory

Powder XRD works on the principle that a sample of a material crushed to a fine powder will on average have a certain proportion of crystals suitably oriented to diffract impinging x-ray radiation at an angle of 2θ (the remainder of the crystals will not contribute) [673]. Thus it is necessary to finely grind the dried samples. The angle θ is related to the interplanar spacing *, dhkl, through BRAGG’s law, which is usually stated [673] n λ = 2 dhkl sin θ ,

[4-1]

where λ is the wavelength of incident radiation and n is the “order of the reflection” — an integer that may be taken as unity in this equation. Although the a n g l e s of diffraction are controlled by the shape of the underlying repeat crystal unit, the i n t e n s i t y of the diffracted radiation (at given angles) depends upon the identity and arrangement of atoms at lattice points, which enables the chemical species making up the sample to be identified [673].

Peaks may be broadened as a result of diffraction effects due to small crystallite size, to lattice distortion, or to structural faults, aside from inherent instrumental limitations [673]. Broadening due to small crystallite size can be modelled using the SCHERRER equation [280] d = Ж λ / B cos θ ,

*

[4-2]

The faces of the crystal repeat unit are conventionally described in a shorthand notation “(hkl)”, called the MILLER indices, which can be interpreted as the planes with normals given by the vectors [h,k,l] [673, 773].


269

D. I. VERRELLI

where d is the crystallite size, B is a characteristic peak width [c], and Ж is a factor close to unity called the SCHERRER constant [cf. 632, 673, 1065, 1099]. d is a volume-weighted mean in the direction perpendicular to the (hkl) plane, and thus can vary between diffraction peaks [e.g. 965, 1065]. Various relations can be used to establish the correct value of Ж, however these rely on knowledge of the crystallite shape and orientation for the given peak [see 632]. When Ж is taken as identically equal to unity (a reasonable approximation for many purposes), d becomes the a p p a r e n t crystallite size [632, 673]. The SCHERRER formula gives useful results in many, but not all [280], situations: it is suited for determinations with 2 ( d ( 100nm [1065]. Even samples that appear ‘amorphous’ by XRD may have short-range crystallinity detectable by other techniques [520].

4▪2▪1▪2(b)

Reference data Although

ferrihydrite

is

of

considerable

importance [...], often its presence is greatly underestimated because of the difficulty in its definitive identification and because of its common designation as amorphous iron oxide, [...] etc. — JAMBOR & DUTRIZAC (1998) [520]

The diffractogram peak locations and relative intensities for the crystalline phases are very well characterised, and can be found in standard references [e.g. 1, 280].

Pseudoböhmite can be identified from broad peaks in its powder x-ray diffractogram [cf. 622]. These broad peaks [748, 1099] coincide with strong reflections of böhmite [749]. This is an indication of a nanometre-scale crystallite structure: crystallite sizes of 3 to 6nm have been reported [121, 223, 870, 1150].

270



Table 4-9: XRD peaks for pseudoböhmite [499, 500, 584, 748, 1099, 1150].

2θ Cu Kα

dhkl

[°]

[pm]

hkl indices

Comments

9.6

921

?

May be an artefact

12.8 to 14.1

627 to 690

020

–

28.1

317

120

–

38.3

235

031

May be 140

49.2

185

200

May include overlap with 051a before

55.6

165

151

–

65

143

002

Overlapping with 231b before and 180c after

72

131

?

–

86

113

?

–

Notes c

a

Crystal repeat unit

051 peak has 2θ ≈ 48.0° Cu Kα; dhkl ≈ 189pm [1099].

b



The relative intensities of the peaks seem to vary according to the degree of crystallinity [748]. The peak locations change somewhat due to decreasing hydration upon ageing [1150]. Completely crystalline böhmite may be most readily distinguished by the shifting of the strongest diffraction peak to d020 ≈ 611pm [584, 748, 1099] from around 670pm [584, 1099, 1150] — larger spacings have been associated with smaller crystallite sizes [940] — along with the narrowing of all peaks.

Given that 2-line ferrihydrite is relatively amorphous (considering a range of lengthscales), peaks (or ‘bands’) in its x-ray powder diffractograms are exceedingly broad [279, 520]; however the peaks are relatively consistent and reproducible. The powder XRD diffractogram of 2-line ferrihydrite shows two characteristic bands (very broad peaks) corresponding to d110 ≈ 254pm (2θ ≈ 35.3° Cu Kα) and d300 ≈ 147pm (63.2°) [258, 280, 520]. Additional weak, broad peaks may be masked by these stronger peaks, showing up only as asymmetry [cf. 965, 1053].


271

D. I. VERRELLI

4▪2▪1▪2(c)

Equipment

A Philips Analytical PW 1800 x-ray diffractometer (maximum 40kV(peak) / 30mA) equipped with a copper x-ray tube (Cu Kα *, λ = 154.056pm) scanning in 2θ-increments of 0.02° from 5° to 70° was used. By equation 4-1 this corresponds to interplanar spacings, dhkl, from 134 to 1766pm. The sample holder is constructed of an aluminium material (most intense peak at about 234 [250] to 236pm [128]). If there is insufficient sample to completely cover the base of the sample cell, then this material’s response will show up in the diffractogram. For the case of a very small amount of sample, the required amount of sample can be reduced by using a suitably sized, thin glass slide as a stage. As this is amorphous, it should not contribute any peaks to the diffractogram (and will also avoid spurious peaks from the sample holder). Analysis was carried out in two ways: • using XPLOT for Windows analysis software (version 1.29, CSIRO, Australia, 1997); and • ‘manually’ by reference to published peak data (2-line ferrihydrite (approximate) [520], calcite [250], aluminium [128, 250], and all others [279]; and these are consistent with the standard Powder Diffraction File [1] where listed).

4▪2▪1▪2(d)

Samples

A number of laboratory and plant sludge samples were analysed by powder XRD. Owing to the possibility of changes due to ageing of material, more detailed information regarding the experimental chronology is provided in Table 4-10 (alum sludges) and Table 4-11 (ferric sludges), along with the usual information regarding generation conditions. Except where otherwise indicated, all drying was at ambient temperature in a desiccator [cf. 499, 1053].

*

Electric dipole radiation makes up the most intense x-rays, and is generated by transition of electrons between the shells of an atom [673]. Transition between the K shell and the L shell results in Kα lines in the x-ray spectrum [673], which are the most intense. (The notation Kα follows the convention established by SIEGBAHN (circa 1925); the more systematic equivalent IUPAC-recommended notation is K-L2,3 [see 529].) These lines are technically doublets, made up of Kα1 and Kα2 lines, however this distinction is often conveniently ignored [673].

272



Table 4-10: Generation conditions for alum sludge samples characterised by powder XRD.

Sample Raw water source and date

High-pH lab.

Low-pH lab.

Low-dose plant

Freeze–thaw

Winneke

Winneke

Winneke

As for previous

2004-05-21

2004-06-02

2005-07-01

14

12

–

"

0.87

0.83

–

"

2004-05-27

2004-06-23

2005-07-01

2005-07-04 –

True colour [mg/L Pt units] [10/m]

A254nm Generation date

2005-07-19 a Dose

[mg(Al)/L]

80

80

1.9

As for previous

pH

[–]

7.6

4.8

6.2

"

Hydrolysis ratio

[–]

2.99

2.47

–

"

No

No

Yes

Yes

Drying date

2005-07-20

2005-07-20

2005-07-20

2005-07-20

XRD date

~2005-08-22

~2005-08-22

~2005-08-08

~2005-08-08

Ambient

Ambient

Ambient

Ambient

Sample ageing — wet

13.8

12.9

0.6

0.6

[months]

~1.1

~1.1

~0.6

~0.6

Polymer added

Storage

Note:

a

— dry

frozen 2005-07-04, thawed 2005-07-19.


273

D. I. VERRELLI

Table 4-11: Generation conditions for ferric sludge samples characterised by powder XRD.

Sample

Lab.

Lab.

Winneke

Winneke

2004-09-15

2004-09-15

2003-08-21

2005-03-23

9

9

11

8

0.57

0.57

–

–

2004-12-08

2004-11-30

2003-08-21

2005-03-23

[mg(Al)/L]

80

80

1.1

1.5

pH

[–]

6.1

6.1

8.8

9.0

Hydrolysis ratio

[–]

2.88

2.84

–

–

Volume coagulated [L]

1.6

48.4

N/A

N/A

Polymer added

No

No

Yes

Yes

2004-12-08

2006-05-09

2004-12-15 a /

2005-03-30

Raw water source and date

Old plant

New plant

Macarthur WFP Macarthur WFP

True colour [mg/L Pt units] [10/m]

A254nm Generation date Dose

Drying date

2005-03-30 b XRD date

~2005-01-17

2006-07-05

Ambient / Oven c

Storage

Ambient

~2005-01-17 /

2005-04-10 /

2005-04-10

2005-04-20

Refrigerated d, Ambient / Oven e ambient

Sample ageing — wet

0.3

17.2

15.8 / 19.3

0.2

[months]

1.0

1.9

1.1 / 0.4

0.4 / 0.7

Notes

a

— dry

Sampled from centre.

15min at ~70°C.

d

b

Separately sampled from three stratified layers.

Refrigerated until 2004-12-14.

e

c

One portion heated for 10 to

One portion heated for 7d at 80°C.

A blank scan of the empty sample holder was also run (circa 2005-04-13).

The original XRD scans are output in 2θ units and are quite noisy. A central 19-point moving average has been applied to emphasise the underlying signal response. An example of the raw and smoothed data is given in Figure 4-3. The less crystalline samples are the most problematic, as these record lower signals, while the noise appears to be fairly constant (both between samples and as a function of 2θ). The

274



averaging used is a compromise to smooth out noise without obscuring real sample features. Peaks tend to be diminished * in height, but are n o t shifted.

100 Original scan

Relative intensity, I /I ref [–]

90

19–point centred moving average

80 70 60 50 40 30 20 10 0 0

Figure 4-3:

5

10

15

20

25

30 35 40 2θ Cu Kα [°]

45

50

55

60

65

70

Raw and smoothed XRD scans for the Macarthur WFP ferric sludge generated

2005-03-23 and heated at 80°C.

4▪2▪2 4▪2▪2▪1

Results Energy-dispersive spectrometry (EDS)

Results of the laboratory ferric sludge analysis are shown in Table 4-12.

*

The reduction is generally a uniform proportion, although especially narrow peaks would be reduced more.


275

D. I. VERRELLI

Table 4-12: Molar percentages for the incidence of detections corresponding to lumped Kα (peak) radiation of the elements listed, and ratio of Fe to O (or Cl) in laboratory ferric sludges of different ages and ferric chloride reagent. The averaging area is illustrated in Figure 4-4.

Sample:

Fresh sample

9-day-old sample

Ferric chloride

~0.01mm2

~2mm2

~0.01mm2

~2mm2

O

65.53

59.13

63.56

–

Na

0.85

1.06

0.98

–

Al

0.23

0.31

0.25 a

–

Si

1.44

1.59

1.82

–

S

0.26

0.18

0.22

–

Cl

3.15

1.11

0.8

75.72

Fe

28.54

36.62

32.37

24.28

100

100

100

100

0.436

0.619

0.509

(Fe/Cl=0.321)

Area average:

Total Fe/O ratio Note:

a

Value is less than twice the estimated standard deviation.

The phase of iron that is present can be inferred by comparison of the molar Fe/O ratios above with the values in Table 4-4. Various chemical formulæ for ferrihydrite have been proposed, making it difficult to be confident in its Fe/O ratio.

The analysis is further

complicated by the fact that iron may be present in a number of phases, and that all of the iron may not be chemically bound to all of the oxygen. The molar Fe/O ratio is larger for the slightly older sludge than for the freshest sludge, which would be consistent with the development of more-crystalline forms upon ageing. However it can be seen that the variation in the ratio was large between different averaging areas for the nine-day-old sample. Also, the one-day-old sample was treated (albeit for less than 5 minutes) under a heat lamp, which should promote formation of hæmatite (or goethite). The results suggest that ferrihydrite is the dominant phase present in the youngest sample, with possibly a small proportion of goethite or hæmatite.

276



Figure 4-4: SEM image of air-dried laboratory ferric sludge (9 days old): one EDS measurement averaged over approximately 0.01mm2 (centred on largest horizontal face). The concentric circles formed upon drying.

The smooth form of these features suggests the material is very

homogeneous. Drying often results in formation of a polygonal system of cracks [305]. Stresses of up to 400MPa have been reported in drying gels [1097].

For the slightly older sample any combination of hæmatite, goethite and ferrihydrite is possible. The results obtained by averaging over a larger area suggest that the sample contains a large proportion of hæmatite (such that the molar Fe/O ratio is greater than 0.500), with this being mixed with some goethite and/or ferrihydrite. The results obtained by averaging over the smaller area indicate that goethite may actually be the dominant phase of iron that is present, although it is possible for this ratio to be obtained through suitable combination of hæmatite and ferrihydrite.

Based on the above analysis the fresh sludge contains 94% iron oxide (i.e. Fe and O) on a dry basis, while the 9-day-old sludge contained 96%. S u p p o s e an average value of 95% is taken for 80mg(Fe)/L ferric sludges coagulated at pH ~ 6.1. If the coagulant dose were reduced to 10mg(Fe)/L and assuming that the amount of natural material removed remained unchanged, then such sludge would contain around 70% iron oxide and 30% natural material. Reducing the dose to 2mg(Fe)/L would yield 32% iron oxide and 68% natural material using the same assumptions. (This is near the typical optimum dose, and below this dose the assumption of constant natural material independent of dose is less likely to be valid. One can also compare with the median raw water total solids content given as 65mg/kg for Winneke (§3▪2▪2).) This degree of variation suggests further attention needs to 4▪2 : Experimental determination of composition

277

D. I. VERRELLI

be paid to ρS. Natural materials may be assumed to be of lower density than the iron oxide phase(s), and so the py(φ) and R(φ) functions for such sludges would be translated to larger values of φ than high-dose sludges — this would compound the superior dewaterability of low-dose sludges identified already.

The ratio of Fe/Cl in the AR grade ferric chloride (FeCl3) confirms its purity.

Table 4-13: Molar percentages for the incidence of detections corresponding to lumped Kα (peak) radiation of the elements listed, and ratio of Fe to O in plant ferric sludges of different ages. Key values are in boldface.

Sample:

Fresh

Aged Top stratum

Bottom stratum Upper layer

Method a:

Lower layer

S1

S2

A

A

S

V, A

A

S

O

68.46

68.79

79.9

67.96

84.54

64.54

66.58

78.05

Mg

0.15 b

0.11 b

0.45

0.14 b

‒0.09 b

–

0.24 b

0.08 b

Al

0.81

0.86

1.9

1.91

‒0.01 b

1.81

1.98

0.07 b

Si

2.78

3.09

6.23

6.59

0.15 b

7.08

7.5

0.24

P

0.19

0.08 b

–

–

–

–

0.37

0.05 b

S

0.25

0.28

–

0.32

0.02 b

0.34

0.43

0.04 b

Cl

0.37

0.5

–

0.24

‒0.04 b

–

0.18

0.01 b

Ca

2.93

3.06

1.64

2.87

12.06

3.17

3.01

11.73

Ti

–

–

–

–

–

–

0.10 b

‒0.02 b

Mn

0.26

0.14 b

–

0.23

0.65

0.28

0.31

1.02

Fe

23.8

23.08

9.89

19.74

2.72

22.77

19.3

8.74

Total

100

100

100

100

100

100

100

100

0.348

0.336

0.124

0.290

(0.032)

0.353

0.290

(0.112)

Fe/O ratio Note: b

a

A = large-area average; S = spot value; V = sample held under high vacuum for ~12h.

Value is less than twice the estimated standard deviation.

278



For comparison the results of EDS analysis for two plant ferric sludges are presented in Table 4-13. The aged sludge had stratified, and each layer was accordingly sub-sampled.

The two spot analyses for the aged sample were focussed on apparently crystalline fragments (visible in Figure 4-5), and are not representative of the sample overall. The results suggest that this was calcite. While this could derive from natural alkalinity or hardness, considering that Macarthur WFP coagulates at pH 8.5 to 9.0 (see §3▪2▪6▪2), a more likely source is the “lime” added. (Considering that the lime appears as fragments in the sludge, it may not be fully dissolving: part of its effect may be to serve as a nucleation site for material to precipitate on, aside from the ‘indirect’ pH effect.)

Considering the molar ratios of Fe/O, it would appear that a l l of the samples have rather low ratios of Fe/O, consistent with ferrihydrite being the dominant phase. The fresh plant sludge exhibits a higher ratio, which ordinarily would suggest the less crystalline form, except that all of the ratios are below the range expected for crystalline phases. Holding an aged sludge sample under vacuum appears to have had the expected effect of pulling off more water, thereby raising the Fe/O ratio.

Indeed, this aged sample has

increased to an Fe/O ratio similar to, and slightly above, the values for the fresh sludge. The significant change in value demonstrates the level of uncertainty inherent in the assessment. Comparing the three different layers sub-sampled from the aged sludge, no significant difference is evident in the two analyses from the bottom stratum (ignoring the extendedvacuum sample). However, the sub-sample from the top stratum is significantly different, showing less Fe, less Ca, and more O. Al and Si levels are fairly similar to those of the bottom stratum; the Mg levels are marginally higher. Apparently there is much less of the precipitated coagulant, less calcite, and no more silica or clay.

Unless the phases are

exceptionally hydrated, the results suggest the mass of the top stratum comprised more organic material — C is not detected by EDS, but would commonly be associated with both O and H2O. (The organic material would not be detected by XRD either.)


279

D. I. VERRELLI

Figure 4-5: SEM image of grains of calcite in a plant ferric sludge (aged sample).

4▪2▪2▪2 4▪2▪2▪2(a)

X-ray diffraction (XRD) Aluminium

Powder XRD diffractograms for air-dried alum sludges are presented in Figure 4-6 and Figure 4-7.

350


300

mg(Al)/L

pH

Age

Lab.

80

7.6

~15mo

Lab.

80

4.8

~14mo

250 NOTE: All centred 19–point moving averages

200 150 100 50 0 130 150 170 190 210 230 250 270 290 310 330 350 370 390 410 430 Interplanar spacing, d hkl [pm]

Figure 4-6: Powder x-ray diffractograms for air-dried aged laboratory alum sludges.

280



350

mg(Al)/L pH Age Plant 1.9 6.2 ~1mo Freeze–thaw of prev. ~1mo Blank


300 250

NOTE: All centred 19–point moving averages

200 150 100 50 0 130 150 170 190 210 230 250 270 290 310 330 350 370 390 410 430 Interplanar spacing, d hkl [pm]

Figure 4-7: Powder x-ray diffractograms for an air-dried plant alum sludge, original and freeze– thaw conditioned. Influence of blank shown dotted.

The diffractograms are not entirely conclusive in terms of identifying mineral phases present. This can be seen by the presence of only quite broad peaks, and the general absence of sharp peaks. Ignoring the influence of the sample holder (artefacts due to insufficient depth of sample), only two phases could be identified — the remainder of the materials must be wholly amorphous. The broad triangular peaks for the aged pH 7.6 laboratory sludge correspond to nanometresize crystallites of böhmite, or ‘pseudoböhmite’. The even broader humps of the counterpart low-pH sample, which resemble the ‘baseline’ of the freeze–thaw sample, could not be associated with any phase. The relatively sharp peak at 330.2pm for the freeze–thaw conditioned plant sludge likely corresponds to the presence of quartz. It is not clear why this appears of reduced magnitude in the original sludge — possible causes include: preparation (e.g. particle size);

sample inhomogeneity;

sample

differences in the sample ‘matrix’ (e.g. due to freeze–


281

D. I. VERRELLI

thawing). “Preliminary” XRD experiments by PARKER & COLLINS [820] “did not indicate any change in crystallinity” resulting from freeze–thaw conditioning of alum and ferric precipitates (such transformation has been claimed by others [638], and if correct might lie in an increase in crystallite size on zot ageing rather than a true change in phase). VAN DER GIESSEN [397] also reported no change in crystal structure of thawed zots following freezing of ferric precipitates with liquid nitrogen. MÖßBAUER spectroscopy of frozen and thawed ferric precipitates likewise indicated no change in phase [398, see also 1053].

On a qualitative basis the most interesting result is that all of the diffractograms are different. First, there was apparently some difference in the species formed after ageing depending on the coagulation pH: Figure 4-6 clearly demonstrates this (the difference in ages is taken as negligible). Second, there was a difference evident in the diffractograms of plant sludge before and after undergoing freeze–thaw conditioning (Figure 4-7). Finally, there was also a difference between the aged laboratory and fresh plant sludges, with the older sludges tending to show a slightly higher degree of crystallinity (or paracrystallinity).

4▪2▪2▪2(b)

Iron

Powder XRD diffractograms for fresh and aged samples of laboratory and plant ferric sludges are presented in Figure 4-8. The sample of ferric sludge obtained from Macarthur WFP and aged for around 1½ years (mostly refrigerated) had a significantly higher crystallinity than any of the other samples: the most obvious crystalline phase was calcite (which would not be expected to be affected by ageing), although the characteristic signature of goethite was also identified. Many of the same crystalline peaks can be discerned in the diffractogram of the fresh plant ferric sludge — but only barely. Again calcite can be clearly identified; no other crystalline phases are apparent. In particular, no goethite is evident. It is not clear whether the goethite in the aged sludge formed by slow transformation or whether it was formed during or immediately following the coagulation on site, because the two plant samples had difference provenances. 282



The two laboratory sludge diffractograms (before and after ageing) are approximately identical, with no sharp crystalline peaks. They do, however, exhibit two very broad peaks, or ‘humps’, which neatly match the signature of 2-line ferrihydrite.

It is important to

recognise that this pattern also forms the ‘baseline’ of the two plant sludge diffractograms, indicating that they, too, contain a significant proportion of 2-line ferrihydrite.

In the description of the method (§4▪2▪1▪2(d)), it was recorded that samples were generally air dried, so as to avoid heat-accelerated or heat-induced phase transformation (e.g. from ferrihydrite to goethite or hæmatite). Two samples were exposed to mild levels of heating, as shown in Figure 4-9. As with the brief heating in EDS analysis (Table 4-8), the sample drying that took place (around 15 minutes and 70°C) was clearly not sufficient to engender any significant phase transformation. The main difference was the appearance of a small peak at around 234.5pm, which has not been identified (and may be an artefact).


300

250

200

mg(Fe)/L Lab. 80 Lab. 80 Plant 1.1 Plant 1.5 Blank (scaled)

pH 6.1 6.1 8.8 9.0

Age 1 19 17 0.6


150

100

50

0 130 150 170 190 210 230 250 270 290 310 330 350 370 390 410 430 Interplanar spacing, d hkl [pm]

Figure 4-8: X-ray powder diffractograms for a selection of fresh and aged ferric sludges. The aged plant sample is offset by +50 units for clarity. Ages in months.


283

D. I. VERRELLI


300

Plant Plant after 80°C for 7d Lab. Lab. after 70°C for ~10min Blank (scaled)

250


200

150

100

50


Figure 4-9:

X-ray powder diffractograms for a selection of ferric sludges with and without

heating. The plant samples are offset by +100 units for clarity.


300

Bottom stratum (dark, lower layer) Bottom stratum (light, upper layer) Top stratum Blank (scaled)

250


200

150

100

50


Figure 4-10:

X-ray powder diffractograms for a selection of ferric sludges.

progressively offset by +50 units for clarity.

284


The curves are


Finally, the various stratified layers of the aged plant ferric sludge that were analysed by EDS were also analysed by XRD (Figure 4-10). Just as with the EDS, the two layers subsampled from the bottom stratum showed almost identical spectra. The sub-sample from the top stratum has a slightly different pattern. The main difference is that the peaks are less intense, which is relatively unimportant compared to their location and breadth.

Less

intense peaks is consistent with a greater proportion of amorphous material (possibly organic) in the matrix, although this is not the only possible explanation.

4▪2▪3

Discussion

Several of the diffractograms exhibit broadened peaks. The crystallite size may be estimated from the SCHERRER equation (equation 4-2). Ж will be assumed equal to unity. The sample identified as pseudoböhmite in Figure 4-6 has apparent crystallite sizes of order 3.5 to 5.0nm. This is within the range of reported sizes (1 to 25nm) [500, 584, 616, 940, 1150]. The estimate increases slightly as θ increases. The samples identified as ferrihydrite all have similar properties. Analysis of both bands gives apparent crystallite sizes of 2.1nm. This matches well the reported values of 2 to 3nm [cf. 279, 280, 520, 910, 965]. If the broadening of the apparent goethite peaks in Figure 4-8 can be assumed to likewise be due to small crystallite size, then these can be analysed in the same way. The (212), (111), (301), and (101) peaks at ~172, 245, 269, and 418pm were examined, yielding estimates of the apparent crystallite size from 20 to 35nm. These are compatible with published observations for precipitation of ~50nm long needles [910] and <100nm cubes [280]. Poorly crystalline goethite has been previously identified [280].

The dominance of amorphous and paracrystalline species is consistent with raw water constituents such as NOM and silica inhibiting the formation of more crystalline phases in both the aluminium [584, 622, 707, 940] and iron [258, 280, 520] systems. Such species also retard the transformation of amorphous and paracrystalline phases to the (equilibrium)


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D. I. VERRELLI

thermodynamically favoured crystalline phases — principally goethite and gibbsite [280, 388, 520, 583]. Identification of pseudoböhmite at pH 7.6 ([OH‒]added / [Al] = 2.99), but not at pH 4.8 ([OH‒]added / [Al] = 2.47) is also consistent with published observations [500, 584, 749, 870, 895, 940]. 2-line ferrihydrite is an expected product of rapidly hydrolysed Fe(III) solutions in any case [258, 280, 520, 536, 965], however its stability was evidently enhanced due to the presence of other species in the raw water. The presence of goethite is also reasonable, given the high water activity [279, 280, 306], moderate temperature [118, 280, 306, 910], and moderately alkaline pH (8.8) [280, 536, 910, 1008] — although the presence of foreign species would normally tend to promote transformation to hæmatite [280, 520]. Experiments performed in the present work found no evidence for the formation of akaganéite, even upon ageing. Other investigators have identified akaganéite as a product of neutralising FeCl3 [280], but under different conditions, viz. higher (chloride) concentrations and higher temperatures [e.g. 388].

4▪2▪4

Conclusions

The results of the EDS and XRD analysis are not entirely consistent. Further analyses may be informative, however it was found that XRD is the more useful and conclusive technique.

All of the alum sludge samples — including aged samples — were predominantly amorphous. This means that the phases present cannot be identified by XRD techniques. Furthermore, densities of even ‘pure’ amorphous phases are not as well characterised in the literature as pure crystalline phases. Pseudoböhmite was found to be present in one fresh laboratory sample, and this was apparently associated with the (high) pH. The density of this phase is uncertain.

More crystalline components were found in the ferric sludges, namely calcite and goethite. The calcite is presumed to be present due to lime addition at the plant. The goethite was

286



identified in only one sample, which was an aged plant sludge. Aside from these highly crystalline phases, paracrystalline 2-line ferrihydrite appears to be present in every ferric sludge sample analysed. This suggests that it is the initial and dominant phase formed. The density of goethite is well known, but here the proportional composition is unknown. The laboratory ferric sludges are primarily composed of 2-line ferrihydrite, for which the density has been estimated, although organic and inorganic ‘contaminants’ from the raw water could potentially cause a shift.

4▪3 4▪3▪1

Experimental density determination Method

Equations relating the phase densities, mass fractions, and solidosity were presented in §2▪1▪1. Special attention was paid to the solidosity at which the density was measured, higher values of φ leading to more accurate calculations of ρS. This was achieved by centrifuging samples prior to measurement and syringing off the supernatant. The gel-like samples thus obtained could not be directly filled into the density bottles, and so they were left on an eccentric roller mixer (p. 289) overnight, after which they reverted to a more liquid-like consistency [cf. 83, 137, 425, 435, 586, 722, 850, 1014, 1139].

The following procedure was used: 1.

Measure the dissolved solids, ysupernatant, of a sample by drying a known mass of supernatant (filtered if required) at 100°C.

2.

Find the true volume of a volumetric flask (up to 1000mL) or density bottle by filling with purified water at known temperature.

3.

Find the mass of this volume of supernatant at measured temperature (similar to above). Hence compute the liquid phase density of the sample, ρL.

4.

Find the true volume of a small volumetric flask or density bottle by filling with pure water at known temperature.

5.

Find the mass of this volume of (concentrated) sludge at measured temperature (similar to above) by filling flask with aid of a syringe, taking care not to 4▪3 : Experimental density determination

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D. I. VERRELLI

incorporate any air bubbles. (As a method validity check, supernatant can also be added in one test.) The mixture density can be calculated from this data. 6.

Transfer sample from the flask and into a drying vessel: a.

For the 100mL flask, the entire sample is to be dried, the contents are washed into a beaker with purified water.

b.

For the 25mL density bottle, the sample is split between two small aluminium drying pans, and the filled masses of these are recorded.

7.

Dry sample at 100°C to get mass of total solids (i.e. suspended solids and dissolved solids). Hence obtain mass fraction of total solids, ysample.

8.

From mass fractions of dissolved and total solids obtain the mass fraction of suspended solids. From the known volume of the liquid phase in the sludge sample obtain the solidosity, φ, and solid phase density, ρS.

Random errors are conventionally modelled as following a GAUSSian (or ‘normal’) distribution.

(Even where individual errors follow other distributions, typically the

combination of these individual errors will tend towards a GAUSSian distribution.) For the purposes of error analysis, masses measured on the analytical balance were assumed accurate to ±0.0005g, and in all cases these intervals were taken as twice the standard deviation, corresponding approximately to 95% confidence intervals. An exception was the dried mass, where an error of ±0.005g was used, given the difficulty in knowing when drying was complete. Also, the mass of supernatant dried for the dissolved solids measurement was measured on a standard laboratory balance, with an accuracy of about ±0.02g. The temperature was assumed accurate to ±0.5°C, with pure water densities taken from LILEY et alii [665]. The error distributions of the calculated results were computed using a Monte Carlo simulation, where each calculation was repeated (1000 times) with appropriate random deviations to the input variables.

288



4▪3▪1▪1

Equipment

The following equipment was used: • Centrifuge — Jouan CT4-22.

50mL tubes of sludge were typically centrifuged at

190g m/s2 for 60min periods. After decanting, the tubes were manually shaken, topped up with more material, and centrifuged again; quantity of thickened sludge was obtained.

this was repeated until sufficient

(Earlier samples were centrifuged in

500mL HDPE jars at similar accelerations — although in one case 1730g m/s2 was used.) • Eccentric roller mixer — Ratek BTR10. • Alcohol-in-glass thermometer — ‒10 to +50°C. Sample temperatures were recorded immediately prior to density measurement. • Analytical balance — Mettler AE163 (160g capacity, 4 decimal place). • Volumetric flask — 100mL nominal volume, glass. This was originally used because the wide neck facilitated the loading of thickened sludges. While it was found possible to accurately fill these with water (to establish the true volume), loading with sludge was more problematic due to the opacity of the mixture. Five separate flasks were used to obtain independent replicate measurements. This was the maximum size able to be measured on the analytical balance. • Density bottle — 25mL nominal volume, glass. Later measurements were made using smaller volumes of more concentrated sludge. These were loaded by means of a widemouthed syringe.

When loading with water the repeatability was better than

±0.004mL. When loading with sludge similar precision should have been obtained, provided no air bubbles are caught inside (these can be difficult to identify if entrained in the middle of the bottle, as when the sludge is too thick). • Pycnometer — Anton Paar DMA 38. This device operates by the ‘oscillating U-tube’ principle and has a claimed accuracy of ±1kg/m3 [69]. • Oven — Thermoline TED–66F fan-forced dehydrating oven calibrated and set to 100°C [cf. 1139]. Samples were held in a desiccator to cool before weighing.

4▪3 : Experimental density determination

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D. I. VERRELLI

4▪3▪2

Results

4▪3▪2▪1

Liquid phase

In order to obtain solids densities for the drinking water sludges several quantities need to be determined, as outlined in §4▪3▪1. The dissolved solids contents of the supernatant (i.e. liquid phase) have been routinely recorded. Additionally the liquid phase density itself must be accurately known.

While actual

densities were recorded at a measured temperature, it was found convenient to record percentage deviations from the density of pure water at the same temperature (something like a specific gravity). This relative difference was then assumed not to change much within a few degrees Celsius of the measurement temperature. δρL =

ρliquid phase, T − ρpure water, T

[4-3]

ρpure water, T

Results are presented in Table 4-14.

Table 4-14: Liquid phase densities for a range of drinking water sludges.

Raw water

Coagulant

pH [–]

δρL [%]

[mg(Al)/L] Winneke

2004-09-15

80

7.9

0.051

Winneke

2004-06-02

80

4.8

0.064

Happy Valley

2005-05-23

19

6.1

0.021

Winneke

2004-06-02

5.0

4.9

0.011

Winneke WTP

2005-04-05

1.9

6.1

‒0.015

[mg(Fe)/L] Winneke

2004-09-15

80

6.4

0.006

Macarthur WFP

2005-09-21

2.2

8.7

0.021

Macarthur WFP

2005-03-23

1.5

9.0

‒0.005

290



In general it may be expected that the density is increased by the dissolved solids content of the liquid phase, and this in turn would tend to be higher for large coagulant doses and nonneutral pH values where solubilities increase. The two largest values of δρL are indeed associated with this combination of conditions.

Although these differences may seem negligible, in fact a value of 0.021% can correspond to a difference of around 40 to 90kg/m3 in the solids density, which is significant. (Assumption of δρL = 0 leads to an overestimate of ρS.) Needless to say, the measurement temperature must also be recorded with reasonable accuracy.

4▪3▪2▪2

Solid phase

Results of solid phase density determination are shown graphically in Figure 4-11. It can be seen that data obtained at higher values of φ are (generally) associated with smaller error bars, especially for the ferric sludges. Some supernatant samples were also evaluated in this way as ‘controls’ to validate the method, and it can be seen that the solids densities of these controls came out at close to zero, as hoped. The statistical analysis yielded very large error bars for these results, suggesting that they are rather conservative estimates.

Some differences between the various sludges that may influence the average densities of their constituent solids include: • Coagulant dose • Raw water turbidity, true colour • Coagulation pH • Ageing

A better picture of the effect of coagulant dose is obtained by plotting the ρS against coagulant dose, as in Figure 4-12 (although here the coincidence of dose for several data points means the clarity of the error bars is lost).


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D. I. VERRELLI

7000

Lab. alum sludge (1a) Lab. alum sludge (1b) Lab. alum sludge (1c) Lab. alum sludge (2 LD) Lab. alum sludge (3 HD) Plant alum sludge (1) Plant alum sludge (2) Plant alum freeze–thaw (1) Plant alum + algae & PAC (1) Lab. ferric sludge (pH 6.4 a) Lab. ferric sludge (pH 6.4 b) Lab. ferric sludge (pH 9.0) Lab. ferric sludge (pH 5.6) Lab. ferric sludge (pH 6.6 LD) Plant ferric sludge (1a) Plant ferric sludge (1b) Plant ferric freeze–thaw (1) Lab. magnesium (1)

6500 6000 5500 5000

3

Solid density, ρ S [kg/m ]

4500 4000

4000

3500 3000

2700

2500

2500

2000

2050

1500

2150

1000 500 0 -500

NOTE: Error bars represent estimates of the 95% confidence limits.

-1000 -1500 -0.005

0.005

0.015

0.025

0.035

Solidosity, φ [–] Figure 4-11: Solid phase densities for various drinking water sludges as a function of φ. Data obtained using volumetric flasks shown with dotted error bars.

292



5000

0.4 mo. old 1.6 mo. old 1.9 mo. old 0.9 mo. old 0.3 mo. old 0.5 mo. old 4.0 mo. old 5.2 mo. old Al model 0.6 mo. old 1.6 mo. old 0.4 mo. old 0.4 mo. old 0.4 mo. old 0.2 mo. old 0.9 mo. old 1.2 mo. old Fe model

4500

Solid density, ρ S [kg/m3]

4000

pH pH pH pH pH pH pH pH

7.9 7.9 7.9 6.3 6.0 6.1 6.1 6.1

lab. alum sludge lab. alum sludge lab. alum sludge lab. low–dose alum lab. high–dose alum plant alum sludge plant alum sludge plant freeze–thaw alum

pH pH pH pH pH pH pH pH

6.4 6.4 9.0 5.6 6.6 8.7 8.7 8.7

lab. ferric sludge lab. ferric sludge lab. ferric sludge lab. ferric sludge lab. low–dose ferric plant ferric sludge plant ferric sludge plant freeze–thaw ferric

3500

3000

2500

2000 NOTE: Error bars represent estimates of the 95% confidence limits.

1500 1

10

100

Dose [mg(M )/L] Figure 4-12: Solid phase densities for various drinking water sludges as a function of coagulant dose. Data obtained using volumetric flasks shown with dotted error bars.


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D. I. VERRELLI

It is found that the solid phase densities of alum sludges lie around 2 5 0 0 k g / m 3 for all doses, regardless of whether they were generated in the laboratory, pilot plant, or plant. This implies that the precipitated coagulant and natural material removed from the raw water have a density that is roughly the same. This density is between that of pure gibbsite and pure böhmite.

For ferric sludges, it is reasonable to suppose, in the first instance, that the solid phase density in the limit of exceedingly low dose would also be the same. At moderately low doses (from real plants, at high pH), the solid phase density was found to be closer to 2 7 0 0 k g / m 3 . At very high doses, ρS was approximately 4 0 0 0 k g / m 3 . At a moderate dose, an i n t e r m e d i a t e ρS was obtained. Extending this to a more theoretical basis, a simple model for the ferric sludge density has been derived based on a constant 15mg/L of raw water suspended solids removed from the raw water with ρS = 2500kg/m3, and a variable component of precipitated ferric coagulant with a solid ρS = 4260kg/m3 (the density of pure goethite). The amount of coagulum phase is computed as double the coagulant dose as mg(Fe)/L — as found in laboratory work for this study. It can be seen that the model provides a reasonable fit to the data.

There is additional variation that may be due to coagulation pH, raw water turbidity, et cetera, and so in any case the most accurate procedure is to confirm ρS experimentally each time (being sure not to introduce errors, rather than reduce them!). However, the guideline values above yield good estimates in the absence of other data.

For special cases, such as the PAC-laden sludge received, there is no option but to make experimental measurement. For that (nominally algal) alum sludge, ρS was found to be 2050kg/m3 with a high level of certainty. This is significantly lower than any ‘ordinary’ alum sludge measured, and corresponds to the density of activated carbon.

294



4▪3▪3

Model curves

The model curves were obtained by computing overall densities based on: • the mass and density of material removed from the raw water; • the mass and density of precipitated coagulant as a function of dose.

The simplifying assumption was made that the mass of suspended and dissolved solids removed from the raw water is fixed at 15mg/L, independent of dose.

Experimental

measurements indicate this is reasonable at high doses, but may be less accurate at low coagulant doses. It was assumed that both of the model curves should extend back to the same ‘average’ ρS intercept, and a value of 2500kg/m3 appears to give a reasonable fit. This should correspond to the material removed from the raw water. Also, ρS should asymptote to that of the pure coagulant precipitate at high doses; the model assumes that the precipitate phase is not affected by coagulant dose (although this is not necessarily true, a reasonable fit is obtained, and there is insufficient information to support another approach).

Experimental results indicated that coagulation with alum yielded a mass of sludge 4.0 times greater than the dose as Al, slightly more than a previous report of 3.73 obtained by assuming complete precipitation as a hypothetical Al(OH)3·1.25H2O species [783].

For

coagulation with ferric, a mass of sludge 2.0 times greater than the dose as Fe was obtained, slightly less than the value of 2.32 obtained making the same assumptions as for alum [cf. 161].

Considering the scatter and varying degrees of confidence in the individual data points, for the alum sludges a good fit was obtained by taking the pure solid phase density, ρS, as 2500kg/m3, equal to the raw water constituents removed. For the ferric sludges a good fit was obtained by specifying ρS = 4260kg/m3, as for goethite, even though goethite was not the main component present.


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D. I. VERRELLI

4▪3▪4

Discussion

Some differences between the various sludges that may influence the average densities of their constituent solids include: • Coagulant dose — a high dose implies that most of the sludge is precipitated coagulant. This is a good approximation for many of the laboratory sludges. • Raw water turbidity, true colour — e.g. high silt loadings in the raw water in combination with low to intermediate coagulant doses imply that the silt could strongly influence the solids density of the sludge. This is typical of many plant sludges. • Coagulation pH — precipitation products can be affected by pH. Macarthur WFP operates at an abnormally high coagulation pH in the range 8.5 to 9.0. The pH of the laboratory alum sludge was also relatively high, at approximately 7.9. Coagulation pH values for the other sludges were within normal ranges. • Ageing — as sludge ages, solid phases may transform to their most stable state, typically being more dense.

This is generally a slow to very slow process.

The

Macarthur ferric sludge was measured quite fresh (around 1 week after production), while other sludges were somewhat older when measured.

The laboratory ferric

sludge was measured at 3 weeks and at about 7 weeks. The first alum plant sludge, from Winneke WTP, was measured fresh at about 2 weeks old. The second alum plant sludge was the high-dose Happy Valley sample, which was around 4 months old when measured, and the laboratory alum sludge was around 1½ to 2 months old when measured.

Based on the measured densities, one might conclude that gibbsite, α-Al(OH)3, was forming at high alum doses (cf. Table 4-3). However, the XRD studies showed that the solid phase was always amorphous, or at most paracrystalline.

This latter is almost certainly

pseudoböhmite [504, 1099]. Böhmite itself, γ-AlOOH, has a density of 3010kg/m3 [504], however the incorporation of additional water into the pseudoböhmite structure [121, 870, cf. 1099] suggests that the value for pseudoböhmite would be lower, with the best estimates in the range 2500 to 2800kg/m3 [223].

296

There is also data suggesting formation of



pseudoböhmite is favoured more at pH 9 than at pH 7 [870], which may provide an alternative explanation for the higher ρS measured for the pH 7.9 alum sludge.

The ferric sludge data exhibits a strong dependence on dose, with ρS varying from about 2700kg/m3 at the lowest doses, to about 4000kg/m3 at the highest doses. The XRD data suggest that some goethite, α-FeOOH, with a density of 4260kg/m3 [118, 280] may be present — however, again the solid phase is generally either amorphous or paracrystalline. This solid phase is then most likely made up predominantly of 2-line ferrihydrite, with a reported density of 3750 to 3960kg/m3 [280, 520]. For the high-dose ferric sludges ρS appears to exhibit a dependence upon pH, with higher pH yielding lower densities. Although the error bars from all points in the two clusters overlap 4000kg/m3, these were conservative estimates made on individual points: the tight clustering of the points suggests the actual error may be significantly less than this. A lower density may be caused by a shift in the proportions of phases present, or pH favouring the formation of different phases — namely either a less dense amorphous material or akaganéite, β-FeOOH, (ρS = 3560kg/m3) [279, 280].

HOSSAIN & BACHE [494] reported the density of precipitated alum by two techniques. By regression of data from a series of sludges with varying alum dose they estimated the density as 2530±50kg/m3; the pH was 6.0, but similar results were obtained at pH 5.0 [494]. Through direct measurement of alum precipitate collected from distilled water they identified a trend with pH: density was highest (2600kg/m3) at pH 5.5, and dropped off towards about 2400 to 2450kg/m3 at lower (4.5) or higher (7.5) values of pH, all with precision of ±200kg/m3 [494]. Note that the ‘direct’ measurements were made in the absence of NOM and turbidity elements, which may influence the type of aluminium oxide or hydroxide formed. The values are consistent with the spread of estimates calculated in the present work, where a representative value of 2500kg/m3 has been adopted.

The estimates of HOSSAIN & BACHE [494] and KNOCKE, DISHMAN & MILLER [576] for the density of raw water contaminants lie in the approximate range 1500kg/m3 to 1750kg/m3 (see p. 267).


297

D. I. VERRELLI

These values are considerably lower than any estimate obtained in the present work. It may be that the higher estimate, taken by HOSSAIN & BACHE [494] as being more accurate, is subject to some systematic bias; for example, in the present work it was seen that low solidosities led to misleading estimates of solid phase density. The estimate was also very sensitive to correction of liquid phase density and supernatant dissolved solids. Neglecting to correct for supernatant dissolved solids, specifically, can be shown to lead to density underestimation of 20 to 80kg/m3 for high-solids samples (φ ~ 1%V) depending upon the dissolved solids concentration, and much greater errors for samples that have not been partially dewatered prior to measurement, viz. 250kg/m3 (φ ≤ 0.4%V). In the latter case of ‘direct’ measurement, the estimate requires calculation of the differences of pairs of large numbers in order to obtain the volumes and masses of the ‘colloidal’ material. Equally problematic is that it does not allow for a difference between the species which are removed from the raw water by coagulation (e.g. some NOM) and those which are not (e.g. some salts). The measurements on polymer-aggregated sludge likewise neglected the differences due to the presence of dissolved solids. Despite these possible sources of error, the magnitude of the disparity between the previous estimates and those of the present work suggest that a real physical difference may well underlie the data. Such a difference could be caused by variations of the previously studied systems from those of the present work, namely: • higher raw water colour leading to a greater influence upon the overall sludge solid phase density; • inherently different raw water composition; or • the ‘charge neutralisation’ mechanism (lower coagulant dose) favouring the removal of different matter from the raw water. The latter two points would allow that the presently estimated natural matter densities are accurate. The first point would suggest that the model density did not reflect the true natural matter density — however this would not be a critical flaw, as the model adequately represents the o b s e r v e d sludge densities in any case.

298



4▪3▪5

Conclusions

Sensitivity analysis showed that results are sensitive to the solids density employed in computations.

Experimental measurements of the solid phase density has revealed that the average varies around 2500kg/m3 for all conventional alum sludges. This is consistent with the presence of pseudoböhmite, whose density is of order 2500 to 2800kg/m3.

For ferric sludges the data is more sensitive to coagulant dose: high doses (80mg(Fe)/L) gave ρS as 4000kg/m3, compared to only 2700kg/m3 for lower doses closer to those used on fullscale plants (2mg(Fe)/L). The upper limit is consistent with the presence of ferrihydrite or goethite. A guideline for intermediate doses was presented.

Sludges with high PAC content will have a reduced average solid phase density, with the sample measured here yielding 2050kg/m3.

None of the sludge solid phase densities could be generalised as 3000kg/m3, and there was significant variation between sludge types. Given the influence of ρS, it is critical that a reasonable value be used:

the guideline values above will be sufficient in many

circumstances, however individual sample measurements may be required in specific situations.


299

5.

EFFECT OF COAGULANT TYPE, DOSE, AND pH

Knowing ρS it was possible to correctly analyse the settling and filtration data obtained for a large number of water treatment sludges produced by coagulation with alum, ferric or magnesium at a range of doses and pH values.

5▪1 5▪1▪1

Published observations Effect of dose

It has been widely reported that raw water that is high in turbidity produces a more concentrated sludge, which is “less difficult to dewater”, and conversely that low raw water turbidities result in “more difficult” sludge processing [107, 113, 227, 282, 319, 443, 577, 580, 783, 797, 854, 879, 1139]. High coagulant doses, relative to TSS (or turbidity), are reported to result in inferior dewaterability in both the rate and extent of dewatering, for both alum and ferric sludges, and across all φ [115, 319, 577, 580, 783, 879]. This is due to the precipitated coagulant dominating the sludge mass when the turbidity is low [113, 281, 580, 783, 854]. In contrast, experiments by CHANG et alia [236] (see p. 303) showed enhanced filtration rate with increasing alum dose, for all pH values. Addition of coagulants tends to decrease the settled sludge solids concentration monotonically as the dose is increased; e.g. for low-turbidity raw waters it ranges from 1 to 10g/L [161, cf. 281].

The influence of increasing coagulant dose has been associated with a change in the mechanism from charge neutralisation to sweep coagulation [e.g. 577]. It was suggested that coagulation under low-dose ‘charge neutralisation’ conditions should yield minimal electrostatic repulsion between solid surfaces, implying a very high interparticle attraction and thus a higher compressive yield stress [319].

However this

301

D. I. VERRELLI

implies that low coagulant doses would result in a more problematic sludge, which is not generally observed. BACHE et alia [116] concluded that aggregates generated by charge neutralisation (generally low dose), held together by VAN DER WAALS forces, were of order 101 to 102 times weaker than those formed by ‘electrostatic bridging’ (as under sweep or enhanced coagulation — i.e. high doses). This suggests higher doses would have higher py, although possibly with reduced R. The sludge properties in b o t h the charge neutralisation [116] and sweep or enhanced coagulation [816] regimes are often determined by the precipitated coagulant.

Both alum [111, 115] and ferric [360] aggregates have been found to become weaker and rupture more readily at high coagulant doses (above an ‘optimum’). HOSSAIN & BACHE [494], working with coloured, low-turbidity raw waters, reported that alum sludge strength was optimised when the solids contained about 35% precipitated coagulant. BACHE et alia [112] found that aggregate density first increased as the ‘optimum dose’ of alum was approached, and then decreased again with alum doses beyond the optimum [cf. 115].

Df was found to decrease as the alum dose was increased for coagulation of a turbid water [997]. Df was reported to be unaffected by alum dose, or the proportion of humic substance in the aggregates, for coloured, non-turbid water [816]. Increasing coagulant dose implies a higher ionic strength in the supernatant — which reduces the repulsion between like-charged particles — and generally promotes more rapid reaction and lower Df [478, 531, 679]. The presence of high levels of NOM may interfere with this mechanism. Certainly, the influence would be reduced for raw waters of naturally high ionic strength.

5▪1▪2

Effect of pH and hydrolysis ratio

A pioneering systematic investigation by KNOCKE, HAMON & DULIN [577] found that the dewaterability of both alum and ferric sludges improved as the coagulation pH decreased —

302

Chapter 5 : Effect of Coagulant Type, Dose, and pH


across settling and filtration, in both rate and extent. The effects all appeared significant except for the compressibility in filtration [577]. The effect was reportedly magnified when turbidity was low [577], suggesting that the mechanism relates to the form in which the coagulant precipitates. Larger aggregates formed at high pH, but these exhibited poorer dewatering because of their lower density (which dominated any enhancement due to size) [577]. Aside from the direct neutralisation mechanism, higher alkali doses could indirectly reduce the aggregate density by raising the ionic strength, as discussed in the previous subsection.

Reviews for each of the coagulants follow.

5▪1▪2▪1

Aluminium

In the charge neutralisation regime, increasing pH was associated with decreases in aggregate strength of order 10% [111].

Experiments by CHANG et alia [236] on sludges generated by coagulation of 4.6μm clay with alum confirmed an improvement in dewaterability from pH 10, to pH 7, to pH 5.2, in terms of settling and 6900kPa-filtration rates, but they also observed a deterioration in dewaterability when a still lower coagulation pH of 3 was employed. A similar trend was suggested by the data for extent of filtration [236].

In turbid raw water of low colour, decreasing the pH from 8.0 to 6.5 led to significant decrease in Df at low Al doses, but had little effect at higher Al doses [997].

KIM et alia [569] estimated Df to be greater for aggregates formed by sweep coagulation of highly coloured raw water with alum (~2.2) than by charge neutralisation (~1.9). However these results are not entirely conclusive given the unusual size distributions of the ‘aggregates’ — nearly identical to the raw water for charge neutralisation, and bimodal for the sweep coagulation [569].

5▪1 : Published observations

303

D. I. VERRELLI

AXELOS et alia [103] studied the precipitates formed by partial neutralisation of aluminium chloride (AlCl3·6H2O) with sodium hydroxide (NaOH).

At a hydrolysis ratio,

[OH‒]added/[Al] *, of 2.5, primary particles of 1.8nm were found in isolation (25%) and aggregated as ramified chains of up to 40nm size [103]. It was inferred that the primary particles were tridecameric aluminium [103]. The aggregates were found to have Df = 1.42 [103]. At a hydrolysis ratio of 3.0, denser aggregates formed, also up to 40nm in size, with Df = 1.92 [103]. The internal structure was described as a ‘mosaic’, with Al13 polycations no longer identifiable [103]. A later publication by the authors [104] suggested that the low fractal dimensions were due to cluster polarisation, resulting in tip-to-tip collisions and bond formation being favoured. This work demonstrated the great structural difference upon increasing [OH–]added/[Al] by only 0.1 unit to 2.6, where “precipitation starts to occur” and Df = 1.86 [104]. This suggests that 2.6 constitutes a ‘threshold’ for rapid aluminium precipitation, similar to the “flocculation threshold” described for iron(III) (§R1▪2▪6▪3(a)).

Additionally, it was

determined that ordinary cluster–cluster aggregation (DLCA) provided a good model for [OH–]added/[Al] = 2.6 [104]. AXELOS, TCHOUBAR & JULLIEN [104] also proposed a reason why different mechanisms might prevail: at the lower hydrolysis ratio the positive charge on each Al13 polycation unit is greater, leading to a strong polarisation of the surrounding water molecules.

ROČEK et alia [870] reported an increasing crystallinity of the precipitated coagulant (see also §5▪1▪3) under more alkaline conditions, say above pH 7, with respect to both the initial formation of the precipitate and subsequent transformation upon ageing (cf. §4▪2, §8▪1). A more crystalline aluminium (oxy)hydroxide phase has been associated with higher py (i.e. lower φ∞) in centrifugation [870]. Formation of such crystalline phases was found to be favoured under more alkaline conditions and upon ageing (cf. §8▪1) of the wet sludge [870].

*

304

The implication of the article [103] that a species of formula Al(OH)2.5 forms is misleading.



The crystallinity of the aluminium phase was not *, however, found to resist capillary forces [870].

5▪1▪2▪2

Iron

TCHOUBAR, BOTTERO et alia [1008] studied the precipitation of ferrihydrite from ferric chloride at hydrolysis ratios up to about 3, which is above the threshold for rapid precipitation.

In this case the precipitate size increased from about 12nm to 0.2μm as

[OH‒]added/[Fe] increased from 1.0 or 1.5 up to 2.7 [1008]. It was suggested that the precipitates found for [OH‒]added/[Fe] of 2.0 to 2.5 at 400s may be clusters made up of primary particles as small as ~1.6nm, having Df ~ 1.7 [1008].

The

constant size of the primary particles, equated to “polycations” in the paper, was attributed to the strong internal shell complexation of chloride ions with ferric ions, such that the olation and oxolation reactions necessary to increase the polycation size are limited [184]. Precipitates produced at the lowest hydrolysis ratios, [OH‒]added/[Fe] = 1.0, did not show clear fractal properties at 400s [1008]. It was suggested that these precipitates may be linear clusters of ~1.6nm primary particles at 400s, compacting slightly to “slightly branched” structures at 3600s comprising perhaps as few as 8 primary particles [1008], implying very low ‘apparent’ Df values. At larger hydrolysis ratios (2.0 and 2.5), an apparent Df of 1.74 was estimated [1008]. At the largest hydrolysis ratio, the apparent Df increased further up to 2 [1008]. It was expected that increasing [OH‒]added/[Fe] would lead to more primary particles being precipitated, but with reduced surface charge and (hence) reduced electrostatic repulsion [1008]. Interestingly, the cluster size was found to decrease over time [1008].

These workers, BOTTERO, TCHOUBAR et alia [184], also studied the hydrolysis and precipitation of ferrihydrite from ferric nitrate solution at various hydrolysis ratios. Similar results were found as for ferric chloride, except that the size of precipitate clusters was found to depend upon the hydrolysis ratio [184].

*

A study by VISHNYAKOVA et alia (1970) published the opposite statement [870].


305

D. I. VERRELLI

In coagulation of non-turbid water of moderate TOC with ferric chloride, Df was found to increase significantly as the pH was decreased from 7.5 to 5.5 [1082].

There was no

significant change when the raw water was turbid and of low TOC [1082].

A number of experiments on ferric systems have investigated the production of aggregates by s l o w hydrolysis.

This can be effected through the use of slowly-dissolving lime

(Ca(OH)2) as alkali [388]; gradual or step-wise addition of strong bases such as sodium hydroxide [388]; or use of a buffer * [679]. Denser aggregates were found to form [388]. These techniques reduce ‘interfacial disequilibrium’ effects [146] — which may be significant in industrially relevant systems — thereby reducing the rate of deposition of precipitate onto nucleation sites [388]. They may also reduce the number of nucleation sites, encouraging the formation of larger particulates [388].

5▪1▪2▪3

Magnesium

Higher alkali concentrations were found to decrease by about 2 orders of magnitude the volume of magnesium hydroxide sludge synthesised from crystals of various magnesium salts in potassium hydroxide, which was associated with the ability of alkaline conditions to facilitate crystallisation [890].

5▪1▪3

Effect of coagulant

Most of the literature comparing alum and iron sludges reports that the ferric sludges dewater further [107, 854, 879, 1023] and dewater faster [281, 754, 1095] than alum sludges [827]. Yet the reasons given are often dubious [e.g. 1023]. Some authors refer to different specific gravities of about 3.4 and 2.4 [e.g. 754] [cf. 389]. However these are numerically incorrect (they are for the pure hydroxides, cf. §4▪1▪2) and conceptually incorrect, as they ignore aggregate structure.

Other authors [827] have

‘explained’ the difference as due to the lower “bound water content” of ferric aggregates

*

306

On the other hand, TAMBO & WATANABE [997] found no significant change in Df with changing alkalinity.



compared to alum sludges. It is arguable whether this is a cause or an effect! WAITE [1095] attributed the difference to a higher growth rate for ferric flocs. However this could also suggest a more porous structure (see §R1▪5▪5, §R1▪5▪6▪1).

In contrast, HARBOUR et alia [443] found that the use of ferric coagulants led to lower final solids concentrations than alum. The dewatering behaviour of ferric sludges also appeared to vary less than that of alum sludges [443]. Another study [355, 1055] estimated clay–ferric– polymer flocs of a given size to dewater slightly slower — interpreted as due to a more open, less dense structure — but to a slightly greater extent than the supposedly-corresponding clay–alum–polymer flocs.

Limited characterisation of ferric and magnesium coagulation aggregates in one study showed that they had moderately high Df, but within the range of values obtained for alum [997].

Several authors [227, 315, 879, 911, 1139] have noted poor dewaterability of ‘magnesium hydroxide‘ sludges. MULBARGER and co-workers found that the presence of high levels of magnesium in softening sludges caused a deterioration in both the r a t e of settling and e x t e n t of dewatering (in both the settling/thickening regime and in filtration) [227]; work by CALKINS & NOVAK [227] was consistent with these observations. However, it is notable that CALKINS & NOVAK [227] found that magnesium levels did n o t affect the r a t e for f i l t r a t i o n .

In contrast, several other authors reported benefits in sludge quantity [251] and quality (especially dewatering rate) [160, 911, 916, 1021, 1022] with magnesium coagulation. Apparently the magnesium aggregates even form faster than alum aggregates [1021]. RANDTKE found that, for a given raw water loading, less coagulant is required when magnesium is chosen as a coagulant, and the quantity of sludge is reduced [251]. It is not clear what the volume would be on an equal dosage basis. SEMERJIAN & AYOUB [916] reported that the amounts of sludge generated were usually greater, prior to dewatering, but that this was “partly” offset by the improved dewaterability (in both settling and filtration).


307

D. I. VERRELLI

The favourable behaviour of magnesium sludges has been attributed to the higher crystallinity of the precipitates, in comparison to either alum or iron sludges [911]. Magnesium aggregates have been described as less “filamentous” and more “granular” [1022].

The magnesium sludge incorporates crystalline calcium carbonate (CaCO3) as a

major constituent by mass, making the aggregates “much larger and heavier” than corresponding alum aggregates [942].

Hence a high * ratio of calcium (carbonate) to

magnesium (hydroxide) (e.g. molar ratio > 10 [227]) suggests better sludge dewaterability † — although even in lime–softening sludges the amount of aluminium and iron hydroxides present also has an effect [911]. Therefore the ratio of crystalline to (implicitly amorphous) hydroxide material is “a more realistic measure [predictor?] of the dewatering process” [911].

SAKHAROV et alia [890] reported that the volume of magnesium hydroxide sludge synthesised from crystals of various magnesium salts in potassium hydroxide was somewhat less when generated from the sulfate salt than from the chloride salt.

It is of interest to consider whether a slow precipitation rate caused by the c o a g u l a n t , rather than the a l k a l i (see §5▪1▪2▪2), would yield similar results — if so, then magnesium would seem to be favoured over aluminium or iron. This chapter looks to explore this hypothesis in detail through assessment of material dewatering properties.

5▪2

Materials and methods

Sample generation conditions for the alum sludges discussed in the following sections are presented in Table 5-1. Of interest is the unusually high true colour reading and 254nm absorbance for the raw water of 2003-09-22, although this apparently did not affect the magnitude of the ‘optimal’ dose.

*

Results presented [911] indicate that the sludge dewaterability is similarly poor when the Ca/Mg ratio is moderate (say, around unity) as when it is low.

†

This is taken empirically on the basis of the final solids content after a certain dewatering operation [911], and thus may be controlled by a combination of permeability or compressibility factors.

308


[10/m]

5▪2 : Materials and methods

No

2.52

6.0

10

≤2

0.64

12

2003-12-18

Winneke

Lab. 10|6.0

No

2.25

6.0

5.0

≤1

0.66

10

2004-01-08

Winneke

#

No

2.02

5.8

4.0

≤2

1.83

42

2003-09-22

Winneke

No

0.74

6.0

1.5

≤1

1.07

19

2004-05-11

Winneke

Yes

–

6.1

1.9

–

–

–

2005-04-05

Winneke

#

Lab. 5.0|6.0 Lab. 4.0|5.8 a Lab. 1.5|6.0 Plant 1.9|6.1

This sample was generated in 1L square jars using a paddle mixer, with NaOH added first (the only such sample).

No

Polymer

a

2.69


Note

6.0

79

~4

1.14

[–]

[mg(Al)/L]

Dose

pH

[mg(Al)/L]

set pH

Optimum dose at

A254nm

[mg/L Pt units]

22

2006-01-05

and date

True colour

Winneke

#

Lab. 79|6.0

Raw water source

Sample


Table 5-1: (a) Generation conditions for alum sludge samples with coagulation pH ≈ 6. Samples

for which replicate data was presented in §3▪5▪4 are marked with a hash symbol, #.

309

310

[10/m]


No

2.99

7.6

80

~2.5

0.87

14

2004-05-21

Winneke

Lab. 80|7.6

No

2.47

4.8

80

≤1

0.83

12

2004-06-02

Winneke

Lab. 80|4.8

No

4.21

8.4

5.0

~2.5

0.87

14

2004-05-21

Winneke

No

0.82

4.9

5.0

≤1

0.75

10

2004-06-02

Winneke

No

5.06

8.4

2.5

~2.5

0.87

14

2004-05-21

Winneke

Lab. 5.0|8.4 Lab. 5.0|4.9 a Lab. 2.5|8.4

The characterisation of this sample by filtration occurred approximately 3½ months after generation.

No

Polymer

a

3.15


Note

8.6

80

~2.5

0.87

[–]

[mg(Al)/L]

Dose

pH

[mg(Al)/L]

set pH

Optimum dose at

A254nm

[mg/L Pt units]

14

2004-05-21

and date

True colour

Winneke

#

Lab. 80|8.6

Raw water source

Sample

D. I. VERRELLI

Table 5-1: (b) Generation conditions for alum sludge samples with coagulation pH ≉ 6. Samples

for which replicate data was presented in §3▪5▪4 are marked with a hash symbol, #.


Generation conditions for alum sludges obtained from Happy Valley pilot plant are given in §5▪6▪2. Details for the ferric sludges are presented in §5▪7▪1. Details for the magnesium sludge are presented in §5▪11▪1.

The data points plotted for py(φ) were obtained by filtration and (in some cases) centrifugation. Combination with batch settling tests allowed a curve fit to be generated using B-SAMS. The R(φ) graphs show filtration data as connected points, while the data from settling analyses using B-SAMS are plotted as curves with only the terminal points shown individually; no interpolations are shown between data from settling and filtration (cf. §3▪5▪1▪1).

5▪3

Alum sludges: variation of dose

The effect of coagulant dose on alum sludge dewatering is best studied by holding the coagulation pH constant. In the following subsections, dose response effects are considered at three separate pH values. In a few cases data was not able to be collected at high solidosity due to sample volume constraints.

5▪3▪1 5▪3▪1▪1

Results and discussion Intermediate pH (6)

Dewaterability data for sludges coagulated at pH 6.0±0.2 are presented in Figure 5-1 and Figure 5-2.

To improve clarity, only one run (identified with a hash symbol, #) is shown where ‘replicate’ samples (i.e. ‘similar’ coagulant dose and coagulation pH) are available. The companion data is presented in §3▪5▪4, and shows good agreement between replicates.

5▪3 : Alum sludges: variation of dose

311

D. I. VERRELLI


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 mg(Al)/L Lab. 79 Lab. 10 Lab. 5.0 Lab. 4.0 Lab. 1.5 Plant 1.9

1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

pH 6.0 # 6.0 6.0 # 5.8 6.0 6.1 # 1.E+0

Solidosity, φ [–] Figure 5-1: Effect of coagulant dose on py(φ) for a range of alum sludges at pH 6.0±0.2.

Figure 5-1 shows that py(φ) generally deteriorates as the coagulant dose increases, meaning

that the maximum potential solidosity at a given applied pressure differential (or bed height) decreases. Equivalently, the pressure required to yield a given equilibrium solidosity is increased. In filtration py(φ) is essentially the same for all alum sludge produced at the given pH with doses of 5mg(Al)/L or more, suggesting that at these doses the precipitated coagulant is dominating the filtration behaviour. There is greater divergence in settling.

312



2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10

mg(Al)/L Lab. 79 Lab. 10 Lab. 5.0 Lab. 4.0 Lab. 1.5 Plant 1.9

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

pH 6.0 # 6.0 6.0 # 5.8 6.0 6.1 #

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-2: Effect of coagulant dose on R(φ) for a range of alum sludges at pH 6.0±0.2.

A similar tendency is observed for R(φ), shown in Figure 5-2, neatest for the low-φ data. In the filtration data the resistance seems first to increase with increasing dose, up to perhaps 5mg(Al)/L, at which point the tendency reverses, and the resistance decreases.

Examining the detail of the two figures, it seems at first somewhat surprising that the 4.0mg(Al)/L sludge exhibits significantly better py(φ) properties than the 5.0mg(Al)/L sludge. Along with the 20% decrease in coagulant dose, the likely causes are the raw water quality (a


313

D. I. VERRELLI

difference of 300 to 400%) and generation in small jars * (see note in Table 5-1(a)). The slight pH difference is presumed negligible (the conditions are not near the Al solubility curve — see Figure 3-3).

5▪3▪1▪2

High (8½) and low (5) pH

Supporting data obtained at pH values of approximately 8½ and 5 are presented in Figure 5-3 and Figure 5-4. The plant data curve is shown as a reference.

Although fewer samples were studied at these pH values, the trends identified in §5▪3▪1▪1 are also evident here. Specifically, there is clearly a trend for py to increase with increasing coagulant dose (no ‘plateau’ level could be identified). R also consistently increased with increasing coagulant dose, although no data was available at high solidosity for the pH 5 materials (no ‘reversal’ could be identified).

These results are consistent with previous experimental dewatering findings [319], as well as the finding that aggregates are less compact (lower Df) at high coagulant doses [997].

The pH 4.9 low-dose laboratory sludge py(φ) curve does not follow the form of the other curves, with divergence at low φ. It is not immediately clear whether this is a real effect, and what the cause(s) might be if so.

*

This was the first sludge characterised that is presented in this thesis. Minor differences may exist in experimental procedures, such as handling of the sludge, that naturally develop over time with operator experience. (Differences in shear environment are investigated more systematically in §7▪2.) The settling test was also terminated after 20 days, leading to underestimation of φg of likely magnitude < 10%.

314




1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

mg(Al)/L

pH

Lab. 80 Lab. 5.0 Lab. 2.5 Lab. 80 Lab. 5.0 Plant 1.9

8.6 8.4 8.4 4.8 4.9 6.1

1.E-1

#

# 1.E+0

Solidosity, φ [–] Figure 5-3: Effect of coagulant dose on py(φ) for a range of alum sludges at pH 8.5±0.1 and pH 4.9±0.1. The pH 4.9 sludge was about 3½ months old when characterised.


315

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 mg(Al)/L Lab. 80 Lab. 5.0 Lab. 2.5 Lab. 80 Lab. 5.0 Plant 1.9

1.E+09 1.E+08 1.E+07 1.E-4

1.E-3

1.E-2

1.E-1

pH 8.6 8.4 8.4 4.8 4.9 6.1

#

# 1.E+0

Solidosity, φ [–] Figure 5-4: Effect of coagulant dose on R(φ) for a range of alum sludges at pH 8.5±0.1 and pH 4.9±0.1. The pH 4.9 sludge was about 3½ months old when characterised.

5▪3▪2

Conclusions

Dewaterability of alum sludges appears to deteriorate as the coagulant dose is increased, in agreement with the literature. At a threshold of about 10mg(Al)/L, py(φ) does not increase further, suggesting the precipitated coagulant dominates sludge behaviour, but R(φ) may recover slightly to lower values.

316



5▪4

Alum sludges: variation of pH

5▪4▪1

Results and discussion

The effect of varying the coagulation pH has been studied in greatest detail at the limit of very high coagulant doses, where the precipitated coagulant will dominate dewatering behaviour. Dewaterability curves are shown in Figure 5-5 and Figure 5-6. Comparisons can also be made for three laboratory sludges coagulated at a relatively low dose of 5mg(Al)/L, as in Figure 5-7 and Figure 5-8.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3

mg(Al)/L Lab. 80 Lab. 80 Lab. 79 Lab. 80 Plant 1.9

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

pH 8.6 7.6 6.0 4.8 6.1

# # # 1.E+0

Solidosity, φ [–] Figure 5-5: Effect of coagulation pH on py(φ) for a range of alum sludges at 80mg(Al)/L dose.

5▪4 : Alum sludges: variation of pH

317

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 mg(Al)/L Lab. 80 Lab. 80 Lab. 79 Lab. 80 Plant 1.9

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

pH 8.6 # 7.6 6.0 # 4.8 6.1 # 1.E+0

Solidosity, φ [–] Figure 5-6: Effect of coagulation pH on R(φ) for a range of alum sludges at 80mg(Al)/L dose.

The trend in both py(φ) and R(φ) (Figure 5-1 and Figure 5-2) shows a significant deterioration in dewaterability as the coagulation pH is increased above pH ~ 6. This is true across the entire span of solidosities observed.

The system pH has three key influences on the coagulation process: • it will alter the overall solubility of the metal; • it will alter the speed of the hydrolysis reaction; • it may also influence the favoured precipitate phase.

318




1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3

mg(Al)/L Lab. 5.0 Lab. 5.0 Lab. 5.0 Plant 1.9

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

pH 8.4 6.0 4.9 6.1

# # 1.E+0

Solidosity, φ [–] Figure 5-7: Effect of coagulation pH on py(φ) for a range of alum sludges at 5mg(Al)/L dose. The pH 4.9 sludge was about 3½ months old when characterised.

From published plots of the solubility of aluminium [90, 155, 326] (see §R1▪2▪3), it is seen that solubility has a minimum at pH ~ 6. An increase in solubility would thus be associated with an increase in pH above 6, suggesting a lower ‘driving force’ for precipitation, leading to a more compact floc. It is postulated that this would exhibit greater dewaterability, so it is unlikely that this mechanism is controlling the behaviour here. This is reasonable, given that the differences in solubility are small in comparison with coagulant doses of 80mg(Al)/L.

5▪4 : Alum sludges: variation of pH

319

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 mg(Al)/L Lab. 5.0 Lab. 5.0 Lab. 5.0 Plant 1.9

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

pH 8.4 6.0 4.9 6.1

# # 1.E+0

Solidosity, φ [–] Figure 5-8: Effect of coagulation pH on R(φ) for a range of alum sludges at 5mg(Al)/L dose.

The hydrolysis ratios of the laboratory-generated sludges were presented in Table 5-1. These represent average values for the homogenised mixture; instantaneous values may be higher locally, leading to greater interfacial disequilibrium [146].

From the table we see that the two high-dose samples generated under acidic conditions have hydrolysis ratios close to the probable threshold value, while the samples generated under alkaline conditions have significantly higher hydrolysis ratios. This is consistent with the slow (RLCA) formation of compact, readily dewaterable aggregates at low pH, and the increasingly rapid formation (DLCA) of loose, open aggregates at higher pH that are more difficult to dewater. 320



Note that due to the natural pH and buffering capacity of the raw water studied here, the hydrolysis ratio actually decreases sharply at the lowest coagulant doses (for both Al and Fe — see Table 5-4). This suggests two synergic mechanisms arise as the coagulant dose is reduced that both work to reduce the reaction rate, and leading to higher fractal dimensions, and hence improved dewaterability. Of course, this pre-supposes that the rate of reaction is sufficient to generate aggregates of reasonable size in the available time — if the rate were so slow that minimal precipitation and aggregation occurred, then of course the kinetics of dewatering would suffer.

5▪4▪2

Conclusions

High alkali doses lead to high coagulation pH values and correspond to high hydrolysis ratios. Under these conditions the precipitation and aggregation rate is likely to be rapid, leading to the formation of quite open aggregate (and network) structures. Conversely, low alkali doses yield low pH values and hydrolysis ratios, and the slower reactions are expected to result in more compact aggregate structures. These predictions are supported by the experimental observations, which showed that the dewaterability deteriorated as the pH was increased above about 6, or as the hydrolysis ratio increased above about 2.7. The findings are also consistent with the published literature.

5▪5

Alum sludges: combined dose–pH effects

While it is interesting from a fundamental point of view to isolate the individual effects of coagulant dose and coagulation pH upon sludge dewaterability, for practical purposes an analysis of their c o m b i n e d effect should be made. This is particularly important in terms of establishing the relative importance of the two effects when each, taken individually, would predict opposite changes. It is helpful, then, to present the data as functions of both variables, as in the contour plots following.

5▪5 : Alum sludges: combined dose–pH effects

321

D. I. VERRELLI

The program NEIGHBOUR.BAS, written by WATSON [1104], was used to create the contour plots. Some cosmetic and syntactical changes to the code were made, and it was run under QuickBASIC version 4.5 (Microsoft, U.S.A., 1998).

The settings implemented were as

recommended, in particular natural neighbour processing was used (this produces a DELAUNAY triangulation) to linearly estimate gradients, which in turn were “blended” with direct linear surface interpolation to give a “fairly taut” surface [1104].

Appendix S12

presents a brief discussion of the sensitivity of the contours. Common mathematical software packages do not implement these specific contouring methods; MATLAB (The MathWorks, U.S.A.) can conveniently produce suitable contour plots without blended gradient interpolation.

Figure 5-9 is a contour plot [1104] of the estimated gel point for laboratory-generated alum

sludges * as a function of coagulant dose and coagulation pH.

The main effects are a

tendency for the gel point to increase as the coagulant dose is reduced below about 10mg(Al)/L. There may also be a tendency for φg to increase if the pH rises above about 8.5, although there is insufficient data in the region to be certain (cf. §S12). Behaviour at intermediate to high doses is less variable, and the variation present is probably influenced by experimental scatter.

BACHE & HOSSAIN [111] identified a trend for the effective aggregate density to be maximised at a coagulant dose of 5mg(Al)/L; this suggests a corresponding extremum in the gel point. This does not match the results presented in Figure 5-9. However, BACHE & HOSSAIN [111] were treating raw water with true colour of order 10 times greater than in the present work, and they examined a smaller domain of coagulation conditions.

*

All laboratory alum sludges produced under the ‘standard’ conditions are included.

This excludes

sludges treated with polymer, spiked with dMIEX, aged, frozen, or subjected to extra shear. For reference, the raw water dates of included sludges are: 2003-08-04; 2003-09-22; 2003-12-02; 2003-12-18; 2004-01-08; 2004-02-11; 2004-02-13; 2004-05-11; 2004-05-21; 2004-06-02; 2006-01-05; and 2006-06-09. Constitutional data for these sludges appears in Chapter 3, Chapter 5, and Chapter 7.

322



100

0.0020

0.0015 0.0010

Dose [mg(Al)/L]

0.0025

0.0020 0.0015

10 0.020

0.0025 0.0030 0.0035

0.0055

0.0040 0.0045

0.0050

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 5-9: Contour plot of estimated gel point, φg, (i.e. at py → 0+) for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. Approximate solubility limits of Al are shown as dashed lines.

It is also useful to compare the contours with the approximate aluminium solubility curves. Approaching the left and lowermost (off chart) part of the solubility envelope, there is a tendency for φg to increase. Under both of these conditions the low dose relative to Al solubility suggests a slower precipitation and coagulation process that may be expected to result in denser (and possibly smaller) aggregates. The same trend is evident approaching the solubility envelope at high pH, albeit to a smaller degree. This is presumably due to the high alkali dose resulting in rapid reaction almost regardless of coagulant dose. This is also consistent with the tendency in the bottom left of


323

D. I. VERRELLI

the plot for the variation to increase rapidly with decreasing pH (i.e. alkali dose). A further consideration is the accuracy of the solubility envelope: the curve displayed is an estimate of equilibrium behaviour at low ionic strength — experimental error or deviation from either equilibrium or low ionic strength may widen the envelope (see §R1▪2▪3). It is proposed that the slight increase in φg at high doses and intermediate pH (leading to the appearance of a minimum at intermediate doses) is due to a change in the ‘effective’ composition of the sludge, from a complex mixture of NOM and aluminium precipitates to a solid mass dominated by precipitated coagulant. This effect appears to be less important than the reaction rate effects stemming from alkali and coagulant doses.

Figure 5-9 is complemented by Figure 5-10, which indicates the compressibility at high

pressure.

At low alum or alkali doses, the pH does not show any significant effect

(horizontal contours); however, it becomes at least as influential as dose in the high dose range (diagonal and vertical contours). φ may decrease (undesirable) at py = 50kPa with either increasing dose or increasing pH, although not in all regimes. The trends are outlined in Table 5-2.

Table 5-2: Schematic of key trends and features identified in Figure 5-10 (py = 50kPa). Note, symbol ↓ denotes decreasing and symbol ↑ denotes increasing.

Dose > 10mg(Al)/L

Dose < 10mg(Al)/L

Coagulant dominates sludge

Coagulant dominates sludge

Slow coagulation

Fast coagulation

φ ↓ marginally as dose ↑

φ ↓ as dose ↑ and pH ↑

NOM and coagulant both influence

NOM and coagulant both influence

sludge

sludge

Slowest coagulation

Fast coagulation

φ ↓ as dose ↑

φ ↓ as dose ↑

pH < 6.0

pH > 6.0

A plot of [OH–]added/[Al] shows that the rapid coagulation threshold lies around pH 6.0 for the higher doses (see §3▪2▪4▪1), consistent with the delineation here.

324



100 0.05

Dose [mg(Al)/L]

0.03

0.04

10

0.05

0.06 0.07 0.08 0.09

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 5-10: Contour plot of solidosity, φ, at py = 50kPa for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. The co-ordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines.

Figure 5-11 and Figure 5-12 depict the variation of φ as a function of coagulant dose and

coagulation pH for fixed values of R:

5×1010Pa.s/m2 (corresponding to settling) and

1×1014Pa.s/m2 (corresponding to filtration), respectively. At the lower end of the R(φ) curve, increases in dose tend to shift the curve to lower values of φ (undesirable) until a minimum is reached; further increases in dose result in a partial reversal to somewhat higher values of φ. In general the contours are horizontal, indicating relative insensitivity to pH.


325

D. I. VERRELLI

100

0.00175 0.00175

Dose [mg(Al)/L]

0.00150

0.00100 0.00125

10

0.00125

0.00150 0.00175 0.00200 0.00225 0.00250

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 5-11: Contour plot of solidosity, φ, at R = 5×1010Pa.s/m2 for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. The co-ordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines.

At the upper end of the R(φ) curve, broadly similar behaviour is observed, although the lowdose, low-pH sludge could not be plotted. Here there is a stronger trend for φ to decrease as pH increases.

326



Dose [mg(Al)/L]

100

0.05

0.04

0.04

0.05

10 0.03

0.05 0.03 0.06 0.07 0.08 0.09 0.10

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 5-12: Contour plot of solidosity, φ, at R = 1×1014Pa.s/m2 for laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. The co-ordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines.

For both sets of data a minimum (undesirable) appears at moderate dose, 5 to 10mg(Al)/L, at a fixed pH of 6.0. It is not clear why this should appear, except that it is most likely to arise where there is a transition between one dominant mechanism and another. A similar feature can be made out in φg (Figure 5-9). Solubility effects may be expected to dominate the lowdose and extreme-pH behaviour; the influence of NOM on the sludge properties is expected to become negligible at high coagulant dose: the transition between these regimes may manifest as a local minimum. Finally, it may be observed that for a fixed pH of 6, the


327

D. I. VERRELLI

nominal hydrolysis ratio (§3▪2▪4▪1) indicates a transition to fast coagulation approaching the highest doses.

100

12

8

Dose [mg(Al)/L]

12

10 20

16

20

12

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure 5-13:

Contour plot of hindered settling function, R, [1013 Pa.s/m2] at py = 50kPa for

laboratory-generated alum sludges as a function of coagulant dose and coagulation pH. The coordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines.

Having considered the hindered settling curves in isolation, it is of interest to consider the value of R for a fixed value of applied pressure. This is, interpreted as py, and so the corresponding value of R may be understood as the equilibrium cake (or bed) resistance, e.g. at the face of a permeable membrane.

328



Only a single value of py, 50kPa, is selected (this can be directly compared with Figure 5-10). The data do not permit a low (settling range) value to be used. The data are more sparse than the other plots, and furthermore the underlying spot values (not shown) exhibit much greater scatter. No obvious trends can be identified.

Overall the first four contour plots show: • greater variation in properties at low dose, i.e. <10mg(Al)/L, with o lower py and R at decreasing doses, and o insensitivity to pH;

• less variation in properties at intermediate and high doses, with o weak tendency for R to decrease again (from a maximum) with increasing dose, o a strong tendency for both py and R to increase with pH increasing above 6, and o a weak tendency for py to decrease but R to increase with pH decreasing below 6.

The best dewatering behaviour is thus found at low dose. This is the sludge most likely to be dominated by the natural constituents of the raw water.

(It is also the sludge whose

generation conditions most closely match those of the plant — see §5▪6▪1.) Although no sensitivity to pH was identified at the lowest doses, operational constraints will likely determine this property, in particular the high solubility of Al at pH values much different from 6. The worst dewatering behaviour is found at high dose and high pH.

The final contour plot, which does not show any simple trend, demonstrates the danger of drawing conclusions based on R(φ) in situations where R(py) may be more relevant.


329

D. I. VERRELLI

5▪6

Alum sludges: comparison with plant and pilot plant data

5▪6▪1

Winneke WTP

In each of the graphs presented already in this chapter, a sludge collected from Winneke WTP was plotted for comparison purposes. Another sample, collected on a different date, was described in §3▪5▪4, and had very similar dewaterability. These materials were both produced at low coagulant dose with pH ≈ 6, so that comparison to similar laboratory sludges is best seen in Figure 5-1 and Figure 5-2. From the preceding discussion it is expected that sludge generated under these conditions would have good dewatering characteristics. It is seen that the expectation is fulfilled, with the plant material properties generally being slightly inferior to the 1.5mg(Al)/L sludge and similar to the 4.0mg(Al)/L sludge, except for R(φ) at low φ, where it exhibited the fastest kinetics of all.

The plant sludge is therefore consistent with the previously identified trends.

Minor

deviations could be due to polymer conditioning at the plant, as well as temporal variation in raw water quality.

5▪6▪2

Happy Valley pilot plant

Alum sludge was obtained from pilot plant trials undertaken in Happy Valley, South Australia. In general these sludges were generated under as similar conditions as could be maintained in practice, with the adjusted variable of interest being the coagulant dose. This varied by a factor of approximately half a decade, from 6 to 19mg(Al)/L. Further details are presented in Table 5-3. It can be seen that the pH was not held perfectly constant. There is also a greater range of variability in the quality of the treated water than for the laboratory samples.

330



Table 5-3: Generation conditions for Happy Valley pilot plant sludge samples.

Sample

High dose

Medium dose

Low dose

Happy Valley

Happy Valley

Happy Valley

2005-05-23

2005-05-11

2005-06-14

26

41

29

Raw water properties Raw water source and date True colour

[mg/L Pt units]

A254nm a

[10/m]

2.15

2.51

1.90

Turbidity

[NTU]

6.9

6.1

15

19

13

6

6.1±0.1

6.4±0.2

7.0

Coagulation conditions Dose pH

[mg(Al)/L] [–]

Polymer and dose

Magnafloc LT-22 Magnafloc LT-22 Magnafloc LT-22 [mg/L]

0.11

0.11

0.11

[mg/L Pt units]

2.7

4.6 b

6.0

A254nm a

[10/m]

0.51

0.65 b

0.79

Turbidity

[NTU]

0.13

0.12 b

0.61

Supernatant properties True colour

Notes b

a

These measurements were carried out on site and reported in units of 100/m.

Measurements on the supernatant of the received sludge gave: true colour = 9mg/L Pt units;

A254nm = 0.14 ×10/m; turbidity = 1.4NTU.

Results are shown in Figure 5-14 and Figure 5-15.

5▪6 : Alum sludges: comparison with plant and pilot plant data

331

D. I. VERRELLI


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 19 mg(Al)/L , pH ~ 6.1 13 mg(Al)/L , pH ~ 6.4 6 mg(Al)/L , pH ~ 7.0

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-14: Variation in compressive yield stress with coagulant dose for various Happy Valley alum pilot plant sludges.

The key conclusions reached based on earlier laboratory work are strongly supported by the compressive yield stress data in Figure 5-14, namely: • Dewaterability improves (py and R decrease) with decreasing coagulant dose, as the material removed from the raw water (NOM, turbidity) comes to dominate behaviour. • Beyond a certain coagulant dose — 10mg(Al)/L, say — the coagulant precipitate dominates equilibrium behaviour, and further increases in coagulant dose have little effect.

332



2


1.E+15

1.E+14

1.E+13

1.E+12

1.E+11

1.E+10

19 mg(Al)/L , pH ~ 6.1 13 mg(Al)/L , pH ~ 6.4 6 mg(Al)/L , pH ~ 7.0

1.E+09 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-15: Variation in hindered settling function with coagulant dose for various Happy Valley alum pilot plant sludges.

The hindered settling function data in Figure 5-15 does not show a clear monotonic trend, but this too is precisely in line with previous findings for laboratory sludges, where the dewaterability enhancements with decreasing dose were not as significant, and there were instances of the resistance actually seeming to decrease again at quite high coagulant doses.

Note that although the coagulation pH was not truly constant for the three trials, it is assessed as not significantly affecting the dewatering of the sludges presented here. The reasoning for this is that the variation in pH is not too large, and moreover an i n c r e a s e in pH would normally be associated with a d e c r e a s e in dewaterability (the opposite of what

5▪6 : Alum sludges: comparison with plant and pilot plant data

333

D. I. VERRELLI

is seen here).

In terms of sludge dewatering properties, any effect of the pH here is

dominated by the coagulant dose effect.

All of these samples had 0.11mg/L of Magnafloc LT-22 * flocculant added. This indicates that the effects of altering the coagulant dose (or, potentially, the pH) to generate a different kind of sludge cannot readily be eliminated through the addition of a small amount of flocculant.

5▪6▪3

Other plants

A number of plant alum sludges in Australia and the U.K. have been characterised by other researchers † working on the same project, and using largely the same characterisation techniques [976]. These indicate that the laboratory-generated sludges cover approximately the same range of dewatering properties as sludges from full-scale plants. It is difficult to make more precise comparisons due to lack of consistency in estimation of ρS (see §4▪1▪3▪2) and the prevailing plant conditions. It is often difficult to assign an identified variation in dewaterability to an individual plant processing condition, due to non-systematic variation between samples, and moreover the plant processing conditions are often not fully known (e.g. the sludge’s shear history — see Chapter 7).

Characterisations were also performed using a slightly different technique by WANG and colleagues circa 1992 [880, 1097], and the data exhibit behaviour consistent with that found in the present work — compare Figure 5-18 and Figure 9-22 — albeit that the caveat with respect to ρS applies here too (their measured solid phase densities are included in Table 4-7; those for the alum sludges appear slightly low). KWON’s (1995) filtration permeability and compressibility data for a WTP sludge [1036] are comparable to that of the present work. This sludge was obtained from a plant in Busan,

*

Manufactured by Ciba Specialty Chemicals and described as a “high molecular weight cationic polyacrylamide” [35]. It is understood to have a low charge density.

†

ANNA TAYLOR (YW); MARTIN R. TILLOTSON (YW); RENE D. FROST (UU); NEVILLE J. ANDERSON (CSIRO); PETER J. HARBOUR (CSIRO); and ANTHONY D. STICKLAND (The University of Melbourne) [976].

334



Korea, treating raw water of 8 to 15NTU turbidity and 4 to 6mg/L TSS with “15 to 20ppm” PACl * at pH ≈ 6.7 [615]. The sludge contained 7.2%m Al, 2.0%m Fe, and 3.0%m Mn on a dry basis [615]. The data of KOS & ADRIAN (1975) [598] are also comparable — see Figure 9-20 and Figure 9-21 — albeit for an alum sludge dosed with powdered activated carbon (cf. §8▪3).

5▪7

Ferric sludges: variation of dose and pH

After identifying a number of interesting relationships between the treatment conditions and alum sludge dewaterability, it is of interest to investigate whether the same trends are also true of ferric sludges.

5▪7▪1

Experimental

Six ferric sludges were generated in the laboratory and contrasted with two plant samples obtained from Macarthur WFP (§3▪2▪6▪2). Details of these samples are presented in Table 5-4.

*

Probably equivalent to ~1mg(Al)/L, based on a typical liquid PACl concentration of ~5%m Al [161, 1085, 1140, 1141] [cf. 430].

5▪7 : Ferric sludges: variation of dose and pH

335

336

[10/m]

5.1 2.84 No

5.6

0.83

No

[–]


Polymer

pH

[mg(Al)/L]

Dose

160

[mg(Al)/L]

set pH

5.0

0.56

0.56

~4

7

~4

Optimum dose at

A254nm

[mg/L Pt units]

2004-08-18

Winneke

7

2004-08-18

and date

True colour

Winneke

Lab. 5.0|5.6 Lab. 160|5.1

Raw water source

Sample


No

2.96

7.3

80

–

0.57

9

2004-09-15

Winneke

Lab. 80|7.3

No

2.84

6.1

80

–

0.57

9

2004-09-15

Winneke

Lab. 80|6.1

No

2.78

5.6

80

–

0.57

9

2004-09-15

Winneke

Lab. 80|5.6

No

2.46

6.6

8.5

~10

1.17

24

2005-11-16

Winneke

Yes

–

9.0

1.5

–

–

8

2005-03-23

Macarthur

Yes

–

8.6 to 8.7

2.2

–

–

12

2005-09-21

Macarthur

Lab. 8.5|6.6 Plant 1.5|9.0 Plant 2.2|8.7

D. I. VERRELLI

Table 5-4: Generation conditions for ferric sludge samples.


5▪7▪2


Dewaterability results are presented in Figure 5-16 (py) and Figure 5-17 (R).

Before examining the behaviour in detail, it is apposite to comment on the most striking feature of the two graphs, and that is the similarity between the samples, and especially between the laboratory samples.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2

mg(Fe)/L

Lab. 160 5.1 Lab. 80 7.3 Lab. 80 6.1 Lab. 80 5.6 Lab. 8.5 6.6 Lab. 5.0 5.6 Plant 2.2 8.7 Plant 1.5 9.0

1.E-3 1.E-4 1.E-5 1.E-3

pH

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-16: Compressive yield stress for laboratory-generated and plant ferric sludges. The leftmost curve is for the 80mg(Fe)/L pH 5.6 sample.


337

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 mg(Fe)/L 1.E+10

Lab. 160 5.1 Lab. 80 7.3 Lab. 80 6.1 Lab. 80 5.6 Lab. 8.5 6.6 Lab. 5.0 5.6 Plant 2.2 8.7 Plant 1.5 9.0

1.E+09 1.E+08 1.E-4

pH

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-17: Hindered settling function for laboratory-generated and plant ferric sludges.

There is less variability than was seen for the alum sludges, and there are two likely causes: • the range of generation condition combinations assessed was narrower in absolute terms for the ferric sludges than for the alum sludges (i.e. less a b s o l u t e variation in inputs); and • the solubility envelope is much wider for Fe(III) than for Al, and so ferric coagulation is less sensitive to either pH [see also 1124] or dose (i.e. less r e l a t i v e variation in inputs).

338



Now considering the individual curves, it can be seen that a few behave alike, and these have been plotted using the same line style (but different point symbols). These categories can be generalised as: • high-coagulant-dose laboratory sludges — at least 80mg(Fe)/L; • low-coagulant-dose laboratory sludges — less than 10mg(Fe)/L; and • plant sludges — dose ~ 2mg(Fe)/L and pH ~ 9.

This suggests strongly that coagulant dose is the dominant influence on the dewaterability of ferric sludges.

In terms of application, it would be most desirable to operate at low

coagulant dose, which is the same recommendation as for alum coagulation.

The curves for the three 80mg(Fe)/L sludges are almost identical, again indicating insensitivity to pH. The only significant deviation is the lowest pH sample, for which a lower gel point is estimated, however this on its own is inconclusive.

Indeed the

160mg(Fe)/L sample has a lower pH again, but a higher estimated gel point. It may be noted that despite the possibility of density variation with pH (cf. §4▪3), a fixed value, ρS = 4000kg/m3, was used for all of the high-dose ferric sludges. If the value of ρS were actually greater for the low-pH sludges, then replotting the curves would suggest that those low-pH sludges had inferior dewatering properties (cf. Figure 4-1 and Figure 4-2) — a different conclusion to that reached for alum sludges.

The sludge coagulated at 160mg(Fe)/L and pH 5.1 exhibits superior equilibrium dewatering to the three 80mg(Fe)/L sludges. This material was very difficult to settle fully, with many extremely fine ‘pin flocs’ being formed. It may be hypothesised that under such conditions the flocs form slowly, with greater ordering, and with a smaller final particle size. It may be expected that such flocs would compact to a bed or filter cake of higher density for a given applied particle pressure. It appears that pH (linked with solubility) was the dominant effect in controlling the form of the flocs here, given that the coagulant dose and hydrolysis ratio are both reasonably high (Table 5-4). Given the stated difficulty in attaining complete settlement of the sludge coagulated at 160mg(Fe)/L and pH 5.1, it is rather surprising that this material did not exhibit vastly


339

D. I. VERRELLI

inferior permeability. In fact, its permeability in settling cannot be distinguished from the other laboratory sludges, and was no worse (if not better) than the other high-dose sludges at high solidosity. Two factors that may be relevant to this result are that the material was here characterised above its gel point, and the material in the sub-sample is also that portion of the sludge which d i d settle more rapidly than the persistently suspended ‘pin flocs’.

The two ‘low’ dose laboratory sludges display almost identical behaviour in dewatering. A particular advantage over the ‘high’ dose samples is seen at high solidosities, which reduces as φ decreases. This suggests that at large lengthscales the aggregates are similar, but are different at small lengthscales. The fine structure forms through a perikinetic mechanism, and (nano)crystallite morphology may have a significant influence.

The larger structure is expected to form through an

orthokinetic mechanism (and perhaps differential sedimentation). Although the chemical conditions are different, it may be that in orthokinetic coagulation these are less important to how the structure develops.

The two plant sludges are discussed in the following section.

5▪7▪3

Conclusions

The laboratory ferric sludges exhibit less variability in their dewatering properties than the laboratory alum sludges, which is likely due to the low solubility of Fe(III) across a wider pH domain than for Al. This is consistent with the absence of a strong correlation between dewaterability and pH for these sludges. Nevertheless, the same trend of worsening dewaterability with increasing coagulant dose was seen with ferric sludges as had been seen with alum sludges. The published literature strongly supports the finding of a negative association with ferric dose.

The literature overall suggests that high pH should also be detrimental to the

dewaterability of ferric sludges, but the effect was not observed in all studies [e.g. 1082]. Some detail may have been lost in the pH comparisons due to the residual uncertainty in ρS.

340



5▪8

Ferric sludges: comparison with plant data

5▪8▪1

Macarthur WFP

Two fresh ferric sludges from Macarthur WFP were characterised, as presented in the previous section. These were found to exhibit significantly better dewatering properties, in terms of both py and R, than the laboratory sludges.

This difference is most likely

attributable to the low coagulant dose at which the sludges were produced, being less than half the lowest laboratory dose. At such doses, the influence of NOM and other raw water constituents becomes important, or even dominant. Therefore it is important to be mindful that the laboratory and plant sludges plotted in Figure 5-16 and Figure 5-17 were obtained using d i f f e r e n t raw water sources (unlike for the alum sludges). The plant sludges were also produced at much higher pH than the laboratory sludges. Although this may seem significant, three factors suggest that it might not be: 1.

the high-dose laboratory sludges were found to be insensitive to pH;

2.

the two plant sludges were produced at similar pH, but exhibit very different py(φ) curves; and

3.

the solubilities (see Figure 3-3) and hydrolysis ratios (cf. §R1▪2▪6▪3(a)) were not close to any threshold values.

Hence it may be concluded that the favourable behaviour of the plant ferric sludges is due to the influence of the raw water constituents, given that the precipitated coagulant will make up a smaller fraction of the solid mass.

The difference between the two plant sludges themselves is also most likely attributable to seasonal differences in the raw water constituents. Although the plant sample with the lower py(φ) curve had a ferric dose 46% higher than the other plant sludge, the raw water colour was also 50% higher, and likely comprised NOM of a different character (spring versus autumn). Following on from this, it was mentioned in §3▪2▪6▪2 that the spring sample (Plant 2.2|8.7) was treated with over three times the polyDADMAC dose as the autumn sample (Plant 1.5|9.0).

5▪8 : Ferric sludges: comparison with plant data

341

D. I. VERRELLI

Finally, it may be remarked that the R(φ) curves of the plant ferric sludges neatly overlie one another at high solidosities (i.e. from filtration data). Whatever structural features were differentiating the resistance at lower solidosities — perhaps thin, fragile fractal aggregate layers of precipitated ferrihydrite — appear to have been strained into oblivion as higher stresses are applied [cf. 241, 416, 1040]. Apart from the similarity of the stated generation conditions, there is no obvious reason why this should be so, given the differing behaviours at low solidosity and in py(φ).

5▪8▪2

Other plants

The above variations in ferric sludge dewatering behaviour were not observed by HARBOUR et alia [443]. A good part of the variation depends upon the variation in ρS with ferric dose. The previous work included a somewhat narrower range of coagulant doses (2.4 to 30mg(Fe)/L), and used a different value of ρS. It also was unable to isolate coagulant effects from flocculant and raw water quality effects.

A number of plant ferric sludges in Australia and the U.K. were characterised by other researchers * working on the same project, and using similar characterisation techniques [976]. These indicate that the laboratory-generated sludges cover approximately the same range of dewatering properties as sludges from full-scale plants. It is difficult to make more precise comparisons due to lack of consistency in estimation of ρS (see §4▪1▪3▪2) and the prevailing plant conditions. It is often difficult to assign an identified variation in dewaterability to an individual plant processing condition, due to non-systematic variation between samples, and moreover the plant processing conditions are often not fully known (e.g. the shear history of the sludge — see Chapter 7). Further high-φ dewaterability data computed for (small-scale) ‘plant’ ferric sludges obtained from the treatment of Antarctic tip overflow waters [787] were comparable to those of the plant ferric sludges in the present work.

*

ANNA TAYLOR (YW); MARTIN R. TILLOTSON (YW); RENE D. FROST (UU); NEVILLE J. ANDERSON (CSIRO); and ANTHONY D. STICKLAND (The University of Melbourne) [976].

342



Independent data from WANG et alia [1097] (see §5▪6▪3), is also compatible with the filtration data for plant ferric sludges obtained in the present work.

5▪9 5▪9▪1

Comparison of alum and ferric sludges Compressive yield stress and hindered settling function

A comparison of the dewatering behaviour of alum and ferric WTP sludges is presented in Figure 5-18 and Figure 5-19. This shows overlaid curves indicative of the best and worst

properties identified for laboratory sludges produced from each coagulant type, along with representative plant curves. Of course, this does not cover the complete range of possible coagulation conditions, it covers only those characterised in the present work — although these do include the typical range of full scale conditions.

It can be seen that the py(φ) and R(φ) curves for a range of representative alum and ferric sludge samples substantially overlay one another. This result is at odds with the conclusions reached by Harbour et al. [443], and is attributed to the greater degree of control exercised here over the coagulation conditions, and the more accurate values used for ρS.

The key feature distinguishing the dewatering characteristics of alum and ferric sludges is the larger degree of variation observed for the alum sludges generated for the present work, which is consistent with both anecdotal industrial experience and the solubility properties of the two metals. Still, when more extreme doses or pH values are considered, as for the plant sludges, the variation is substantial for both coagulant types.

In general the ferric sludges are seen to behave like an ‘average’ alum sludge. A single plant ferric sludge exhibits significantly lower py and R — however this is an exceptional sample, and cannot be considered conclusive.

5▪9 : Comparison of alum and ferric sludges

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D. I. VERRELLI


1.E+3 1.E+2 1.E+1 1.E+0 Poor lab. alum — 80 , 8.6 Poor lab. ferric — 80 , 5.6 Good lab. ferric — 5.0 , 5.6 Good lab. alum — 1.5 , 6.0 Plant alum — 1.9 , 6.1 Plant ferric — 2.2 , 8.7 Plant ferric — 1.5 , 9.0

1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-18: Comparison of compressive yield stress for alum and ferric sludges. The numbers shown in the legend are the coagulant dose and coagulation pH.

A fair comparison of the two coagulant types would contrast the properties of the sludges obtained from industrially practicable coagulation conditions when a given supernatant quality target is attained for a certain raw water. In the present work adequate quality was achieved in terms of true colour *, however many other quality parameters were not monitored. Certain pH conditions may not be practical on

*

True colour in the s u p e r n a t a n t was reduced to ≤ 2mg/L Pt units for a l l of the laboratory treatments conducted in the present work, with the e x c e p t i o n of the a l u m treatments with coagulation p H > 8 (3 to 10mg/L Pt units) and the m a g n e s i u m sludge (3mg/L Pt units). Similarly, these supernatants had A254nm ( 0.3×10/m except for the treatments with low alum dose at pH ≈ 8.4 (~0.5×10/m and ~0.7×10/m).

344



a full scale plant due to issues including cost, corrosion, and metal solubility or leaching. Coagulant doses in many cases were far higher than the estimated ‘optimum’. Finally, on a real plant the coagulation conditions would be interlinked with flocculation conditions, clarifier operation, et cetera [cf. 754].

Hindered settling function, R [Pa.s/m2]

1.E+15 1.E+14 1.E+13 1.E+12 Poor lab. alum — 80 , 8.6 Poor lab. ferric — 80 , 5.6 Good lab. ferric — 5.0 , 5.6 Good lab. alum — 1.5 , 6.0 Plant alum — 1.9 , 6.1 Plant ferric — 2.2 , 8.7 Plant ferric — 1.5 , 9.0

1.E+11 1.E+10 1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-19: Comparison of hindered settling function for alum and ferric sludges. The numbers shown in the legend are the coagulant dose and coagulation pH.

5▪9▪2

DARCY’s law permeability, KD

To facilitate comparison with other published literature, and illustrate the practical equivalence of KD and R, Figure 5-19 is recast in terms of the DARCY’s law permeability, KD


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D. I. VERRELLI

(§2▪3▪1), using equation 2-121. Although the viscosity is almost certainly ηL ≈ 1mPa.s, to minimise assumptions the quotient KD / ηL is plotted in Figure 5-20.

Permeability over viscosity, K D/η L [m2/Pa.s]

1.E-05 Poor lab. alum — 80 , 8.6 Poor lab. ferric — 80 , 5.6 Good lab. ferric — 5.0 , 5.6 Good lab. alum — 1.5 , 6.0 Plant alum — 1.9 , 6.1 Plant ferric — 2.2 , 8.7 Plant ferric — 1.5 , 9.0

1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 1.E-12 1.E-13 1.E-14 1.E-15 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-20: Comparison of KD / ηL for alum and ferric sludges. Data of Figure 5-19.

5▪9▪3

Solids diffusivity

It has been popular among some authors recently to present their dewaterability characterisations in terms of the solids diffusivity, D [e.g. 443, 444, 787, 974, 976]. In order to facilitate comparison, the solids diffusivity is presented now for the same materials given in the preceding sub-section.

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Figure 5-21 shows the solids diffusivity plotted according to two calculations. The first

utilises the formula defining D, which requires the derivative of py. This was obtained analytically based on the functional fit output by B-SAMS following analysis of combined gravity settling and filtration data. Unfortunately the global py(φ) functions do not always fit the filtration data well locally. Hence the second calculation involved fitting the filtration data only. It was found that the most robust means of doing this was by fitting a power law to the variable dV 2/dt :c.f. as a function of φ∞, and then applying equation 2-136. Power-law fits to the py(φ∞) filtration data were concordant.

1.E-06

Solids diffusivity, D [m2/s]

1.E-07

1.E-08

Poor lab. alum — 80 , 8.6 Poor lab. ferric — 80 , 5.6 Good lab. ferric — 5.0 , 5.6 Good lab. alum — 1.5 , 6.0 Plant alum — 1.9 , 6.1 Plant ferric — 2.2 , 8.7 Plant ferric — 1.5 , 9.0

1.E-09

1.E-10

1.E-11

1.E-12 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-21: Comparison of solids diffusivity for alum and ferric sludges — full curves on log–log scale. The numbers shown in the legend are the coagulant dose and coagulation pH.


347

D. I. VERRELLI

2 Solids diffusivity, D [m /s]

1.E-07


1.E-08

1.E-09 0.00

0.05

0.10

0.15

0.20

0.25

Solidosity, φ [–] Figure 5-22: Comparison of solids diffusivity for alum and ferric sludges — filtration data only on log–linear scale. The numbers shown in the legend are the coagulant dose and coagulation pH.

These solids diffusivities based on filtration data only are also plotted alone in Figure 5-22 on log–linear co-ordinates, for ready comparison with other literature.

Inspecting firstly individual materials in Figure 5-21, it can be seen that in general there is agreement between the curves and the points, at least on the scale shown. A couple of curves do deviate at the highest solidosity, and others fluctuate in a physically unrealistic manner. As implied earlier, the plotted points should be taken as the true behaviour at high solidosity.

348



Now contrasting the various materials one with another, it can be seen that the shapes and trends of the curves are not all the same.

Specifically:

some curves exhibit an initial

maximum in D, followed by a decrease; others suggest monotonic increase of D with φ; and still other curves are intermediate in nature, appearing to increase steadily to a plateau. §S10▪2 illustrates that the shape of the D (φ) curve is strongly affected by the form of curve fit chosen for py(φ) and R(φ), and especially to the interpolation used between the settling data and the filtration data. Focussing on only the filtration data points in Figure 5-22, there is likewise no consistent trend across all materials, with some decreasing, others increasing, and still others remaining roughly constant. If anything, the common link between the most strongly decreasing D (φ) data sets is that they arise at the lowest solidosities and — consistent with that — tend to be labelled as ‘poorly dewaterable’. Despite that tag, the same materials also have the highest magnitudes of D, which is typically interpreted in the literature as synonymous with favourable (i.e. fast) dewatering kinetics. The reason for the correlation between low solidosity (hence ‘poor’ equilibrium dewatering) and high solids diffusivity (supposedly ‘good’ dewatering kinetics) is apparent from the definition of D (equation 2-63), which requires the derivative of py. Consulting Figure 5-18 it seems prima facie that the slopes of all curves in the range corresponding to filtration are roughly the same; this is not correct. Remember that the data has been presented on log–log co-ordinates, and so the gradient of the curves toward the right of the graph (i.e. at higher solidosity) is actually significantly lower. This is easily demonstrated by considering the change in compressive yield stress associated with each curve for an increase in solidosity from 0.02 to 0.05: Δφ is then constant, while Δpy varies from ~2.26kPa to ~258kPa, which is two orders of magnitude difference!

Even larger differences in gradient pertain as the

solidosity is decreased. This overwhelms the generally larger R values associated with the “poor” sludges, which would conventionally be expected to yield lower D values. Moreover, simple interpolation of R(φ) for the “poor” laboratory alum sludge, say, results in a curve that actually undercuts some of the other curves at intermediate solidosities, leading to a twofold boost in the value of D here.


349

D. I. VERRELLI

The perplexing nature of D (φ) is best illustrated by comparing the relative positions of the two plant ferric sludges and the “good” laboratory ferric sludge in Figure 5-21 and Figure 5-22 (D ) in contrast to their positions in Figure 5-18 (py) and Figure 5-19 (R) in the previous

sub-section. The py(φ) and R(φ) curves consistently show both plant sludges performing better than the “good” laboratory sludge across all measured solidosities in both extent and rate of dewatering. Yet the solids diffusivity curves would seem to imply that above the low solidosities corresponding to gravity settling — i.e. for φ T 0.01, relevant to centrifugation and filtration — the “good” laboratory ferric sludge is intermediate in behaviour to the two plant sludges! It is sometimes stated or implied in the literature that the relative positions of the D (φ) points extracted from filtration experiments summarise the dewaterability of the materials, or at least their ‘filterability’. On this basis Figure 5-22 would imply that the two plant ferric sludges would behave very differently in filtration, with the “good” laboratory sludge lying intermediate: the filtration throughput predictions based on this data presented in §S13▪5, however, show this to be entirely false.

The foregoing exemplifies the dangers of inferring qualitative dewaterability information based solely on D (φ) curves, and especially based on D (φ) from filtration data only. (The latter is almost as parlous as the much-criticised [e.g. 651, 976] ‘single point’ empirical characterisations.)

It is emphasised that, for any dewaterability characterisation,

comparison, or prediction, a p a i r of parameters m u s t be used, chosen from py(φ), R(φ), and D (φ) [cf. 105, 787]. Which two are selected is not of theoretical import, but in practice can have a bearing on accuracy (due to the need for extra numerical differentiation, say) or intuitive interpretability.

This is actually implicit in statements such as “the solids

diffusivities lie further to the left”, which assumes that the data for the materials being compared were calculated at their respective equilibrium solidosities corresponding to the same p r e s s u r e ;

i.e. the solids diffusivity is routinely t a c i t l y treated as if it is

parameterised by the compressive yield stress [e.g. 443, 444, 976]. (Although experimentally this may be a practical interpretation, it does not arise from any fundamental grounds.)

350



The statement that D (φ), on its own, conveniently summarises dewaterability [e.g. 443, 444, 976] [cf. 975] is seen to be false in general.

5▪10 Industrial implications Results from the foregoing characterisations can be used directly in optimising the treatment operation with respect to sludge production — i.e. maximising the quality and minimising the quantity of sludge. Of course, the range of options available is constrained by the requirement to assure the quality of the treated water. Such optimisation could commence simply with the trends, which yield the knowledge that higher doses are to be avoided, where possible.

Additionally, high pH values are

problematic for alum sludges — if high pH is desirable in consideration of the product drinking water quality, then perhaps ferric coagulation should be adopted (as at Macarthur WFP).

Aside from simply considering the qualitative trends, it is possible to use the py(φ) and R(φ) data as inputs to models of the sludge dewatering unit operations, in order to obtain quantitative predictions that are of use in both operation and design [e.g. 973, 974]. Many operations may be satisfactorily modelled, including settling, thickening, and filtration — with the assumption that dewatering proceeds in one dimension. A presentation of an application of the alum sludge data to filter press modelling is made in §S13, to illustrate the analysis. Further, the predictions then allow treatment conditions to be correlated with throughput, rather than the material properties. This is advantageous for two reasons: it is of more immediate interest to WTP operators and designers; and it is a convenient summary of the c o m b i n e d influences of py(φ) and R(φ), for the given material and dewatering operation.

A detailed investigation of filter press modelling that uses parameter estimates from the present work is presented in Appendix S13, illustrating the use of py(φ) and R(φ) data as model inputs. The results are conveniently expressed in terms of throughput (volumetric solids flux, φ0 Q).

5▪10 : Industrial implications

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D. I. VERRELLI

An advantage of this approach is that a concrete measure of the difference in dewaterability for a number of sludges can be obtained.

The disadvantages are the additional effort

required for modelling, the possibility of magnifying or introducing errors (due to sensitivity to uncertainties in the input parameters, or due to numerical issues with the model implementation), and the decrease in generality. Throughput results generally reflected conclusions reached earlier by comparing py(φ) and R(φ) curves. However, sensitivity was observed to the estimated gel point, and to small mismatches between smoothed and interpolated B-SAMS parameter curves and the experimental data points. In some cases it will be worthwhile to finesse the curve fits offered by B-SAMS (see §S13▪7). The results also confirmed that industrial WTP filtration operations tend to be limited by the kinetics, as quantified by R(φ) with φ → φ∞, rather than the equilibrium state, quantified by py(φ∞).

Nevertheless, membrane resistance did not significantly affect the r e l a t i v e

dewaterability of different sludges.

5▪11 Magnesium sludge Use of magnesium as a coagulant in water treatment was encouraged several decades ago, and research seemed promising. Some reports in the literature did suggest problems with sludge dewaterability, however. A brief investigation using magnesium as a coagulant seeks to test the claims of magnesium dewaterability. Beyond this, it is hoped that this research will identify any major effects arising from the lower valency (+2) of this metal species.

Use of magnesium species as coagulants was promoted by a number of workers in the 1970’s, chief among them A. P. BLACK [e.g. 156, 1022], with the potential to recycle the coagulant under certain circumstances seen as a major advantage. Although not taken up enthusiastically by industry, development has continued slowly: more recently papers have been published on water treatment [166, 711] and wastewater or effluent [916, 1001] treatment. Where the early work emphasised the use of magnesium carbonates, oxides and hydroxides [156], magnesium chloride (MgCl2) may also be used [166, 1001].

352


An advantage of


magnesium chloride is that it is highly soluble in water, allowing stock solutions to be made up in the same way as for ferric and alum coagulants in the present work. In order to precipitate the magnesium species so that it can have a coagulating effect it is necessary to add alkali until quite a high pH is reached — a key difference from the case of alum or ferric coagulants is that the MgCl2 solution is not very acidic, and alkali addition results in a much higher pH for this case.

The published literature indicates that the

optimum coagulation pH lies between 11.0 and 11.5 [166, 251, 711, 916, 997, 1020, 1022].

A typical dose for water treatment is likely to be of order 1 to 10mg(Mg)/L [251, 997, 1022], however doses up to 100mg(Mg)/L have been reported [711]. For effluent treatment doses as high as 1000mg(Mg)/L have been reported [1001].

5▪11▪1 Experimental In order to ensure the generation of a sufficient quantity of sludge, a high dose of 80mg(Mg)/L was selected. (On a mass basis this is equal to the uppermost doses generally used in the present work for aluminium and iron coagulation, but note that the lower relative molecular mass of magnesium means that the corresponding dose on a molar basis is higher than for iron, although still similar to that of aluminium.) The target pH was chosen to be 11.0, as this was deemed more practical than pH 11.5, and also safer. The actual experimental pH was 10.9. It was anticipated that the above dose would be high enough for the precipitated magnesium species to make up the bulk of the sludge, and to dominate the dewatering behaviour. Although it was expected that the majority of added magnesium ions would precipitate out of solution at this pH, subsequent tests of the supernatant indicated that approximately 53mg(Mg)/L remained in solution. There were no indications that the assay * was grossly in error, and a possible explanation for the high residual concentration is that magnesium’s comparatively slow precipitation kinetics may have meant that pH continued to decrease even after completion of the slow-mix and settling phases, so that either a significant

*

Titration with EDTA disodium salt using calmagite indicator at pH ~ 10, as per the U.S. Standard Methods [334].

5▪11 : Magnesium sludge

353

D. I. VERRELLI

proportion of dissolved magnesium was not induced to precipitate or else some precipitated magnesium redissolved — the latter would be more difficult to account for. Although the measurement is at variance with equilibrium predictions, it is consistent with the practical experimental results obtained by THOMPSON, SINGLEY & BLACK [1022] (Figure R1-2).

Details of the raw water quality and other parameters for the magnesium sludge generation are summarised in Table 5-5.

Also shown are the details for two alum sludges

representative of the range of typical behaviour of laboratory-generated sludges.

Table 5-5: Generation conditions for sludge samples used in batch centrifugation.


Magnesium

Low alum

High alum

Winneke

Winneke

Winneke

2006-01-05

2004-05-11

2004-05-21

15

19

14

0.82

1.07

0.87

80

1.5

80

10.9

6.0

8.6


[10/m]

Dose

[mg(M)/L]

pH

[–]

5▪11▪2 Results The magnesium sludge was characterised according to the usual methodology, and its dewatering properties are shown in Figure 5-23 and Figure 5-24. It was found to behave much like a low-dose alum sludge.

354




1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 1.E-4

80mg(Mg)/L, pH 10.9 1.5mg(Al)/L, pH 6.0 80mg(Al)/L, pH 8.6

1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-23: Compressive yield stress of a magnesium sludge (nominal conditions quoted — see discussion in text) compared to the range of typical laboratory alum sludge behaviour.


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D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 80mg(Mg)/L, pH 10.9 1.5mg(Al)/L, pH 6.0 80mg(Al)/L, pH 8.6

1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 5-24: Hindered settling function of a magnesium sludge (nominal conditions quoted — see discussion in text) compared to the range of typical laboratory alum sludge behaviour.

5▪11▪3 Discussion If the behaviour of this magnesium sludge had been different to any alum sludge previously characterised, then some interesting conclusions could be drawn. As this one sample lies within the envelope of behaviour observed for other coagulants, it cannot be concluded that magnesium sludges are generally any more or any less easy to dewater. To make more definite statements in this direction would require a substantial experimental effort to characterise a range of magnesium sludges produced under a range of dose and pH conditions (as has been done for alum and ferric sludges in the present work). The analysis

356



is also somewhat complicated by the effective magnesium dose apparently being considerably lower than the nominal dose of 80mg(Mg)/L (nevertheless, even a dose of 30mg(Mg)/L can be considered ‘high’ for the raw water used here).

The conclusion that can be drawn from this brief investigation is that the difference in behaviour between magnesium and alum sludges (and ferric sludges, for that matter) appears n o t to be large, and this contradicts literature statements [227, 879, 911] that dewatering magnesium sludges (or sludges containing high levels of magnesium) is especially problematic. Indeed magnesium’s inherently slower rate of precipitation may be expected to give rise to more compact aggregates (higher fractal dimension), with potential dewatering advantages. This accords with the positive reports on magnesium sludge properties that have appeared [e.g. 251, 916, 1022].

5▪11▪4 Conclusions The high-dose magnesium sludge generated behaved very similarly to a low-dose, pH 6 alum sludge, with favourable dewatering properties. The results prove that magnesium sludges are not especially difficult to dewater, relative to other coagulant sludges, as claimed by some writers. Alum and ferric sludges exhibit improvements in dewatering at lower doses, and this may also be true for magnesium sludges. If there is an improvement relative to alum and ferric sludges, it may be due to the slower kinetics of the magnesium coagulation process.


357

6.

EFFECT OF RAW WATER QUALITY At any one [water treatment] works, sludge quality will vary seasonally and possibly even daily. — DILLON (1997) [315] [see also 618]

Natural fluctuations in raw water quality can cause large changes in the consistency of WTP sludge produced [315, 1023] through changes in the size, morphology, and strength of the underlying aggregate or floc structure [524]. It is tempting to assume that if raw water of high colour and/or dissolved organic carbon (DOC) — and low turbidity — is difficult to treat, then the resultant sludge will likewise be difficult to dewater. Leaving aside for a moment the likelihood that such problematic water would require higher coagulant doses (and the consequent effects on dewaterability implied by Chapter 5), this is not a necessarily true premise [see 524]. The effect of high levels of colour and DOC in the raw water upon resultant sludge dewatering behaviour was investigated by spiking raw water samples with dialysed MIEX waste brine eluate (henceforth “ d M I E X ”), as described. Adding this nearly ‘natural’ colour to raw water was deemed to be the best compromise [cf. 569] given the impracticability of procuring large quantities of raw water of naturally high colour (or turbidity). Raw water colour and DOC have been increased for a few samples by spiking with dMIEX.

6▪1

Published observations

A range of experimental studies have variously shown improvements, no change, and degradations in dewaterability of WTP sludges as NOM or TOC levels were increased. This may be due to a balance between incorporating a lower proportion of coagulant and turbidity, and a higher proportion of NOM.

Furthermore, there may be stoichiometric

optima, increases or decreases either side of which would result in poorer dewaterability. Findings of inferior dewaterability were more common. 359

D. I. VERRELLI

6▪1▪1

NOM is beneficial

VILGÉ-RITTER et alia [1082] found that the presence of NOM significantly increased the fractal dimension of aggregates formed from ferric chloride. In conditions typical of conventional water treatment, Df was estimated at 2.4 (pH 5.5) and 2.3 (pH 7.5) for a turbid, low-TOC river water, and 2.9 (pH 5.5) and ~2.1 (pH 7.5) for a non-turbid lake water of moderate TOC [1082]. The decrease in Df at higher pH was attributed to adoption of less dense conformations by the NOM due to increased electrostatic repulsion arising from greater deprotonation [1082].

Other studies showed that dense aggregates of aluminium hydroxides (Df ~ 2.3) precipitated in the presence of organic acids were “built by uncondensed monomers” [707, 708], which suggests consideration of a formation process analogous to particle–cluster aggregation (see §R1▪5▪6▪3).

In studies of magnesium coagulation, spiking of ‘natural’ colour “seemed to” increase both the size and settling rate of the aggregates [1021].

6▪1▪2

NOM has no significant effect

PAPAVASILOPOULOS & BACHE [816] reported that aggregates formed by neutralising alum were the same size as aggregates formed by coagulating humic acids, from which they inferred that the strength of the aggregates was unchanged [see also 116].

Detrimental effects of NOM on the sludge properties can be counteracted by preoxidation of the raw water [331, 480].

6▪1▪3

NOM is detrimental

Increasing “natural” colour and decreasing turbidity in the raw water gave decreased values of Df for alum [478], ferric and magnesium sludges — although the coagulant doses were

360

Chapter 6 : Effect of Raw Water Quality


also typically higher than for the clay suspensions [997]. Smaller NOM species were found to inhibit the formation of large aggregates [478].

Coagulation of a model raw water spiked with kaolinite clay and sodium humate showed that for a given ratio of alum to clay, py increased and φg decreased when humate was added [319].

This was attributed to interaction between humate and precipitating aluminium

species; at very low alum:clay ratios the effect of humate is less significant [319]. It was found that humate caused strong decreases in particle surface charge (measured as ζpotential) [319]. The effect of organic species on the formation or transformation of solid Fe and Al phases is detailed in §R1▪2▪5▪3(b) and §R1▪2▪6▪3(d), and summarised in §4▪2▪3; see also §5▪5.

Increased levels of incorporated NOM in alum WTP sludges were found to yield inferior dewatering rates in both settling [107] and filtration; with minor decreases in compressibility [331]. Higher levels of NOM incorporation apparently corresponded to smaller, less dense (lower Df) aggregates for either alum or ferric coagulation [331, 525, 526] [cf. 524] *. (Such systems would presumably have a larger total surface area, allowing more NOM adsorption.) The high-NOM aggregates were also reported to be more prone to breaking up due to exposure to shear [525]. The effects were correlated against the ratio of TOC to Al dose [331].

Trials in Auckland indicated that NOM-rich alum WTP sludges could dewater to only about half the solids concentration as clay-rich sludges did, implying a higher compressive yield stress:

however this was calculated on a mass basis [797].

On a volume basis, the

concentrations (or solidosities) may well have been much more comparable (cf. §4▪1▪2). DILLON [315] indicated that dewatered mass concentrations were quite consistently ~5%m lower for the soft, NOM-rich sludges typically derived from U.K. upland waters [see also

*

Earlier work indicated that the t y p e of NOM present is just as important, with aggregate size exhibiting positive correlation with SUVA254nm (see §R1▪1▪4▪2) [524]. However it did n o t correlate with NOM treatability indicated by maximum DOC removal [524].


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D. I. VERRELLI

1139], which matches the Auckland data in settling, but predicts greater convergence as dewatering progresses.

It should be noted that outside of the enhanced coagulation regime, the level of NOM removal can also vary in turn with pH (or coagulant dose) [331]. Thus, a coagulation pH that is sub-optimal in terms of NOM removal may ipso facto yield a more dewaterable sludge, offsetting or even overwhelming the ‘pure’ pH effect (see §5) [331]! This would be most relevant to high-colour, low-turbidity waters: the difference in mass of NOM removed would need to be significant, while the absolute mass of TSS removed would have to be much the same.

The presence of especially ‘active’ biological matter was reported to decrease the size and settling rate of WTP aggregates [480] [cf. 1139]. The presence of high concentrations of algæ tends to lead to ‘light’ sludges of low solids concentration [161]. The dewatering behaviour of algæ-containing WTP sludges has been found to be greatly affected by ageing: with the possibility of an initial improvement (in rate) due to ‘bio-flocculation’ by polymers exuded by the algæ, followed by a significant deterioration [811].

6▪1▪4

NOM has a mixed effect

While not directly measuring compressive yield stress, the research of HARBOUR, DIXON & SCALES [445] into the effect of NOM upon the shear yield stress, τy, of alumina suspensions is relevant to the present discussion. A trend was observed whereby the pH corresponding to maximum τy shifted from the i.e.p. of alumina to progressively lower values as more NOM was added to the system [445]. Significant effects were observed at relative NOM levels as low as 0.001 (mass of TOC per mass of alumina) [445] — although it must be noted that the specific surface area of the alumina particles (d0 ~ 300nm) would be considerably lower than the specific area of WTP sludge precipitate. τy was most sensitive to charged (and neutral) hydrophilic NOM species, which are more likely to adopt a conformation extending out

362



from the particle surface as a ‘hairy layer’ (the hydrophobic humic and fulvic NOM fractions tend to adopt flatter conformations) [445, 446]. These trends indicate that for coagulation at a given ‘intermediate’ pH (somewhat below the i.e.p. of the bare solid precipitate), increasing the amount of NOM in the system could result first in an increase, and later a decrease in τy. It is reasonable to suppose that a related trend could hold for py, which would provide one explanation for the range of responses reported.

6▪2 6▪2▪1

Experimental Dialysed MIEX eluate (“dMIEX”)

The MIEX eluate was derived from the treatment of Mt. Pleasant raw water (South Australia). This raw water has high turbidity (of order 60NTU), but is prechlorinated, so the true colour (~5mg/L Pt units) and DOC (~4mg(C)/L) are quite low [64, 760]. The MIEX eluate was collected in early April 2004; at this time of year the water is typically difficult to treat by coagulation, with SUVA254nm of order 2 L/mg.m [760].

The MIEX eluate was dialysed to reduce its ionic strength. Tubing from two manufacturers was used: • Viskase Membra-Cel MD25-14 16mm dry diameter, 14000g/mol molecular mass cut-off • Membrane Filtration Products Cellu·Sep T1 29.3mm dry diameter, 3500g/mol molecular mass cut-off The dialysis procedure followed was to dialyse approximately 400mL (small diameter) to 1800mL (large diameter) of MIEX eluate in 4500 to 3000mL (respectively) of purified water over several days with gentle stirring. The dialysis buffer water was replaced several times, until a relatively stable conductivity of around 40mS/m was attained — corresponding to a conductivity in the dialysate (i.e. the “dMIEX”) of around 70mS/m.

The conductivity was reduced by around 2 orders of magnitude; at the same time the DOC of the MIEX eluate also decreased, though only by about 1 order of magnitude, still remaining approximately 2 orders of magnitude above the level in the raw water prior to 6▪2 : Experimental

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D. I. VERRELLI

spiking. Colour and 254nm absorbance values (A254nm) also changed, and hence specific ultraviolet absorbances (SUVA254nm), being the ratio of A254nm to DOC. Details are given in the table below (Table 6-1). Values for undialysed MIEX eluate have a higher uncertainty: this is due to the need to greatly dilute those samples and extrapolate readings. The DOC and (hence) SUVA254nm values for raw water before spiking are also more uncertain due to the difficulty in obtaining an accurate measurement of DOC at the low end of the scale. (Cf. Table 6-2.)

Table 6-1: Change in MIEX eluate properties upon dialysis, and change in ‘raw’ water properties upon spiking with dialysed MIEX eluate to approximately 1.25%V. Values for undialysed MIEX eluate have an uncertainty of around ±20%.

Property

MIEX eluate Undialysed

Winneke raw water 2004-07-05

Dialysed

Before spiking

1.25%V dMIEX

(“dMIEX”) Conductivity

[mS/m]

Spiked with

13000±1000

70

10

11

~4400

560a , 580b

~2.1

10

1060±40

140

0.61

2.44

SUVA254nm [L/mg(C).m]

~2.3 to 2.5

2.5a , 2.4b

~2.9

2.4

Colour [mg/L Pt units]

9000±500

2200

7 to 9

39±2

DOC

[mg(C)/L]

A254nm

[10/m]

Notes b

a

Using the tubing with the larger cut-off.

Using the tubing with the smaller cut-off.

The essential constancy of the SUVA254nm value suggests that the loss of organic species (large, at roughly 87%, compared to a decrease in conductivity of approximately 99.4%) did not discriminate significantly between NOM fractions with different SUVA254nm values. This somewhat surprising result * is consistent with the MIEX eluate initially containing a

*

GJESSING, EGEBERG & HÅKEDAL [400] isolated NOM from a range of source waters using reverse osmosis (RO): the processing effected an increase in SUVA254nm in every case, with the average rising from about 3.9 to 4.1L/mg.m. Increases in SUVA are associated with an increase in the average molecular mass of the organic species, which is consistent with greater probability of retention of such species in isolation processes such as RO.

364



disproportionately large fraction of small, highly-charged NOM species (compared to ‘average’ raw water).

The MIEX r e s i n is indeed generally expected to take up

proportionally more low-molecular-mass, highly charged components and less uncharged (neutral hydrophilic) species [172] — although one study [339] recorded a slight increase in the proportion of (highly) coloured species in the e l u a t e , suggesting that the proportion of large (coloured) components is increased. Another consideration is that humic substances may be more linear rather than spherical in shape [458], so that the nominal cut-off values could be misleading. Manufacturers often base molecular mass cut-off values on filtration of globular proteins, which have a different structure to humic and fulvic acids [565]. It has been found that this difference in properties tends to mean that the effective cut-off for NOM species is lower than the specified value [512, 565]. It is not clear what proportion of NOM would typically be retained or passed by tubing with a nominal 3500g/mol cut-off [compare 647, 935].

Although the SUVA254nm results suggest non-specific losses of NOM species in dialysis, complete spectrophotometric scans indicate that relative losses of UV-absorbing components are slightly greater than of visibly coloured components (data not shown here).

Coloured water was made up by spiking volumes of raw water with 1.25%V dMIEX.

6▪2▪2

Sludges

The key information relating to the dMIEX sludges is found in Table 6-1 (‘raw water’ quality) and Figure 6-1 and Figure 6-2 (coagulant dose and coagulation pH). Turbidity was unaffected by spiking with dMIEX. The particulars of the comparison, non-spiked sludges can be read from Table 3-14 and Table 5-1.

Aside from this it is useful to be able to refer to a few key parameters side by side, as in Table 6-2.

6▪2 : Experimental

365

D. I. VERRELLI

Table 6-2: ‘Raw water’ quality and coagulation conditions for dMIEX sludges and non-spiked sludges (the latter in parentheses, where different). Dashes indicate that no measurement was made.

Sample

High pH

Medium pH

Low pH

Low dose

39 (14)

37 (22a)

37 (12)

40 (10)

2.51 (0.87)

2.54 (1.14a)

2.40 (0.83)

2.43 (0.57)

‘Raw water’ quality True colour

[mg/L Pt units]

A254nm

[10/m]

DOC

[mg(C)/L]

9.2 (–)

9.4 (–)

8.7 (–)

9.4±0.4 (–)

[L/mg(C).m]

2.7 (–)

2.7 (–)

2.8 (–)

2.6±0.1 (–)

‘Optimum’ dose [mg(Al)/L]

– (2.5)

7.5 (4a)

– (≤1)

7.5 (≤1)

80

80 (79)

80

5.0

SUVA254nm

Coagulation conditions Dose

[mg(Al)/L]

pH

[–]

8.7 (8.6)

5.8 (6.0)

4.8

6.0

Hydrolysis ratio

[–]

3.15

2.71 (2.69)

2.47

2.03 (2.25)

[mg/L Pt units]

3 (2)

1

1

2 (0)

0.56 (0.28)

0.26 (0.16)

0.29 (0.21)

0.30 (0.15)

Supernatant quality True colour A254nm

[10/m]

DOC

[mg(C)/L]

3.4 (–)

1.7 (–)

2.0 (–)

2.4±0.1 (–)

[L/mg(C).m]

1.6 (–)

1.5 (–)

1.4 (–)

1.3±0.1 (–)

Dry solids generated [mg/L]

300 (290)

350 (360)

370

27 (16)

Δ(DOC)/Dry solids [mg/mg]

0.019 (–)

0.022 (–)

0.018 (–)

0.26 (–)

SUVA254nm Sludge

Note

a

A replicate produced from raw water of lower colour and absorbance (requiring half the ‘optimum’ dose)

showed the same dewatering properties — see §3▪5▪4.

The comparisons are generally quite uniform, with two exceptions. The representative nonspiked sludge selected for the pH 6 case was generated from raw water of atypically high colour. However it is clear from §3▪5▪4 that this did not affect its dewaterability. Also, the hydrolysis ratios of the low-dose sludges are significantly different. There are two factors that have led to this. First, the ionic environment is obviously altered by the dMIEX spike, aside from any buffering or other compositional differences in the original raw waters. Second, the hydrolysis ratio is more sensitive at low coagulant doses (cf. §3▪2▪4▪1). 366



It may be noted from the table that SUVA254nm decreases markedly upon treatment of the dMIEX-spiked water. This indicates that organics that absorb UV light less strongly are more resistant to removal by coagulation.

Although no values were recorded for the non-spiked treatments, approximate initial quality is implied by Table 6-1 (“Before spiking” column) and supernatant quality is assumed similar to those of the spiked cases. While not a focus of this study, it is observed that — for the high coagulant dose cases — treatment appears most effective around pH 6, and significantly worse at high pH. This is consistent with measurements on other samples (§5▪9▪1, cf. §5▪6▪2) . On a similar note, it is observed that the non-spiked water generally yields a better quality supernatant. This seems intuitive, except that the high coagulant doses would be considered far above the ‘optimal’ doses for efficient treatment. This is consistent with the concept of recalcitrant organics that are almost immune to removal by coagulation.

6▪3

Results

The organic content of some raw waters was artificially increased, as described, to investigate the relationship between true colour, DOC, or ultraviolet absorbance of the raw water and the dewaterability of the resultant sludge. Results are presented in Figure 6-1 and Figure 6-2.

In interpreting the graphs it is useful to refer to the replicate characterisations presented in §3▪5▪4: first, these indicate the extent of ‘natural’ variation that would be expected even if dMIEX were not added; second, the pairs chosen in Figure 6-1 and Figure 6-2 are somewhat arbitrary in three of the four cases, where more than one set of results is available for the non-spiked sludge.

To begin with we may observe for these new sludges some of the trends identified earlier. The sludge at pH 8.7 shows the worst dewatering with the highest py(φ) and about equal

6▪3 : Results

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D. I. VERRELLI

highest R(φ). The sludge at 5mg(Al)/L exhibits the lowest py(φ), although its resistance to dewatering is not the lowest in the high-φ range. The pH 5 and pH 6 high-dose dMIEX sludges display similar dewatering behaviour at large φ, which is again broadly consistent with the results of Chapter 5 for high-dose alum sludges.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2

mg(Al)/L dMIEX: Lab.: dMIEX: Lab.: dMIEX: Lab.: dMIEX: Lab.:

1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

80 80 80 79 80 80 5 5

pH 8.7 8.6 5.8 6.0 4.8 4.8 6.0 6.0 1.E-1

Solidosity, φ [–] Figure 6-1: Compressive yield stress for laboratory alum sludges generated from spiked (dMIEX) and non-spiked (Lab.) raw water.

368



2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 mg(Al)/L dMIEX: Lab.: dMIEX: Lab.: dMIEX: Lab.: dMIEX: Lab.:

1.E+10 1.E+09 1.E+08 1.E-4

1.E-3

80 80 80 79 80 80 5 5

1.E-2

pH 8.7 8.6 5.8 6.0 4.8 4.8 6.0 6.0 1.E-1


Hindered settling function for laboratory alum sludges generated from spiked

(dMIEX) and non-spiked (Lab.) raw water.

Comparing the spiked sludge behaviour with ‘control’ sludges should indicate the influence of raw water colour on sludge formation and dewatering. Given the previous finding that low coagulant doses resulted in a higher proportion of NOM (and turbidity) in the sludge, which was beneficial to dewatering, it may be expected that spiking the raw water with additional organic material would have a similar effect to a decrease in coagulant dose. Given that the additional NOM is of order 10mg(C)/L, this would be expected to have a greater influence on behaviour at the lower alum dose of 5mg(Al)/L.

6▪3 : Results

369

D. I. VERRELLI

No consistent trend attributable to the spiking can be found that is valid across all sludges and solidosities.

There is a weak tendency for the dMIEX sludges to possess superior

dewatering qualities (both rate and equilibrium) at high solidosity, however the shifts are mostly small, and the tendency is not without exception. At lower solidosities there seems instead to be a weak tendency for the dMIEX sludges to possess inferior dewatering qualities.

In view of this mixture of often marginal shifts, it is appropriate to examine in detail only those changes that are larger than the expected experimental variability.

These are

summarised in Table 6-3.

Table 6-3: Summary of significant changes in behaviour associated with spiking of dMIEX.

Sludge

py(φ)

R(φ)

80mg(Al)/L, pH 8.7

–

dMIEX slightly worse at high φ

80mg(Al)/L, pH 5.8

–

–

80mg(Al)/L, pH 4.8 5.0mg(Al)/L, pH 6.0

dMIEX much worse at low φ  (dMIEX much worse at low φ) dMIEX slightly better at high φ

dMIEX slightly worse at low φ

From the table it would appear that, overall, elevated levels of NOM are more likely to lead to inferior dewatering. This hypothesis needs closer examination.

In assessing the entries in Table 6-3 reference should be made to the analyses in §3▪5▪1▪2, which suggest that significant uncertainty is associated with the routine gel point determination procedure in general. This consideration relates directly to the high-dose, low-pH sample that exhibits a markedly reduced φg estimate. This low estimate of φg is in turn responsible for shifting the lower part of the R(φ) curve. Nevertheless, the duplicate measurements of φ0 for the gravity batch settling test are in excellent agreement, and the change in dewaterability is much larger than the variability indicated by the replicate sludges presented in §3▪5▪4, suggesting there is a real change. It is not clear why these conditions in particular should give rise to a significant deviation in behaviour, in particular in the gel point — presumably it must be due to the pH, rather than 370



dose. Changes in pH would affect the solubility of various species differently. NOM species are known to adopt different conformations as a function of ionic strength (or pH) [409, 1086], and are generally more globular at high ionic strength or pH [1024]. Furthermore, the NOM had been exposed to chlorine, ion-exchanged, recovered in a brine, and then dialysed (§6▪2▪1), which could have affected its properties significantly [cf. 331, 480]. The results appear to be counter to those of VILGÉ-RITTER et alia [1082] (§6▪1▪1), who found that low pH would increase Df in the presence of NOM. The disagreement is possibly due to the presence of different NOM species in the two sets of experiments.

It is not clear why the high-dose, high-pH dMIEX sludge shows (slightly) slower dewatering properties at high solidosity. Given that this is an isolated instance, it is not considered further.

Slightly slower dewatering is estimated for the low-dose dMIEX sludge at low solidosity. It is believed that this is a consequence of the marginal (non-significant) decrease in the estimate of φg for this sample. The final shift to be considered is the most interesting. Although the improvement in py(φ) for the low-dose sludge at high solidosity is not massive, it is still significant. Moreover, this low-dose sludge was expected to be the most sensitive indicator of changes in raw water quality.

6▪4

Discussion

The single low-dose dMIEX sludge has a significantly lower compressive yield stress at large φ than corresponding non-spiked sludge. In the absence of evidence to the contrary, it is appropriate to treat the decrease in py(φ) as a real effect. Results for sludges produced from raw waters of relatively low colour and DOC have shown that, for a given coagulation pH, the dewaterability tends to deteriorate above a certain coagulant dose, until a plateau is reached where, presumably, the precipitated coagulant dominates the dewatering behaviour (see §5▪1▪1, §5▪3). Another way of stating this finding would be to say that as the ratio of coagulant to NOM is d e c r e a s e d below a certain

6▪4 : Discussion

371

D. I. VERRELLI

threshold, the dewaterability i n c r e a s e s . Whereas the previous investigations varied this ratio by controlling the coagulant dose, here the ratio has been reduced by spiking the raw water with additional NOM.

It can also be seen from Table 6-2 that the estimated optimum coagulant dose for the dMIEXspiked raw water has increased roughly in proportion to the increases in true colour and DOC over that of the natural raw water, as expected. So it can be seen that the results to date can also be considered from the point of view of a ‘ r e l a t i v e ’ c o a g u l a n t d o s e ; namely, one normalised by the ‘optimum’ dose. That is, the optimum dose is taken as a practical, lumped measure of NOM. Unfortunately, the optimum dose is difficult to quantify, and undesirably subjective. Also, it has already been pointed out that it does not necessarily follow that raw water that is difficult to coagulate will produce sludge that is difficult to dewater. In such a case it may be stated that a decrease in the relative coagulant dose (below a threshold value) will result in an improvement in dewaterability, whether this is due to a reduction in the coagulant dose or an increase in the optimum coagulant dose, or both. The low-dose sludge provides some evidence to support this contention. The high-dose sludges should be unaffected by this mechanism, but may be more sensitive to changes in NOM conformation as a function of pH.

Physically, R(φ) is expected to increase if aggregate density (or Df) or size decreases: both of these lead to narrower flow paths for a given φ. In fact, for fractal objects (here “natural” fractal aggregates) density and size are inversely correlated [e.g. 217] (see §R1▪5▪3). The underlying structural reasons behind an improvement in py(φ) are generally that the aggregates formed are more dense (higher Df) or the aggregates are smaller — or both. This demonstrates that the ‘opposite’ shifts observed for the low-dose sludge are not physically incompatible.

Suppose that the aggregates formed are both smaller and denser in the case of the sludges generated from more highly coloured (spiked) raw water. Such structures may arise if the reaction rate were decreased, as discussed in §5▪4 and §R1▪5▪6▪1. They may also arise due to

372



the presence of an increased number of nucleation points or the formation of an external repulsive layer (perhaps NOM) on the aggregates that reduces further aggregation of existing clusters.

To explain the decrease in estimated φg it is necessary to propose a second level of structure, such as the adherence of a thick ‘fluffy’ layer of material, perhaps NOM, to the surface of the otherwise hard and small particulates. This could result in the formation of a network at lower φ, but would be readily compressed so that it would have no influence on dewatering at higher solidosity. HARBOUR, DIXON & SCALES [445] have also recently speculated about the formation of such a “soft” NOM layer on alumina particles.

Finally, it is notable that the largest shifts upon spiking of the raw water are observed for the low-dose and the low-pH materials.

It is clear that the NOM will make up a greater

proportion of the sludge for the low-dose case. However in both cases it may be noted that the predicted reaction rate is low (see the hydrolysis ratio in Table 6-2).

6▪5

Conclusions

The improvement in dewaterability for the low-dose sludge is likely due to a decrease in the proportion of precipitated coagulant in the sludge. The high-coagulant-dose sludges are most likely dominated by the precipitate, even with the spike; they may be susceptible to the negative influence of NOM reported in the literature, but a consistent trend of this nature is not observed herein.

The effect of raw water true colour or NOM content was investigated, and suggested that high colour may give rise to smaller, denser aggregates with ‘fluffy’ surfaces that form a network at lower volume fractions of solids, and settle slower, but which could potentially be filtered to higher cake solid volume fractions. However, the results were not entirely conclusive, and confirmation of the hypothesis would require further experimentation. It is plausible that raw water true colour or NOM may have different effects on dewaterability

6▪5 : Conclusions

373

D. I. VERRELLI

depending upon the coagulation conditions — even aside from the significant variation of NOM fractions and species in natural raw waters.

374


7.

EFFECT OF SHEAR AND POLYMER ADDITION

Throughout a water treatment plant the process and waste streams are subjected to varying degrees of shear. In some places this is intentional, with some functional objective, to wit: • dispersion of treatment chemicals; • increasing the frequency of particle collision in order to facilitate aggregation; and • as an aid to dewatering, as in a centrifuge or belt filter press, where the shear is believed to help break the aggregate or gel structure. In other places the shear occurs as a ‘side effect’ of: • conveying the streams through pipes or channels, from one unit operation to the next; • pumping, in order to overcome hydrostatic or hydrodynamic head; • tortuous paths through valves, elbows, filter beds, et cetera; and • flow into and through devices (e.g. filter presses). The sludge will be at varying degrees of concentration when exposed to these shear fields. Shear effects (if any), are anticipated to depend upon shear intensity and exposure time, solidosity, and aggregate structure. The primary dichotomy that may be considered is whether the shear is imparted during the coagulation or flocculation process (or shortly thereafter), while the suspension is still highly dilute, or whether the shear is imparted after the sludge has undergone some degree of dewatering and is thus more concentrated (perhaps to the point of having formed a network).

In WTP’s polymers are added for the purposes of enhancing separation.

In some

circumstances the focus may be on supernatant clarity (as turbidity, say), such as in a clarifier. In other situations the focus may be on the sludge itself, such as in a filter press. As with shear, the addition of polymer ‘flocculant’ during the aggregate formation stage will be treated separately to the addition of polymer ‘conditioner’ to the settled sludge. 375

D. I. VERRELLI

Polymers suitable for various conditioning duties are identified in §R1▪3▪3▪3.

Identification of trends based on shear and polymer addition will support making design or operating decisions on water treatment plants so as to optimise the dewaterability of the sludge generated. Conversely, if treatment requirements do not allow much flexibility in this regard, the trends will be useful in suggesting where more dewatering effort is required.

7▪1

Previous investigations and experience

7▪1▪1

Polymer addition

Addition of an appropriate polymer at an appropriate dose is conventionally expected to strongly bind primary particles, clusters or aggregates into large, porous flocs [114, 237, 518, 840, 1101] [cf. 526]. Studies of the fractal structure have variously found a moderate decrease [526], no change [997], or even a slight increase [404] in fractal dimension, Df. In the last case note that the influence of a larger diameter could still result in a nett d e c r e a s e in density (see §R1▪5▪3). The increased size is correlated with faster settling [117, 319, 333, 505, 1145] and filtration [443, 534, 580, 788, 789, 816]. The highly porous structure results in reduced resistance to dewatering in filtration [237].

On the other hand, the increased strength appears to result in an increase of the compressive yield stress [117, 237, 315, 319, 429, 1139, 1145] — although several researchers have concluded that changes in compressibility are not significant [443, 534, 580, 816].

The

changes may (or may not [319]) be most evident at low solidosity, with a significant decrease in the gel point [840]. Despite this, addition of polymers has been reported to increase the solids concentration of both alum and ferric sludges in practice [161, 315, 854]. This could be attributed to the influence of dewatering r a t e — generally the limiting parameter industrially — although DE

GUINGAND [435] did report decreasing py (and increasing φg) following polymer

conditioning of red mud [cf. 628].

376

Chapter 7 : Effect of Shear and Polymer Addition


Increased polymer doses can also increase the latency time (see §9▪1) prior to settling [840, 842], consistent with a (meta)stabilised structure.

While TAMBO & WATANABE [997] agreed that flocculation increased both the strength and size of WTP aggregates, they found no significant change in Df, suggesting the structure was not greatly changed. Moreover, ZHAO [1146] reported that Df actually increased, along with dagg, upon conditioning an alum sludge. This could still be consistent with an apparent increase in porosity if it is the space b e t w e e n flocs that is opening up into wider channels.

Where flocculant is used alone, without any coagulant, to aggregate particles by a b r i d g i n g mechanism, then the interparticle repulsion persists [860]. This may result in more voluminous structures in the absence of external stresses. On the other hand, it may also minimise ‘surface friction’ between particles, allowing them to potentially dewater faster or further than coagulated networks [860]. Flocculation of negatively charged particles (Na-bentonite and silica) with cationic polymers of low charge density produced flocs consistent with this mechanism [620, 1101].

The

resulting flocs are sticky and weak [1101], and described as “liquid-like”, with only shortrange ordering — no fractal structure was evident [620]. These are not very shear sensitive, but have ordinary “filtration properties” [171]. This contrasts to the action of c h a r g e n e u t r a l i s a t i o n . This can be an important factor in polymer flocculation (or conditioning) [237], seen in the common regulation of polymer dosage by monitoring the ζ-potential [171, 225, 1101]. Observations of AZIZ et alii [106] show that for polymer-only WTP sludges the flocculant dose controls dewaterability; the sludges are highly compressible, but suffer reduced permeability [see also 171, 444].

(Greater

compressibility was also reported in an American study [797].) Overall this results in slower dewatering than for alum sludges [106], although direct filtration may ameliorate this at low φ [171]. The low molecular mass of polymers commonly used as ‘coagulant aids’ (e.g. polyDADMAC) favours charge patch aggregation over bridging, and this results in the formation of strong flocs [1140].

7▪1 : Previous investigations and experience

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D. I. VERRELLI

Polymers of high charge density yield strong, voluminous [1101] fractal flocs [620]. These have good “filtration properties”, but are more sensitive to shear [171]. The difference may be due to the enhanced chain rigidity due to repulsion between the charge moieties [620].

Polymer conditioner is typically added downstream of the pump and immediately before the intended dewatering unit operation [e.g. 161] to allow sufficient mixing without excessive shear.

7▪1▪2

Shear

The importance of shear in inducing aggregation is discussed in Appendices R1▪4 and R1▪5▪6▪4. Those sections reflect the general tendency for research on aggregate or sludge shearing to focus on microproperties.

Aside from shear rheology, there has been little

published research on macroscale properties relevant to dewatering.

Shear may affect the structure of aggregates in different ways depending on whether the aggregates are exposed to the shear field while they are forming, or only after they are fully formed [481]. Increasing the system solidosity can lead to a decrease in the steady state aggregate size for a given turbulent shear rate [921].

7▪1▪2▪1

During formation

Aggregates formed in intense velocity gradients are expected to be more compact, and thus stronger; larger aggregates tend to be less dense, and therefore more susceptible to shear [518]. Similarly, weakly-bonding systems (corresponding to RLCA) are more susceptible to shear [441, 481]. For turbulent orthokinetic aggregation it was reported that larger aggregates were more compacted than smaller aggregates, and had higher Df, because the larger aggregates were more susceptible to shear-induced restructuring [961]. Industrial observations imply that a high mixing intensity in the nominally slow-mix phase of coagulation–flocculation will result in a floc that is rather tough, and will not readily penetrate a granular media filtration bed [754]. 378



It may be expected that only ‘free’ coagulant readily forms new bonds. This is consistent with the observation that sweep flocs will form quickly under continuous, moderately high speed mixing, but will then be broken up as the mixing is maintained [430], due to the coagulant having become ‘expended’. The small particulates formed at the end of a long rapid mix stage may be considered to no longer have ‘fresh’, ‘active’ surfaces, and they do not aggregate well during the subsequent slow mix stage [see 1140]. On the other hand, omitting the rapid mix phase altogether, and continuously stirring at slow speed, results in medium-sized flocs that are formed at a slower rate [369, 430]. This is presumably due to a failure to adequately distribute the coagulant homogeneously throughout the sample volume.

Experiments by OWEN et alia [807] cleverly demonstrated that kaolin aggregates formed through flocculation at a higher mixing intensity will have a denser, more compact structure which will settle faster than flocs o f t h e s a m e s i z e flocculated more gently. This can be described as a ‘ d e n s i f i c a t i o n ’ of the flocs as a function of the flocculation shear rate. Of course, as the mixing intensity is increased, the proportion of large flocs will eventually tend to decrease in response to the increased shear stresses. This can also be considered in terms of the characteristic timescales for the ‘competing’ processes of particle collision, polymer adsorption and re-conformation, and rupture — see §R1▪3▪1. At short timescales increased shear can actually lead to formation of larger aggregates (both coagulated and flocculated) [430]. However this corresponds to a transient maximum in dagg, and the rate of rupture quickly (within minutes) increases to establish a dynamic balance between formation and breakage that ultimately produces a smaller equilibrium aggregate size [430] [cf. 913, 914]. The timescales relevant to typical WTP process operations are rather long, so the details of the initial kinetics are of interest only insofar as they might influence the internal structure of the aggregates finally formed, and the ‘stable’ aggregate size can be taken as representative.

Large increases in apparent Df have been reported due to the imposition of a shear field as aggregates are forming. Shearing generally results in densification at the longer lengthscales


379

D. I. VERRELLI

through the preferential breakage of relatively weak parts of the aggregate, which would generally correspond to the more open, porous parts, where the density of interparticle bonds is lower [481, 799, 920]. Several researchers have supposed that the fragmentation can occur purely due to the hydrodynamic stress across individual aggregates [e.g. 116, 819, 968, 996] [cf. 581]. However it appears that often the attrition of fragments is predominantly due to collisions between clusters [441, 1018] — in an aggregate growth regime (as distinct from the shearing of preformed aggregates).

Increases in Df on smaller scales have also been reported, and attributed to particles ‘rolling’ over one another [481, 799]. In some cases shear densification appears to have proceeded equally on all lengthscales [441, 481, 679].

Occasionally the large-scale structure may be more open than the small-scale structure. This can be an ‘artefact’ caused by further aggregation of densified clusters in the time between ceasing the shear and commencing the characterisation [467].

Restructuring can also occur at the molecular or atomic level (e.g. by surface diffusion [842]) [143, 467].

These changes in the contact areas between particles can be interpreted as

‘ageing’ of the interparticle bonds [143]. Thus, newly-formed inter-aggregate bonds may be relatively weak (especially in the RLCA case) and quickly break, whereas aged bonds will only rupture infrequently [143]. The mechanism behind the ageing was proposed to be a gradual decrease of the interparticle gap after collision and initial bond formation: restructuring (by ‘rolling’) and rupture would be easier in the earlier stages [143]. Ageing could be indirectly enhanced by shearing through an improvement of the kinetics of relevant surface chemical reaction(s) [467]. While ‘ageing’ may result in densification at the smallest scales [467], it could also impede densification at larger lengthscales [143].

Batch settling and centrifugation tests on the aggregate suspensions showed that densified aggregates tended to form a more compact sediment [467].

380


The differences between


‘sheared’ and ‘unsheared’ samples were most significant for settling under gravity only; at a higher centrifugation rate (453g m/s2) the differences were insignificant, suggesting that the microstructure had been disrupted [467]. As the differences in microstructure were observed at the smallest lengthscales, while structure is expected to collapse first at large lengthscales [467], it seems that the low-speed centrifugation rate (50g m/s2) disrupted only the long-range structure, which was the same in both cases.

In several investigations the aggregate structure was found to be unaffected by shearing [920, 1047]. This can be due to: • aggregate sizes much smaller than dKolmogorov (see §R1▪4▪4▪3) [cf. 481]; • an insufficient variation of G — shear rupture is associated with the KOLMOGOROV lengthscale, which varies (roughly) with G‒1/2 (see §R1▪4▪4▪2) *; • inadequate magnitude of G, so that perikinetic aggregation dominates; • formation of rigid interparticle bonds [441, 1047]; • the presence of adsorbed surface groups (or interposition of much smaller primary particles [441]) that hinder the coagulated particles from rolling into tighter configurations (as to relieve hydrodynamic stress) [85]. In the last two cases aggregate size and growth rate may be affected by shear; also, break-up can occur at large enough G, so that changes in Df in response to shear are still possible [1047]. Rigid bonds are expected for coagulation in the primary minimum of a DLVO-type interparticle potential, bonds formed through ‘flocculation’ in a secondary minimum would allow rotation [1047]. The lower the remaining repulsive interparticle forces, the less flexible the connection [441].

*

SPICER et alia [961] (cf. p. 383) found little difference in shearing aggregates (preformed at G = 50s‒1) at 300 and 500s‒1, although these were much more effective than a spike of 100s‒1. For G = 50, 100, 300 and 500s‒1, dKolmogorov ~ 141, 100, 58, and 45μm respectively.


381

D. I. VERRELLI

Clusters tend to orient along streamlines, where they exist, which promotes more linear structures * [85, 143] — although this has been reported for shear ranging from 14s‒1 [143] to 29000s‒1 [85]. (The classification as laminar flow can be a simplification, as streamlines have been observed to be perturbed around large clusters, so that particles or small clusters following those streamlines would not collide as otherwise expected [441].)

Although several researchers have interpreted increases in (apparent) fractal dimension at larger values of dagg as evidence that shear has effected densification on larger lengthscales (as above), MEAKIN [729] presented an analysis which indicated that at least a small degree of increase in the apparent value of Df can be expected as dagg (or rather, the mass) increases, as an artefact of the calculation procedure (and the finite aggregate size, cf. §R1▪5▪2).

While TAMBO & WATANABE [997] agreed that the compactness of the aggregate population would tend to increase at higher agitation intensities, they found that this was due to a decrease in aggregate sizes, with Df unchanged.

(Recall that smaller aggregates are

i n h e r e n t l y denser for constant Df < 3, for equal dagg.) TAMBO & HOZUMI [996] reported that for a given value of G (140 to 3000s‒1) aggregate diameters were larger for lower alum doses, higher coagulation pH, or higher polyacrylamide flocculant dose. However all materials essentially correlated to the same relative reduction in size in response to the slow mix G value [996].

Polymer-flocculation experiments on alumina suspensions by AZIZ [105] suggested that increased rapid mixing time led to an inferior dewatering rate at low solidosity, but an improved rate at higher solidosity.

*

Modelling of polarisable aggregates by JULLIEN (1985), which found Df = 1.42, supports this contention [143].

382



7▪1▪2▪2

After formation, before settling

It has been suggested that aggregates formed under quiescent conditions and subsequently sheared may be less affected by shear, as restructuring (especially on small lengthscales) would require the break-up of many interparticle bonds [481].

Both experimental and

computer simulation studies indicate that shear restructuring of aggregates grown perikinetically occurs rather on longer lengthscales [703]. In contrast to the suggestion made in the preceding section, after formation it is DLCA aggregates that are anticipated to be more susceptible to shear, due to their more open structure (lower bond density) [666]. The interpretation of the KOLMOGOROV turbulence microscale as an approximate upper limit on aggregate size is supported by experimental studies on preformed aggregates too [961].

Classic experimental work by LIN et alia [666] investigated the effect of exposing aggregates of 7.5nm gold particles formed under DLCA conditions to shear. Scattering experiments showed that as the shear stress was increased, the loose fractal structure of the aggregate was disturbed at steadily decreasing lengthscales [666]. For the system studied, the original fractal structure (Df ~ 1.84) always persisted at lengthscales less than about 0.10μm (regardless of aggregate size) [666]. However, at the larger lengthscales the structure seemed to contract to a denser form, manifest in an increased apparent fractal dimension (up to 2.6 for the smaller aggregates, up to 2.8 or more for the larger aggregates) [666]. Break-up of the aggregates was not identified in this experiment [666].

SPICER et alia [961] studied the effect of different shear schedules upon 0.87μm monodisperse polystyrene spheres coagulated with aluminium sulfate in a stirred 2.8L baffled tank (cf. p. 381). Exposing aggregates to a high shear rate spike resulted in slight decreases in dagg but increases in Df after steady-state was reattained (at G = 50s‒1) [961]. On the other hand, exposing the aggregates to high shear with a gradual, ‘tapered’ decrease back to the original intensity resulted in considerable decreases in dagg with slight increase in Df and aggregate density when equilibrium was re-established [961]. Rupture of bonds between the particles and the precipitated aluminium species was described as irreversible [961], as it is statistically (entropically) highly unfavourable for the


383

D. I. VERRELLI

bonds to reform (to the same extent). It was speculated that this would result in a decrease in collision (bond-forming) efficiency [961], which is known to lead to the formation of denser aggregates (see §R1▪5▪6▪1). An interesting result was the observation of a dip and subsequent increase in aggregate density after the high-shear spike, attributed to (first) the reformation of larger aggregates and (then) the restructuring of those aggregates [961].

An early investigation by SONNTAG & RUSSEL [953] found very large changes in Df for a system of 0.14μm monodisperse polystyrene spheres aggregated in a quiescent state, and subsequently sheared in a COUETTE device in a turbulent regime [cf. 1047]. In order to isolate the effect of hydrodynamic shear gradients, the shear rate was repeatedly ‘spiked’ up to 6000s‒1 for short times, which was expected to minimise rupture due to particle collisions [953]. Light scattering indicated that Df increased from 2.2 to a high value of 2.48 in response to the shearing [953]. (Df for the unsheared aggregates had itself apparently increased from a low initial value of 1.6, ascribed to ‘spontaneous’ structural rearrangement [953] — although another ‘ageing’ mechanism may have been involved [cf. 667].) The magnitude of these changes is surprisingly high in contrast to comparable studies.

For sweep-coagulation sludges break-up of aggregates by shear appears to be irreversible [430]. At high stirring speeds (e.g. 300 to 400rpm, G ~ 330 to 510s‒1) in jar testing of kaolin suspensions, the breakdown occurs very rapidly:

of order < 10s [430, 1140, 1141].

Reformation was observed to only about one third of the undisturbed extent, and at a rate of order 10 times slower [430]. Given the relatively rapid rate of floc formation following the rapid mixing phase, it may be that, after an extended period of slow mixing, there is little ‘free’ coagulant remaining that is available to form new bonds. If that is the case, then aggregate reformation under these circumstances (sweep coagulation) depends upon the combination of hydroxides that have already precipitated and formed discrete clusters. It is hypothesised that the charge neutralisation regime is more amenable to floc reformation, because the mechanism depends upon electrokinetics (which is a state property) rather than

384



enmeshment (which is a function of path) [cf. 1141]. Observations on aggregates formed by a polymer charge-patch mechanism support this [1141]. The extent of particle aggregation following exposure to high shear, being a very rapid process, is apparently independent of the initial size of the aggregates or the previous (lower) shear regime [430].

7▪1▪2▪3

After formation and settling

After settling aggregates are likely to be more susceptible to shear, as the closer ‘packing’ will lead to increased collision frequency between aggregates [355, 1055], and higher localised velocity gradients in the reduced spaces between aggregates. The ISO standard on sludge sampling [8] recognises that the physical characteristics of the sludge “may change” on passing through a pump, due to shear on particulate matter [see also 789]. Large flocs formed by polymer addition are seen as especially susceptible to shear [e.g. 315]. Different pumps impart different intensities of shear.

Although peristaltic pumps are

recognised as ‘low shear’ devices, there appears to be a dearth of quantitative scientific data in the literature: what does exist is a fair amount of anecdotal evidence based on experience in the field [e.g. 23, 25]. A possible limitation in the ability of peristaltic pumps to minimise imparted shear may occur at higher pressures, where pulsation becomes more significant [25] and may cause some (minor) product degradation. BUSHELL, AMAL & RAPER [216] observed break-up of hæmatite aggregates when passed through a 1.5m length of 6mm diameter tubing using a peristaltic pump at 52mL/min. These conditions equate to a REYNOLDS number of only 184, giving laminar flow, with G ~ 29s‒1 and an exposure time of 49s. These conditions do not seem harsh, and may not represent the true total stress on the aggregates due to the mechanical action of the peristaltic pump rotor. Other plant operations may also impart significant shear to the sludge [e.g. 417].

The investigations of KNOCKE & WAKELAND [580] into shearing of settled alum WTP sludges in a stirred-tank geometry suggest that significant reductions in dewatering (viz. filtration) rates require characteristic velocity gradients T400s‒1. In similar experiments NOVAK &


385

D. I. VERRELLI

BANDAK [788] reported a doubling in CST (from ~100s to ~200s) as G was increased from 260 to 1400s‒1.

DE GUINGAND [435] reported an increase in both the rate and extent of dewatering, including an increase in estimated φg, for both settling and centrifugation, following shearing of flocculated red mud suspensions.

The high sensitivity of many samples to agitation and vibration is well known. The question arises as to whether the non-sheared material properties have industrial relevance [1035]. A related question is whether the characterisation processes themselves damage the aggregates present in the sludge [cf. 580], e.g. leading to underestimation of aggregate dimensions [as in 388].

The shear imparted to aggregates of 140nm polystyrene particles upon passing through a sudden contraction in laminar flow was found to cause a loss in aggregate mass, while the radius of gyration was practically unaffected [955]. This was interpreted as the preferential rupture from the surfaces of the aggregate parallel to the flow streamline, due to the irrotational nature of the flow, leading to the formation of a more prolate shape [955]. This ignores the possibility of rotation due to the velocity gradient imparting forces upon the particle that are not isotropically distributed.

Settled WTP sludge is shear thinning and thixotropic [112, 580, 722, 880, 1123], in that its apparent viscosity decreases if sheared at a higher rate or for a longer time * (respectively) [924]. However the recovery of the apparent viscosity upon reduction of the shear strain rate is incomplete [112, 722]. There is an immediate partial recovery, the speed of which has been ascribed to a reversion of the balance between bond breakage and reformation [722] [cf. 412]. Hence the drop in apparent viscosity upon shearing has been attributed to two different mechanisms: one reversible, the other irreversible (‘rheodestruction’ [924]) [722]. Intuitively, the reversible reduction ‘should be’ due to bond rupture, and specifically rapid

*

386

Ageing effects [see 1097] are a separate concept [286].



fragmentation of the aggregates into large clusters, rather than erosion of individual units from the surface [722]. The mechanism for the irreversible change in material rheology was then concluded to be progressive structural rearrangement, i.e. densification of aggregates or clusters [722].

An alternative or complementary mechanism to explain the irreversible

component may be simply the reduced ability of ‘old’ clusters to form new bonds for some modes of aggregation (e.g. pp. 383, 384, 421). The sheared samples were found to settle further [722] [see also 1139], consistent with densification. For ‘pure’ alum precipitates significant viscosity reduction was reported at shear strain rates less than 80s‒1 [112].

7▪2

Shear during coagulation

Shear may be imparted to the sludge during the coagulation or flocculation process or shortly thereafter (while the suspension is still highly dilute), or after the sludge has undergone some degree of dewatering and is thus more concentrated (perhaps to the point of having formed a network). The coagulation (and flocculation) process is conventionally considered as occurring in two stages, namely a rapid-mix phase of short duration, in which the treatment chemicals are dispersed, followed by a (nominally) slow-mix phase of longer duration, in which adsorption and aggregation take place. It is presumed that increasing the rapid-mix speed, may serve to marginally decrease the time for practically ‘complete mixing’ to be completed, assuming a reasonable original speed. That is, once a rapid-mix speed is established that achieves practically complete mixing, further increases in the rapid-mix speed will not have much effect. Furthermore, as aggregates of reasonable size have generally not yet been formed in this short period of time, aggregate breakage is not an issue. This investigation has looked exclusively at the effect of altering the slow-mix speed, of a constant 20 minutes duration.

7▪2 : Shear during coagulation

387

D. I. VERRELLI

7▪2▪1

Materials and methods

Two pairs of conditions have been examined, both with similar specifications except that the characteristic velocity gradient, G, in the slow-mix phase was alternately 13s‒1 or 84s‒1, while for each pair the coagulant dose was alternately ~80mg(Al)/L or 5mg(Al)/L. (In the rapidmix phase G was of order 250s‒1 in all cases, and did not vary significantly.) The higher intensity is representative of the upper design limit on slow mix speeds. For a discussion of the significance of G see §3▪3▪2, §R1▪4▪3 and §R1▪4▪4▪2. For industrial conditions see §R1▪4▪5. Key data are presented in Table 7-1. The effect on other mixing parameters may be inferred from Table 3-5 or calculated from the formulæ in §R1▪4.

Table 7-1: Generation conditions for alum sludge samples used to investigate the effect of shear.

Sample

High dose

High dose, fast

Low dose

Low dose, fast

Raw water source

Winneke

Winneke

Winneke

Winneke

2006-01-05

2005-04-05

2004-01-08

2004-04-05

22

4

10

4

1.14

0.34

0.66

0.32

and date True colour [mg/L Pt units] A254nm

[10/m]

Dose

[mg(Al)/L]

79

79

5

5

[–]

6.0

6.3

6.0

6.3

[s‒1]

254

254

241

254

[s‒1]

13

84

13

84

[s]

59

18

65

18

[μm]

274

109

281

109

d / Pé 1/3 at 293K b [μm]

0.5

0.3

0.5

0.3

pH Rapid mix G Slow mix G Circulation time a dKolmogorov

Notes a

Indicative mean value calculated from V / (Da3 N) — see §R1▪4▪4▪1, p. 723.

b

For Pé = 1, require d e q u a l to this value; For Pé = 1000, require d t e n t i m e s l a r g e r than this value.

388



Although it was attempted to maintain all variables aside from the slow-mix speed as constant for the two sets of sludges, in practice some variables could not be held perfectly constant, and so these may also influence the results.

7▪2▪2

Results

Compressive yield stress and hindered settling function data are presented in Figure 7-1 and Figure 7-2, respectively.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 1.E-4

79mg(Al)/L, 79mg(Al)/L, 5mg(Al)/L, 5mg(Al)/L,

1.E-5 1.E-3

1.E-2

G ≈ 13/s # G ≈ 84/s G ≈ 13/s # G ≈ 84/s

1.E-1

1.E+0


Compressive yield stress for two pairs of sludges subjected to different shear

intensities in the slow-mix phase (given as G). In all cases pH ≈ 6; further details are given in Table 7-1. Hash symbols (#) indicate that replicate samples were characterised (see §3▪5▪4).


389

D. I. VERRELLI

It can be seen immediately that the sludge dewatering properties are n o t especially sensitive to the different intensities of shear. In general there is a much closer dependence of the dewatering properties on the coagulant dose.

2


1.E+15

1.E+14

1.E+13

1.E+12

1.E+11

1.E+10

79mg(Al)/L, 79mg(Al)/L, 5mg(Al)/L, 5mg(Al)/L,

1.E+09 1.E-4

1.E-3

1.E-2

G ≈ 13/s # G ≈ 84/s G ≈ 13/s # G ≈ 84/s

1.E-1

1.E+0


Hindered settling function for two pairs of sludges subjected to different shear

intensities in the slow-mix phase (given as G). In all cases pH ≈ 6; further details are given in Table 7-1. Hash symbols (#) indicate that replicate samples were characterised (see §3▪5▪4).

It is seen that for a given coagulant dose, the compressive yield stresses of the two samples at high pressures (i.e. under filtration) are essentially indistinguishable from one another (Figure 7-1).

390

At lower pressures (as in thickening) there is still not a great degree of



difference: the high-dose sludges are essentially the same, while the low-dose pair show a slight advantage in exposure to more shear. This is reflected in the gel point for this lowdose, high-shear sludge being higher than the corresponding low-shear sludge. However it is not considered that this difference is especially significant, and may be due at least in part to small experimental uncertainties or variations and the subjective choice of ‘optimum’ modelled fit to the data.

The hindered settling function curves for the two samples at high concentrations are also quite similar (Figure 7-2), with the characteristics again showing a stronger dependence upon the coagulant dose than the shear. Furthermore, the small differences that are present cannot be identified with any particular trend, as in one case a marginal decrease in R is found, and in the other an increase. At lower concentrations the tendencies in R mirror those of py, with a tendency to inferior (slower, in this case) dewatering being associated with higher velocity gradients. This is more significant for the low-dose pair.

7▪2▪3

Discussion and conclusions

A likely mechanism for the observed behaviour comes from an intuitive understanding of the effect of shear during the slow-mix stage: it prevents large aggregates from forming. Any very large aggregates that do form will be quickly broken apart again due to the increased shear levels present, with the effect that the population of aggregates generated will have smaller sizes. Higher levels of shear are also likely to result in denser aggregate structures. Such behaviour would imply that the high-shear aggregates would settle and generally dewater more slowly, due to their smaller size. This is in accordance with observations. However, it may also be expected that denser particles would allow more compact beds to be (eventually) formed — this would imply lower compressive yield stresses, for which no experimental evidence was found. This might indicate that the two types of aggregates have very different sizes, but only marginally different aggregate structures (and hence aggregate densities).


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D. I. VERRELLI

This seems reasonable in the context of the py(φ) curves, which were essentially unaffected by the slow mix shear rate. Furthermore, the least effect was seen at high solidosities, and the greatest effects were seen at low solidosities. This strongly suggests that the changes caused by the increased slow mix shear rates have affected the aggregates only on larger lengthscales, and that they remain unaffected on smaller lengthscales. This accords very well with what is known from both theoretical and experimental studies of fractal aggregates (see §R1▪5), and the notion of the KOLMOGOROV turbulence microscale, below which viscous forces dominate (see §R1▪4). It also makes intuitive sense in that the smallest clusters that make up the aggregates would have been formed in the rapid mix phase, where conditions were unchanged [as in 369]. Table 7-1 shows that the small-scale aggregate structures, up to about 1μm will not be

significantly affected by G, provided the agitation is sufficient to keep the particulates suspended. Moreover, it can be seen that although the increase in G from the base case appears to be large, the corresponding proportional change in dKolmogorov is far smaller, and the transition from perikinetic to orthokinetic aggregation is likewise little affected.

Shear imparted during the slow-mix phase of the coagulation resulted in no significant changes in sludge dewaterability except in the most dilute regimes, where there was a clear increase in the resistance to dewatering, manifested in significantly elevated values of R. This could have a direct impact upon operations such as settling and thickening, but would be less important for centrifugation or filtration. The changes may to be due to the formation of smaller aggregates, of lower mass (and hence lower terminal settling speeds) under the higher-shear regime. The constancy of the py(φ) curves suggests aggregate structure is not significantly affected.

7▪3 7▪3▪1

Flocculation Materials and methods

Two high-molecular-mass polymers were added to alum sludges during the generation phase:

392



• Zetag 7623 — a 10% cationic copolymer of acrylamide and a quaternary ammonium salt, and • Magnafloc 338 — a 10% anionic copolymer of acrylamide and sodium acrylate as described in §3▪2▪5. Both were added during the second part of the rapid-mix stage, 30s after addition of the sodium hydroxide, and with a further 30s of rapid mixing remaining [cf. 521].

The

concentration added was 1000mg/L, made up from refrigerated stock solution (5g/L) and well mixed to ensure homogeneity.

The dose in each case was approximately 1.23mg(flocculant)/L, expected to be equivalent to approximately 3.5kg(flocculant)/t(dry solids), in line with conventional recommendations (§R1▪3▪3▪1).

The details of the sample generation conditions are presented in Table 7-2.

Table 7-2: Generation conditions for alum sludge samples used to investigate flocculation.


High

High + M.

High + Z.

Low

Low + M.

Winneke

Winneke

Winneke

Winneke

Winneke

2006-01-05

2006-01-05

2006-01-05

2004-01-08

2005-11-16

22

22

22

10

27

1.14

1.14

1.14

0.66

1.23


[10/m]

Dose

[mg(Al)/L]

79

79

79

5

5

[–]

6.1

6.0

6.0

6.0

6.0

None

Magnafloc 338

Zetag 7623

None

Magnafloc 338

pH Flocculant Flocculant dose

–

[mg/L(mixture)]

–

1.23

1.23

–

0.62

[g/kg(dry solid)]

–

3.4

3.4

–

26

Due to the large volume of water required to produce sufficient sludge for characterisation at low alum doses, it was not practicable to use the same raw water source in each case. 7▪3 : Flocculation

393

D. I. VERRELLI

7▪3▪2

Results

Results comparing the effects of flocculant addition upon dewatering properties are presented in Figure 7-3 (compressive yield stress) and Figure 7-4 (hindered settling function).

The similarity of the compressive yield stresses (Figure 7-3) for the three high-alum-dose sludges is uncanny. In fact, it surpasses the concordance previously found between even duplicate runs of a given material.

It strongly suggests that across all solidosities the

flocculant has nil effect on the equilibrium condition. Such a result may be expected if the flocculant acts primarily on the outside of aggregates, and does not affect their internal structure, or strength. The py(φ) data for the two low-alum-dose sludges shows more variation, with the flocculated sample exhibiting marginally weaker behaviour in filtration, but a lower gel point. Although this might be due wholly to the flocculant, it is likely that the different nature of the two raw waters has also affected the results. This premise is based firstly on the lack of observable difference in the high-alum-dose sludges. Secondly, it is based on the inter-relation between alum dose and raw water NOM (indicated in Table 7-2 by the surrogates true colour and A254nm). Reduction in NOM and increase in coagulant dose typically lead to the same effect (see §6). Here the unflocculated low-dose sludge was generated form relatively uncoloured raw water, so that the precipitated coagulant makes a greater contribution to the sludge composition. This may be reflected in the similarity between the py(φ) curve for this sludge and for the three high-alum-dose sludges.

There are differences in the R(φ) curves shown in Figure 7-4. There is a small but fairly consistent tendency for the flocculated sludges to have reduced values of R, implying less resistance to dewatering. This is the trend that would generally be expected (if any). The trend is consistent across the two types of flocculant used, and across the range of observed φ, except for the portion of the low-alum-dose curves at low solidosity.

394




1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 79mg(Al)/L 79mg(Al)/L + Magnafloc 338 79mg(Al)/L + Zetag 7623 5mg(Al)/L 5mg(Al)/L + Magnafloc 338

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 7-3: Compressive yield stress for two pairs of sludges where flocculants were added to promote aggregation, compared to ‘controls’ with no flocculant.

Note that for the gravity settling tests, the initial concentration loaded was subject to significant uncertainty for two of the three high-dose tests, and so the differences at low φ cannot necessarily be relied upon. Nevertheless, the excellent concordance of the py(φ) curves, even at low φ, suggests that the estimates used were good, despite the experimental uncertainty. (Uncertainty in φ0 for the low-alum-dose sludges was negligible.)

7▪3 : Flocculation

395

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 79mg(Al)/L 79mg(Al)/L + Magnafloc 338 79mg(Al)/L + Zetag 7623 5mg(Al)/L 5mg(Al)/L + Magnafloc 338

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 7-4: Hindered settling function for two pairs of sludges where flocculants were added to promote aggregation, compared to ‘controls’ with no flocculant.

7▪3▪3


On the basis of published articles, the dosing of flocculant shortly after coagulant and alkali addition is expected to lead to faster dewatering, at the expense of a reduced maximum extent. Flocculation kinetics can be quite slow in dilute systems [428], but here the dosing of coagulant and the long slow-mix period offset this concern. Definite improvements in dewatering k i n e t i c s were observed, with improvements in R of up to a factor of about 2 across all values of φ. (Except for the low-dose sludge at low solidosity.)

396

However the compressive yield stress was remarkably unaffected by the



addition of polymer, suggesting that the flocculant may bind to the outside of aggregates, without affecting their internal structure. The main action of the flocculant may be simply to join smaller clusters or aggregates into larger masses.

7▪4

After settling: shear and polymer conditioning

While the previous sections of this chapter suggested that increased shear and flocculation during the aggregation process had only a minor influence on dewaterability, anecdotal evidence suggested greater effects would be observed where shear and polymer conditioning are applied to a settled sludge, i.e. at higher solidosity. Furthermore, this is a very common situation industrially. The aim of this investigation was to quantify any changes in dewaterability, and assess whether these could compensate for poor qualities in the original sludge.

Polymer is conventionally added in two situations on a water treatment plant.

First,

polymer may be added to the raw water as a ‘flocculant’ at the head of the plant (usually just after coagulant addition), in order to facilitate clarification (based on settling rate). Second, polymer may be added to settled or thickened sludge as a ‘conditioner’, in order to increase the throughput of downstream dewatering operations. In both cases shear is normally imposed to distribute the polymer and encourage floc growth.

Sludge treated with polymer after settling will be called ‘conditioned’.

To do this the

polymer must be mixed in, implying shear after settling — these processes are both covered in this section.

7▪4 : After settling: shear and polymer conditioning

397

D. I. VERRELLI

7▪4▪1

Methodology

7▪4▪1▪1

Materials

Two high-molecular-mass polymers were used: • Zetag 7623 — a 10% cationic copolymer of acrylamide and a quaternary ammonium salt, and • Magnafloc 338 — a 10% anionic copolymer of acrylamide and sodium acrylate as described in §3▪2▪5. Stock solutions were made up at 5g/L approximately 1 day ahead (mixed overnight on an eccentric roller mixer, and refrigerated). The polymers were then diluted to 2g/L (Zetag 7623) and 3g/L (Magnafloc 338) and gently mixed for approximately an hour before use (at room temperature).

The polymers were added to two sludges that had been coagulated at 80mg(Al)/L with different pH values, namely 5.9 and 8.9. Details are provided in Table 7-3. These had been decanted and settled over a number of days to higher solidosities, as given by Table 7-4. The results (§7▪4▪5) will show that the samples were at or somewhat above their gel points, which are given for convenience in Table 7-3. It may be noted that the sheared sludges were also characterised with no polymer addition. Purified water was added as a ‘blank’, to account for dilution effects. (It was intended to add this at an equivalent flowrate to the Zetag 7623. Due to a revision of the polymer dosage, the purified water addition rate was half of the Zetag 7623 dosage rate.) The water and polymer were added at volumetric rates between 1%V and 2 to 3%V (respectively) of the influent sludge flowrate, so dilution effects were expected to be correspondingly small.

398



Table 7-3: Generation conditions and estimated gel points for alum sludge samples used to investigate the effect of polymer conditioning. Parameters for the sheared sludges are identical to those of the unsheared (unconditioned) sludges.

Sample Raw water source and date True colour

pH 5.9

pH 8.9

Winneke

Winneke

2006-06-09

2006-06-09

11

11

0.73

0.73

[mg/L Pt units]

A254nm

[10/m]

Dose

[mg(Al)/L]

80

80

pH

[–]

5.9

8.9

Gel point, φg

[–] 0.0019±0.0002

0.0012

Table 7-4: Solidosities at which the samples were sheared or conditioned.

Sample

Age

Solidosity, φ

[weeks]

[–]

[mg/L(mixture)]

[g/kg(dry solid)]

Shear

1

0.0025

0

0

pH 5.9 + Z.

Zetag 7623

2½

0.0028

40

5.6

pH 5.9 + M.

Magnafloc 338

5

0.0030

90

5.2

Shear

1

0.0015

0

0

Zetag 7623

2

0.0017

40

9.1

pH 5.9 sheared

pH 8.9 sheared pH 8.9 + Z.

Process

Polymer dose

The doses given in Table 7-4 are at the upper end of the range suggested in the literature (see §R1▪3▪3▪1). This is justified in terms of CST observations (see following). Lower doses that provide almost the same degree of flocculation may be financially favoured in industry. ELDRIDGE and co-workers [342] found lower effective polymer doses working with Winneke WTP sludge diluted to ~0.44%m solids, namely 0.5 to 1.3g/kg(dry solid) using Magnafloc 155 (18% anionic polyacrylamide, 12 to 15×106g/mol [134]) and 2.0g/kg(dry solid) with Zetag 8680 (cationic acrylamide copolymer, “ultra-high” molecular mass).


399

D. I. VERRELLI

7▪4▪1▪2

Dose setting by capillary suction time (CST)

Capillary suction time (CST — see §2▪4▪1▪3) was used as an indication of optimal or adequate polymer conditioner dose. The polymers described were added to 100mL of sludge sub-samples. The solidosity of the sludge was measured in the usual way for additional sub-samples. The sludge was mixed in a 150mL glass beaker (56.5mm diameter, ~41.5mm height) using a magnetic stirrer bead (~7.5mm diameter, 40mm length) spinning at ~300rpm. Although the shear was not quantified for this preliminary testing, it can be classified as ‘high’ — it resulted in the formation of a deep vortex (the beaker was unbaffled) that dissipated upon polymer addition. The sludge was pre-mixed for about 15s before polymer addition, to establish a steady state. The mixing was maintained for 5s after polymer addition, and was then stopped immediately. This set-up was nearly identical to that of DE GUINGAND [435] for red mud, except that he stirred for 2min first and then applied 15 to 30s of mixing after polymer addition; he reported no benefit in using a propeller or baffles. The specified mixing was slightly less intense than that recommended by DILLON [315] in the laboratory, viz. 1000 to 1500rpm for 1 to 5s (albeit presumably for larger geometries), and briefer than the 30s allowed by both CORNWELL [282] and ZHAO & BACHE [1145], but appeared to yield satisfactory floc formation. The method was similar to that of KNOCKE & WAKELAND [580], who imposed 5 to 10s of rapid mixing at G ≈ 800s‒1, followed by 30s of slow mixing.

The CST was measured on a Triton – W.R.C. Multipurpose filtration unit TW166 (cf. Triton Electronics, Essex, U.K.) using Whatman (Middlesex, U.K.) 17 CHR chromatography paper in accordance with the U.S. Standard Methods [334] [cf. 130]. Measurements were typically carried out in quintuplicate or quadruplicate. The device and paper were ‘calibrated’ by performing tests with purified water.

Aside from the quantitative CST results, attention was also paid to the qualitative ‘flocculency’ of the conditioned sludge, in particular the size of any flocs formed.

400



7▪4▪1▪3

Shear and mixing rig

The shear and polymer mixing was carried out in large-diameter plastic tubing, to aid characterisation of the velocity gradient (as per §S26▪1). Settled sludge was drawn by a peristaltic pump that would have imposed additional shear as it ‘pinched’ the tubing; this has not been quantified, but is likely to be a minor effect. A schematic of the rig is presented in Figure 7-5.

Tube 2 Pump 2

2.6

Magnified view 2.3

Tube 1

Tube 3

Pump 1

9.5

Magnified view

6.9

7.1

4.8

8.0

Tube 4

4.8

9.7

7.6

12.5

Figure 7-5: Schematic of the sludge shearing and conditioning rig. Dimensions marked on the schematic in small type are the inner diameter at the indicated cross-section [mm]. Sludge was fed through tube 1 and polymer (or water) through tube 2.

The tube was laid out straight and horizontally, to avoid extraneous mixing and shear effects due to coiling [cf. 427, 428]. The downstream tube diameter was chosen to be larger than the anticipated floc size [cf. 428].

Pump 1 was a Watson–Marlow (England) 603S, and Pump 2 was a Watson–Marlow 502S. Tubes 1 and 2 were silicone, to suit the peristaltic pumps. Further details are given in Table 7-5. The estimated absolute roughnesses, e, may be somewhat low — especially if fouling is


401

D. I. VERRELLI

significant *; however increasing e by a factor of 50 gives only ~10% increases in G and ~25% increases in the head loss.

Table 7-5: Tubing details for the sludge shearing and conditioning rig (see Figure 7-5).

Tube

Material

Roughness, e [357]

Length

Inner diameter

[mm]

[m]

[mm]

Tube 1

Silicone

0.003

0.6

9.5

Tube 2

Silicone

0.003

0.6

2.6

Tube 3

PVC

0.002

1.0

8.0

Tube 4

PVC

0.002

1.4

12.5

In order to validate the calculation procedure, the pressure drop downstream of the polymer mixing point was estimated by two methods. Both were most conveniently expressed as head losses in metres of water — essentially equivalent to metres of sludge, due to the negligible density difference. In the first procedure the head loss was measured experimentally by holding the thin silicone tube (Tube 2) vertical and open to atmosphere †. In this mode the rig functioned as an ad hoc capillary rheometer, with the vertical tube serving as a manometer, and the downstream tubing serving as the ‘capillary’. Tapwater and sludge were separately tested at the desired flowrate of the main pump, namely 2000mL/min. The observations are given in Table 7-6.

There is a significant increase in head loss upon switching to sludge as the pumped fluid. Given a constant flowrate, and fixed geometry, it can only be concluded that the rheological properties of the sludge are significantly different to that of water i n t h i s a p p l i c a t i o n . Of prime interest, then, is the ‘effective’ viscosity that applies f o r t h e s h e a r s t r a i n r a t e d i s t r i b u t i o n encountered in this rig. (This is the reason why the ad hoc rheometer used here is the most appropriate measure of effective viscosity.)

*

The tubing was cleaned by ‘pigging’ after use, and so was not extensively fouled.

†

This implies a slight reduction in flow, namely ~60mL/min out of 2000mL/min (~3%), which is negligible.

402



The head loss associated with the sludge is comparable to the 1m recommended by the WRc [315] for a l u m sludge in their preferred plant configuration where mixing is achieved by turbulence induced by an orifice plate (see Appendix S14). It was further recommended that the downstream pipeline G value not exceed 300s‒1 [315].

Table 7-6: Approximate pressure drop, in metres of water, downstream of the T-junction in Figure 7-5. Key values in bold.

Through PVC

Through fittings

‘Minor’ losses

Total

tubing Observations Water

–

–

–

0.48 to 0.57 a

Sludge (pH 8.9)

–

–

–

0.64 to 0.72 a

η = 1mPa.s

0.12

0.08

0.25

0.45

η = 6mPa.s

0.25

0.25

0.10

0.60

Model

Note

a

Range corresponds to observed fluctuation due to pulsation of peristaltic pump flow.

In the second procedure the head losses were estimated from theoretical calculations. The characteristic velocity gradients, G, were exclusively estimated by assuming flow through a pipe (see §S26▪1). These estimates were calculated using the FANNING friction factor, from which head losses though the PVC tubing and through the fittings could also be calculated. As seen in Table 7-6, the ‘minor losses’ due to flow restrictions, expansions, and exit were significant, and were estimated using standard fluid mechanics relations [847, cf. 1043]. The viscosity was first assumed to be that of pure water, 1mPa.s, which yielded a prediction of 0.45m for the overall downstream head loss. This value matched the lower end of the experimentally observed head loss for tapwater, giving confidence in the computation method. For this viscosity the flow was everywhere turbulent. Evidently a higher value of effective viscosity was required for the sludge, in order to account for the greater observed head loss. By increasing η to 6mPa.s a similar concordance was obtained between the theoretical and experimental values of head loss to that previously


403

D. I. VERRELLI

found for water. This suggests that 6mPa.s * is a good estimate of the effective viscosity of the sludge for the bulk flow through the rig. While the solidosity of the pH 8.9 sludge was known to be of order 0.002 (see Table 7-4), it is of interest to calculate the solidosity of solid spheres that would yield the same factor of viscosity increase. For concentrated solid-sphere systems with φ ( 0.40 HAPPEL derived η / ηL = 1 + 5½ φ

10 + 4φ 7 / 3 − (84 / 11)φ 2 / 3 10 − 10φ10 / 3 − 25φ(1 − φ 4 / 3 )

[7-1]

for NEWTONian suspensions [442]. Thus η / ηL = 6 implies φ = 0.30 for an equivalent solidsphere system. It is reasonable to associate this solidosity of 0.30 with the volume fraction of aggregates in the system, φ, although the aggregates will be neither perfectly spherical nor completely impermeable.

An estimated shear schedule is presented in Table 7-7. The characteristic velocity gradients, G, were exclusively estimated by assuming flow through a pipe (see §S26▪1). It is noted that the flow is everywhere laminar [cf. 880]. Operation in the laminar regime is less desirable for this study, as the flow field will be less homogeneous and less isotropic, the distribution of shear stresses will be broader, and mixing of the polymer conditioner will not be as greatly promoted (although evidently it still occurs, presumably strongly influenced by the geometry at the fittings [cf. 315, 741, 780]). The ‘minor losses’ actually comprised a significant component of the total losses. Yet these are not included in the estimation of G, as it is not clear what volume to associate with the minor losses. The magnitude of the ‘minor losses’ indicate that stress due to the converging flow [cf. 955] is an important effect of the fittings, and indeed a significant part of the overall shear regime. Use of fittings was unavoidable, and it was considered that the system was sufficiently well characterised to ensure reproducibility, even if quantitation of G was problematic.

The mean residence time of almost 7 seconds is comparable to the mixing time found to be satisfactory in §7▪4▪1▪2 [see also 428].

*

This is the viscosity of a 50% solution of glycerol (propane-1,2,3-triol, or ‘glycerine’), C3H5(OH)3, in water at room temperature [662].

404



Table 7-7:

Estimated shear schedule, for both unconditioned and conditioned sludges

(η = 6mPa.s).

t

Ga

Re

[s]

[s‒1]

[–]

[μm]

Upstream of polymer addition — tubing ~ total

1.28

280

745

(147)

Downstream — narrow tubing

1.49

474

859

(115)

Downstream — wide tubing

5.10

124

550

(224)

Downstream — all fittings

0.26

580 c

–

(103) c

Downstream of polymer addition — total

6.86

218

–

(–)

Location

dKolmogorov

b

Notes a

Values of G apply to the bulk sludge mixture.

b

dKolmogorov is strictly defined for fully turbulent flow; the values here are qualitative indicators only [cf. 602].

c

This G may be a factor of 4 too low (see discussion in text); the number quoted is the time-weighted mean [cf.

228, 427] of five values ranging from G = 266 to 2193s‒1. These imply dKolmogorov = 53 to 153μm.

Table 7-8: Shear schedule for limiting alternative effective viscosities.

Location

η→∞

η = 1mPa.s Ga

Re

dKolmogorov

Ga

Re

[s‒1]

[–]

[μm]

[s‒1]

[–]

[μm]

Upstream

464

4.5×103

46

280

0

(∞)

Narrow tubing

765

4.2×103

41

474

0

(∞)

Wide tubing

172

2.7×103

86

124

0

(∞)

1045 c

–

35 c

580 c

0

(∞)

334

–

–

218

0

(∞)

Downstream fittings Downstream total

dKolmogorov

b

Notes a

Values of G apply to the bulk fluid.

b

dKolmogorov is strictly defined for fully turbulent flow; the values here are qualitative indicators only [cf. 602].

c

This G may be a factor of 4 too low (see discussion in text); the number quoted is the time-weighted mean [cf.

228, 427] of five values. For η = 1mPa.s, G = 408 to 4502s‒1, implying dKolmogorov = 17 to 56μm.


405

D. I. VERRELLI

We may consider the sensitivity of the shear schedule to the estimated effective sludge viscosity. Table 7-8 provides values of G, Re and dKolmogorov for the two physical limits, namely sludge viscosity identical to water viscosity, and sludge viscosity approaching infinity (as it would theoretically at low shear strain rates). For the low-viscosity limit G roughly doubles, the flow is everywhere turbulent with Re about 5 times higher, and dKolmogorov drops by a factor of about 3. Of especial interest is the high-viscosity limit, which shows that G does not change! This is due to the cancellation between increases in the friction factor and the viscosity: [fFanning]laminar ∝ 1 / Re ∝ η.

Of course, the computations presume that the mixture is microscopically * homogeneous, whereas in fact the sludge contains quasi-solid aggregates, through which there may be negligible flow. In such a case the fluid transport is restricted to the much more confined space between aggregates. The l o c a l fluid velocity, and shear forces, may then be quite high at the aggregate surfaces, while decaying essentially to zero within the aggregates. Naturally we resort to a c h a r a c t e r i s t i c velocity gradient because we anticipate that there will be a distribution of shear in the fluid; what is different here is that the distribution may be distorted and wider due to the presence of the aggregates. There is insufficient information to make such corrections, and the benefit of doing so would be minor.

Other factors that were deemed negligible include material thixotropy and

formation of a liquid film at the tube wall due to particle migration [527] [cf. 874]. With regard to thixotropy, by cycling over a period of 10 minutes — far longer than the rig residence time — the effective viscosity appeared to progressively decrease by less than 10%. Quantitation of shear reduction due to formation of a particle-free boundary layer is problematic, especially with floc sizes approaching the diameter of the tubing itself. No obvious boundary layers were observed through the clear tubing in the experiments. It is also noted that wall ‘slip’ effects are more important at lower shear strain rates [527].

Given the care taken to generate a reproducible shear history, concerns arose over damage to flocs upon loading into cylinders for settling tests. Hence the settling cylinders were loaded

*

406

The relevant lengthscale is presumably of order dKolmogorov (in turbulent flow).



directly from the shear rig: the outlet tube was placed inside the mouth [cf. 281] of the inclined cylinder once steady-state was reached.

(This conforms to VESILIND’s (1979)

recommendation [282].) Two exceptions were the pH 5.9 sheared sample and one run of the Zetag 7623-conditioned sample. In the former case it is expected that incidental shear would be negligible compared to the shear imposed in the shear rig. In the latter case a second settling test was loaded directly from the outlet. While the direct-filling technique minimised incidental shear damage to the flocs upon loading, it also resulted in very high values of φ0 for the settling tests — namely at or above φg (cf. Table 7-4 *). Therefore these settling tests may not yield entirely reliable data.

Of course, damage may also occur upon loading the filtration rig. It was not possible to load this directly from the shear-rig outlet, and so instead extra care was taken to minimise shear through manual loading. Furthermore, settling of the conditioned flocs in the sample vessel meant that it was difficult to load a representative sample. The most reliable technique found was to use a TRULLA spatula to gently scoop up wads of floc and transfer these to the cell. It is expected that incidental shear will have less effect on dewaterability under the higher pressures of filtration.

7▪4▪1▪4

Characterisation

The conditioned sludge proved problematic to characterise in terms of R(φ).

The

conventional method of stepped pressure ‘permeability’ testing often failed for these materials because of: • difficulty in loading a uniform, representative sample without excessive shear; • rapid drainage at lower solidosities; and • rapid (in time) onset of cake compression — for the material as loaded, although some water was able to drain through freely (suggesting a high rate of dewatering), the remaining structure of saturated flocs was quite strong. It was therefore necessary to estimate resistance to dewatering by extrapolating filtration data to obtain the solids diffusivity at φ∞, and from this computing R(φ∞).

*

Actual φ0 values are slightly lower, as Table 7-4 is based on the influent to the shear rig.


407

D. I. VERRELLI

A couple of ‘permeation’ runs were attempted, but these did not yield good data due to: problems loading a sample (shearing, settling); channelling, air break-through, and non-onedimensional dewatering in the air-driven rig [as in 926]; and inability to remove the piston from the cell (to add supernatant) without damaging the cake after piston-driven compression.

The ‘extrapolation’ technique relies on estimating parameters in an equation describing the limiting filtration behaviour as t → ∞ by fitting the equation to experimental ‘compressibility’ filtration run data.

Fitting the data to equation 2-125b yields an estimate of D (φ∞) by

equation 2-127, which in turn permits estimation of R(φ∞) by equation 2-63. The procedure was described by DE KRETSER, SCALES & USHER [606], and by USHER [1063], and was found to produce reasonable estimates of dewatering behaviour for the model zirconium oxide system. The process is somewhat subjective, and optimisation, error/sensitivity analysis, and additional validation work has been carried out (§7▪4▪4).

7▪4▪2

Polymer dose selection

CST results are presented in Figure 7-6 (pH 5.9) and Figure 7-7 (pH 8.9).

The two graphs show fairly similar behaviour, although the CST values for the low-pH sludge are around twice as high. This is somewhat surprising in view of the conclusions reached in Chapter 5, but can be explained by the differences in φ0. It is seen that imposition of ‘high’ shear causes an increase in the CST, corresponding to a decrease in dewatering rate. Presumably this is due to disruption of aggregate or network structure, creating fine fragments, ultimately yielding a mixture with finer pores which hinder fluid escape. The effect may alternatively be explained by the entrained air bubbles observed, which could also block and restrain the flow of liquid.

408



C.S.T. [s]

control

+air

pin

1mm

4mm

10 to 15mm

5 to 8mm

1mm

pin

0.5mm

1.0 to 1.5mm

5 to 8mm

N/A

400

400

350

350

300

300

250

250

200

200

150

150

100

100

50

50

Pure water

2 mL of 2g/L Zetag 7623

1.5 mL of 2g/L Zetag 7623



2 mL of 5g/L Magnafloc 338

1.6 mL of 5g/L Magnafloc 338





None

Sheared

0

0

Figure 7-6: CST values for an 80mg(Al)/L pH 5.9 laboratory sludge at φ0 ≈ 0.0026 conditioned with Magnafloc 338 and Zetag 7623 at various doses. The boxes span the interquartile ranges, the bars span the observed ranges, and the markers represent the medians.

Labels at top are

summary descriptions of floc size.

C.S.T. [s]

control

+air

0.5mm

0.5mm

1 to 2mm

>1mm

N/A

N/A

180

180

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

20

Pure water

Supernatant





Sheared

0 None

0

Figure 7-7: CST values for an 80mg(Al)/L pH 8.9 laboratory sludge at φ0 ≈ 0.0016 conditioned with Zetag 7623 at various doses. Symbols and labels as in Figure 7-6. 7▪4 : After settling: shear and polymer conditioning

409

D. I. VERRELLI

Even quite low doses of polymer are able to compensate for the shear effect, although visible flocculation may not have occurred. For all cases there is a clear trend for floc size to increase with increasing polymer dose, with an associated progressive drop in CST. The optimally flocculated cases have CST’s that approximately match the CST for pure water or the supernatant, which suggests that those flocs are essentially freely draining. (Nominally this draining occurs in the CST cell, but in practice the loaded sub-sample may contain excess ‘free’ liquid due to rapid draining in the 150mL beaker.) It may be noted that the CST’s reported here for water and supernatant are of order 60s, which is greater than commonly observed [e.g. 130, 789]. Given that the results were reproducible, this difference may be attributable to the age of the chromatography paper. Judging by Figure 7-6, the slightly cationic polymer appears to be more efficient than the slightly anionic polymer. It can also be seen that the efficacy of the polymers depends upon the strength of the solution dosed, with decreased efficacy at the higher concentration (i.e. 5g/L). This is presumably due to difficulty dispersing the more viscous polymer solution throughout the sludge.

These measurements led to the choice of polymer doses listed in Table 7-4.

7▪4▪3

Preliminary findings

Before presenting the overlaid results, it is worthwhile discussing the hindered settling function estimates obtained for the two most problematic materials, which were the two sludges conditioned with 40mg/L Zetag 7623. These estimates are presented in Figure 7-8 and Figure 7-9.

Figure 7-8 displays estimates obtained from two stepped-pressure ‘permeability’ runs, and

from the extrapolation method applied to a stepped-pressure ‘compressibility’ run. The latter results are shown as both the original estimates, and in their more-relevant scaled form. The scaling is simply division by a factor of 2.5 — the derivation of this factor is described in §7▪4▪4▪3.

410



The pair of very low R estimates were obtained from a permeability run that went into compression after the first two pressures. Hence there is automatically a problem with the numerical estimation of the rate of change of the filtration kinetics with respect to pressure. Close inspection of the raw permeability run data indicates that constant dt/dV 2 behaviour had not quite been achieved. Another likely reason why these points are so low compared to the other estimates is that the material loaded contained macroscopic pores (between the large, gelatinous flocs) that dewatered/drained readily. Also, in this first run the sludge was carefully poured in, but this nonetheless caused shear rupture of the flocs and separation of the solid and liquid phases; in subsequent experiments on conditioned sludges the materials were carefully transferred in by spatula, which seemed to result in less shear (and probably also increased φ0). The other stepped-pressure permeability run was very well-behaved. By this time all of the properly conditioned sludge had been consumed. However the material generated while the mixing device was coming up to steady state had been collected, and this was carefully loaded and filtered. It is reasonable to expect that this material would have properties intermediate to those of the unconditioned sludge and those of the properly (steady-state) conditioned sludge. Both the unscaled and scaled extrapolation-based estimates lie above the other estimates, but exhibit the same trend as the pre-steady state data. As these results were derived from properly conditioned material loaded by spatula, it is expected that the scaled extrapolationbased results will be most accurate (provided the scaling factor is appropriate).

Figure 7-9 presents data from a stepped-pressure ‘permeability’ run and from the

extrapolation method applied to a stepped-pressure ‘compressibility’ run. The material is the same as in Figure 7-8, except that the coagulation pH was higher. The permeability run exhibited erratic ‘steady’ values of dt/dV 2 for the first four pressures, and then went into compression (in fact, cake compression may have commenced even before this). There were no apparent problems with the compressibility data analysed by the extrapolation method.


411

D. I. VERRELLI

2


1.0E+16

1.0E+15

1.0E+14

Stepped p: aborted Extrapolation P1 Extrapolation P2 Extrapolation R1 Extrapolation R2 Extrap'n P1: scaled Extrap'n P2: scaled Extrap'n R1: scaled Extrap'n R2: scaled Stepped p: preSS Power fit Linear fit Exp. fits Exp. fits

1.0E+13

1.0E+12

1.0E+11 0.01


Figure 7-8: Hindered settling function estimates by various methods for an 80mg(Al)/L pH 5.9 laboratory sludge conditioned with 40mg/L Zetag 7623, listed chronologically. “preSS” denotes material collected before the conditioning operation had reached steady state.

The stepped-pressure permeability estimates were subjected to a jackknife-type analysis [cf. 336] (cf. §S15▪2▪2), in which the calculations were repeated after systematically removing each of the four data points. This analysis shows that the first data point is highly influential: removing it leads to a large increase in the estimates of R almost up to the scaled extrapolation curve, which supports the notion that the estimates based on all four points may be too low.

412



2


1.0E+16

1.0E+15

1.0E+14 Stepped p Stepped p: Jack Extrapolation 1 Extrapolation 2 Extrap'n 1: scaled Extrap'n 2: scaled Power fit Linear fit Unscaled exp. fit Scaled exp. fit

1.0E+13

1.0E+12

1.0E+11 0.01


Figure 7-9: Hindered settling function estimates by various methods for an 80mg(Al)/L pH 8.9 laboratory sludge conditioned with 40mg/L Zetag 7623. “Jack” denotes jackknife results (iterative removal of individual raw data points and re-estimation).

The data overall looks similar to Figure 7-8, in that the unscaled and scaled extrapolationbased estimates lie above the permeability-based estimates, but follow the same trend. Beyond this, it is noteworthy that the hindered settling function values for the conditioned high-pH material seem to lie above (or to the right of) the corresponding values for the pH 6 material — this mimics the behaviour already identified for unconditioned WTP sludges.

A detailed analysis of the practical numerical procedure in which the extrapolation technique is implemented, including the scaling ‘correction’, is presented in the following


413

D. I. VERRELLI

section. For the sludges considered above, the scaled hindered settling function data from the extrapolation method appear to be the best estimates, and are thus the estimates used in the final comparison charts in §7▪4▪5.

7▪4▪4

Optimisation, error/sensitivity analysis, and calibration and validation

7▪4▪4▪1

Optimisation

The computation of φ∞ and hence D (φ∞) by extrapolation of ‘compressibility’ filtration data (in which the run goes ‘practically’ to completion) is a subjective process. The method requires fitting the data around the end of the cake compression stage with the logarithmic equation describing the limiting behaviour (according to the theory) as t → ∞.

There are a few considerations on the sub-set of data to use for the curve-fitting: • Strict applicability of the equation only in the above limit suggests that a few data points right at the end of the run should be taken. • Real experimental data contains ‘noise’, which suggests that many data points should be used to fit the equation parameters. • Experience shows that the last couple of data points regularly contain large relative errors, suggesting that the data points at the very end of the run should be treated with suspicion, and potentially discarded. Clearly these considerations are not all compatible. It is best to repeat the evaluation for a number of sub-sets, and select a ‘best case’ based on any trends identified (e.g. parameter value decreasing as sub-set moved closer to end of run) and on relevant ‘goodness of fit’ statistics. The compromise generally reached for WTP sludges is a sub-set of ‘moderate’ length (around 80 points), excluding only a few of the last data points of the run.

Additionally, the parameter estimation is limited by practical experimental constraints, in that the run (or cake compression stage) may not contain very many data points or may have ended quite far from equilibrium. An assessment on the validity of this method must be made in each case, and in some cases it must be concluded that the method cannot be 414



applied. By way of example, the method is unsuitable for ‘incompressible’ materials (e.g. sand) and for otherwise compressible materials that commence the filtration in a state close to the equilibrium state (e.g. the final stage of a stepped-pressure compressibility test, in which a cake compressed to practical equilibrium at 200kPa is further compressed at 300kPa).

7▪4▪4▪2

Error/sensitivity analysis

As alluded to above, the extrapolation technique is somewhat subjective. Furthermore, reliance on experimental data raises the question of possible ‘noise’ in the raw data. Consequently, it is of interest to examine the sensitivity of the estimates to both experimental random error and procedural specification.

7▪4▪4▪2(a)

Sub-set selection

Sensitivity of the estimates to the selection of the data sub-set for curve fitting and extrapolation can readily be explored in a qualitative fashion by comparing the results based on several choices of sub-set. Typical results, from artificial data *, are presented in Figure 7-10. Based on the inputs, the true values of D (φ∞) and φ∞ were 6.104×10‒9m2/s and 0.02613,

respectively.

Considering first the left-hand column, it can be seen that taking too many or too few points will likely lead to poor estimates: there is an optimal sub-set size. Choosing the value with the highest R2 statistic may not give the best choice, but will often give a reasonable result.

*

The data were produced by fitting the one-term exponential model to real experimental data to obtain a smooth curve (‘base case’) with realistic properties, and then adding a contribution from the second term in the theoretical equation (equation 2-124, cf. §S4) and introducing pseudo-random noise (cf. §S15▪2▪3▪4) in both t and V.


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D. I. VERRELLI

6.0E-9

0.997

4.0E-9 0.996 D(φ_∞) R²(E3)

0.0E+0 0

100

300

400

0.998 D(φ_∞) long D(φ_∞) short R²(E3) long R²(E3) short

2.5E-8 2.0E-8 1.5E-8

0.997

1.0E-8

0.996

5.0E-9

0.995 200

3.0E-8

0.0E+0

500

0.995 0

50

Data points included at end [–]

100

150

200

250

Data points truncated from end [–]

1.000

0.0300

1.000

0.0300

0.0290 0.999

0.0290

0.0280

0.999

0.0280

0.0270

0.0270

0.0260

0.997

0.0260

R [–]

0.0250

2

2

0.0250

0.998 φ [–]

R [–]

0.998

0.0240

0.0240

0.997

0.0230 0.996

0.0220

R²(V²) φ_∞ φ_f (truncated)

0.995 0

100

200

300

400

0.996

0.995

500

0


50

100

0.0220 0.0210 0.0200 150

200

250


1.200

1.200

1.000

1.000

0.800

0.800 R [–]

0.600

2

2

R [–]

0.0230

R²(V²) long R²(V²) short φ_∞ long φ_∞ short φ_f (truncated)

0.0210 0.0200

φ [–]

2.0E-9

0.999

3.5E-8

[–]

0.998 8.0E-9

4.0E-8

2 R for ln(E 3 – V ) versus E 1–E 2ln(E 3–V )

1.0E-8

1.000

4.5E-8 2 Solids diffusivity, D [m /s]

0.999

[–]


1.2E-8

5.0E-8 2 R for ln(E 3 – V ) versus E 1–E 2ln(E 3–V )

1.000 1.4E-8

0.600

0.400

0.400

0.200

0.200

R²(dt/dV²) long R²(dt/dV²) short

R²(dt/dV²) 0.000

0.000 0

100

200

300

400


500

0

50

100

150

200

250


Figure 7-10: Sensitivity of parameter estimates to sub-set specification. Left-hand column: sub-sets of various lengths, finishing at the last available data point. Right-hand column: sub-sets of constant lengths (50 and 250 points), finishing before the last available data point. Top row: Solids diffusivity and R2 statistic for fitting parameter E3 (validity of linearity assumption). Middle row: Equilibrium solidosity and R2 statistic for V 2 data (~ time-dependent extent). Bottom row: R2 statistic for dt/dV 2 data (~ time-dependent rate).

416



The estimates in the right-hand column trend closer to the true values as data from longer times is used, as expected, although scatter may be significant for specific sub-set sizes. An important observation from the right-hand column is that the estimates are basically unaffected by excluding the last 50 data points in the set: this gives confidence in the procedure, as it suggests that even if more data points had been collected in the experiment, the estimates would not change significantly. Unfortunately this is often not the case for real experimental data, where the estimates of φ∞ simply follow φf (that is, the solidosity when the experiment finished). Such cases suggest that if more data had been collected (or used), then the estimates could potentially change significantly.

The graphs in Figure 7-10 also show that outliers can be generated. This emphasises the importance of not relying blindly on an arbitrary choice of sub-set to fit. Generally, graphing is the easiest way to identify suspect results.

Finally, the bottom row of Figure 7-10 indicates that the agreement of the filtration rate data is not very good. Clearly the a v e r a g e rate is about right, as the time-dependent filtrate volume is predicted well. The conclusion is that the functional form does not capture exactly the long-time filtration behaviour. (Again, although the analysis in Figure 7-10 uses artificial data, the same tendency is observed for real data.)

7▪4▪4▪2(b)

Experimental and fitting errors

Experimental and fitting errors (combined) can be assessed in a q u a l i t a t i v e fashion by observing the s c a t t e r as the sub-set specification is varied (as in Figure 7-10). This resonates to some degree with the position taken by ALPER & GELB [89] that in many practical situations the “experimental uncertainties” are most reliably estimated by the “traditional ‘experimental’ method of simply repeating a given measurement an appropriate number of times”. The key disadvantages of this are that obtaining more data may make considerable demands on resources (e.g. personnel time), and the experimental and fitting (or model) errors cannot really be discriminated.


417

D. I. VERRELLI

3.0E-8

0.996 1.5E-8 0.994 1.0E-8 0.992

5.0E-9 D(φ_∞) R²(E3)

0.0E+0 0

100

200

300

400

[–]

2.0E-8

[–]

0.998

R2 for ln(E 3 – V ) versus E 1–E 2ln(E 3–V )

Solids diffusivity, D [m2/s]

2.5E-8

2 R for ln(E 3 – V ) versus E 1–E 2ln(E 3–V )

1.000

0.990

500


3.5E-8

1.000


3.0E-8 0.998 2.5E-8 D(φ_∞) long D(φ_∞) short R²(E3) long R²(E3) short

2.0E-8 1.5E-8

0.996

0.994

1.0E-8 0.992 5.0E-9 0.0E+0

0.990 0

50

100

150

200

250


Figure 7-11: Error estimates (95% confidence intervals) on the equilibrium solids diffusivity and R2 statistic for fitting parameter E3. The material was 80mg(Al)/L, pH 5.9 alum sludge conditioned with Zetag 7623. The filtration pressure was 5kPa. See also the caption to Figure 7-10.

418



A basic approach to approximate fitting errors is to generate confidence intervals on parameters E1 and E2 by extending the ordinary least squares regression analysis and assuming a simple error condition, namely uncorrelated, random errors with a GAUSSian distribution [see 755]. There are two problems with this approach. First, it is unable to estimate the error in E3, which is used to calculate the solids diffusivity.

Second, by

excluding E3, the margins for error in E1 and E2 will be underestimated (see §S15▪1).

A more sophisticated approach lies in assuming an a s y m p t o t i c a l l y GAUSSian error distribution and evaluating the covariance matrix [see 574, 755, 1136]. This would estimate errors in all three parameters, but would still not be entirely valid given the non-linearity of the equations in the present system [755, 1136]. In any case, the present system appears to be numerically ill-conditioned, and it has not been possible to obtain reliable results using this technique. (ALPER & GELB [89] presented a variation of this procedure involving Monte Carlo estimation, but it relies on accurate knowledge of the residuals’ properties.)

Finally, the recommended approach for accurate error analysis is to bootstrap the data points [see 336, 464] (separately for each sub-set of interest). The bias-corrected, accelerated form was adopted. This is a newer statistical technique that is conceptually straightforward, but requires lengthy (automated) computer processing. It has the advantages of not requiring any assumptions about the underlying population, and is able to provide error estimates on any parameter, even those evaluated numerically. Details are provided in Appendix S15. Selected confidence intervals (95%) are shown in Figure 7-11 for a conditioned alum sludge filtered at 5kPa. Key observations from the analysis are that the uncertainty in the estimate of D (φ∞) tends to decrease as the sub-set size is increased and as the selection moves to longer times (towards the end of the run). However the errors in the estimated parameters are typically less than the variation due to alternative sub-set selection. (Note that the bootstrap-derived confidence intervals are wider than those obtained by the other methods described.) It may be concluded that it is n o t necessary to conduct a bootstrap error analysis such as the foregoing on a r o u t i n e basis; the recommended sub-set selection analysis will show the dominant effect.


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D. I. VERRELLI

7▪4▪4▪3

Calibration and validation

7▪4▪4▪3(a)

Approach

As noted above, validation work on the extrapolation method was reported previously by DE KRETSER, SCALES & USHER [606] and by USHER [1063] for a model zirconium oxide system that was coagulated by adjusting the pH to just below the iso-electric point. The result presented is reproduced in Figure 7-12.

3.0E-07 Method 1 Method 2 PhiEnd Est

2 -1

D(φ) (m s )

2.5E-07 2.0E-07 1.5E-07 1.0E-07 5.0E-08 0.0E+00 0.1

0.15

0.2

0.25

0.3

0.35

0.4

Volume Fraction Figure 7-12: Comparison of D (φ∞) data determined from stepped pressure ‘permeability’ run analysis (by two methods) and from the extrapolation method (φ∞ estimation) for zirconia at pH 7.0 [reproduced from 606].

There are two concerns that may be raised. First, in Figure 7-12 there appears to be more scatter in the estimates obtained from the extrapolation method than in the other two methods, with some possible outliers. If just one or two of the “PhiEnd Est” points were omitted, the apparent trends and the conclusions drawn may change significantly. In the original paper [606] the scatter was attributed to “instabilities [in] the filtration data” at very low pressures (1 and 2kPa — below the 5kPa minimum of the present work). 420



The second caveat is that dewatering of the zirconia system described would be more ‘ r e v e r s i b l e ’ than for a material aggregated via either sweep coagulation or polymer flocculation/conditioning.

For example, the dewatered zirconia could conceivably be

resuspended in electrolyte and returned to its original condition (supported to some extent by the experiments of GREEN [422, 424, 425] and CHANNELL et alii [241]);

that is not

conceivable for the WTP sludges studied in the present work. The WTP sludge aggregates are expected to undergo i r r e v e r s i b l e structural deformation and rupture as filtration proceeds [cf. (for thickening) 1139], so that the structure present at the end of the cake c o m p r e s s i o n stage (as used for the D (φ∞) extrapolation method) may be quite different to a structure representative of the cake f o r m a t i o n stage (as used for the stepped-pressure ‘permeability’ run method).

The validation approach of DE KRETSER, SCALES & USHER [606] has been applied now to three WTP sludges. The extrapolation method was required for the two Zetag 7623-conditioned sludges, as these formed large, gelatinous flocs with a structure that defied characterisation by the routine stepped-pressure ‘permeability’ route (see Figure 7-17 and associated discussion). The samples chosen for validation data were: • unconditioned 80mg(Al)/L, pH 5.9 sludge; • the same sludge conditioned with Magnafloc 338 (this polymer did not yield as great a change in floc structure upon conditioning, such that the ‘permeability’ method was still feasible); and • unconditioned 80mg(Al)/L, pH 8.9 sludge. While it was not possible to validate the method using the Zetag 7623-conditioned sludges directly, the materials chosen are as similar as possible (i.e. with identical coagulation conditions, but either without conditioning or with a different polymer), and are believed to be sufficiently representative.

7▪4▪4▪3(b)

Moderate-pH sludges

Estimates from the two different methods are presented for each of the pH 5.9 materials in Figure 7-13 and Figure 7-14. It can be seen that generally the ‘extrapolation’ method yields

higher estimates than the ‘permeability’ method.

Aside from a few outliers (perhaps


421

D. I. VERRELLI

consistent in the last pressure, where there are fewest data points), the two methods predict the same trends. When the outliers are excluded, in both cases the ‘extrapolation’ method overestimates * the value of R by a factor of approximately 2 to 2.5. The results have not validated the ‘extrapolation’ method, but rather cast doubt upon it. The objectives thus become identification of the cause(s) of the discrepancy and calibration of a correction factor (or function).

It is important to note that such a discrepancy does not seem explicable by the ‘subjective’ choice of D (φ∞) outlined in the discussion of sub-set selection (§7▪4▪4▪2(a)) nor can it be explained by experimental error leading to imperfect curve fits (§7▪4▪4▪2(b)), as the uncertainty stemming from these two sources is significantly smaller than a factor of 2.5 (in many, but not all, cases). It is likely that the discrepancy arises due to i r r e v e r s i b l e microscopic s t r u c t u r a l c h a n g e s that occur as WTP sludges are compressed, which may be less significant for more ‘reversibly coagulated’ systems.

Given that two materials are unable to be reliably characterised by any other method, the only practical option † currently seems to be to scale the extrapolation-method estimates down by a simple factor — there is insufficient information for any more complicated function.

This scaling has been carried out on the data presented in the ‘Preliminary

findings’ section (§7▪4▪3), and the factor adopted was 2.5 (constant). The larger factor was chosen on account of the occasionally much larger errors associated with the points identified as outliers in this preliminary validation study.

*

The stepped-pressure ‘permeability’ run estimates may be assumed to be correct here (vide infra).

†

It would, in principle, be possible to iteratively amend the estimates of R(φ) by conducting filter modelling to re-predict (say) experimental h(t) profiles. In practice it would require a great deal of effort to estimate R(φ) by this technique a priori (as distinct from the a posteriori validation carried out in this section, vide infra) — just as has been done in the analysis of transient batch centrifugation data (see §3▪5▪2▪2).

422



2


1.E+16

1.E+15

1.E+14

Stepped 'permeability' Extrapolation 1 Extrapolation 2 Power fit Linear fit

1.E+13

1.E+12 0.00

0.02

0.04

0.06

0.08

0.10

0.12


Figure 7-13: Comparison of estimates of R for an 80mg(Al)/L, pH 5.9 laboratory sludge.

2


1.E+16

1.E+15

1.E+14

Stepped 'permeability' Extrapolation 1 Extrapolation 2 Power fit Linear fit

1.E+13

1.E+12 0.00

0.02

0.04

0.06

0.08

0.10

0.12


Figure 7-14: As in Figure 7-13, except after conditioning the sludge with 90mg/L Magnafloc 338.


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D. I. VERRELLI

Part of the experimental filtration data h(t) was re-predicted for the moderate-pH materials plotted in Figure 7-15 and Figure 7-16, and all showed good agreement (not presented here). This is a validation of both the stepped-pressure ‘permeability’ method (where good data could be obtained) and the correction factor of 2.5 calibrated as described above. It is recommended that additional samples be analysed in this way to confirm that the factor of 2.5 is reasonable (cf. §7▪4▪4▪3(c)).

7▪4▪4▪3(c)

High-pH sludges

While both Figure 7-13 and Figure 7-14 suggested a correction factor of 2.5 (also supported by filtration data re-prediction), the pH 8.9 unconditioned sludge might be a more suitable candidate for determining a correction factor for the pH 8.9 Zetag 7623-conditioned sludge.

Following the same procedure as in §7▪4▪4▪3(b), the ‘extrapolation’ method estimates were found to be a factor of 4.5 (not 2.5) greater than the estimates obtained from the usual stepped-pressure ‘permeability’ method (chart not presented here). For the unconditioned sludge there was no obvious reason to doubt the correctness of the ‘permeability’ results.

Given the association of high pH with rapid precipitation and

aggregation, leading to more open aggregate structures, a higher correction factor relative to the pH 5.9 sludges could be linked with aggregates that are more fragile, and thus undergo greater structural changes. Although no obvious fault could be found in the stepped-pressure data or analysis, subsequent modelling of laboratory h(t) filtration profiles indicated that the ‘permeability’ estimates of R were t o o l o w . Good agreement between the experimental filtration profiles and the re-predictions for the high-pH materials was obtained when: • estimates of R obtained by the ‘ e x t r a p o l a t i o n ’ method are r e d u c e d by a factor of 2 . 5 (identical to that found for the moderate-pH sludges) • estimates of R obtained by the standard stepped-pressure ‘ p e r m e a b i l i t y ’ technique are i n c r e a s e d by a factor of 4 . 5 / 2 . 5 = 1 . 8 . These scalings have been applied in Figure 7-15 and Figure 7-16.

424



At this stage it is not clear why the stepped-pressure ‘permeability’ method would underestimate R for the high-pH sludges.

The modelling results which led to this

assessment cannot be considered entirely conclusive, given that these too can contain errors (cf. §S13▪7), and so more work would be required to establish this with greater certainty. For this section the filter modelling was set up to re-predict h(t) for a stepped-pressure ‘compressibility’ run going from an applied pressure of 20kPa(g) to 50kPa(g). This avoids the problem of reliance upon interpolated data down to φ0 ~ φg. It also avoid the highest pressure data, where cake heights are small (larger relative errors). The py(φ) curve fit was also adapted specifically for this pressure interval.

Membrane resistance was assumed

negligible, given that the starting material was a cake consolidated approximately to equilibrium at 20kPa(g). The errors in this modelling are thus expected to be less significant than those encountered for the work in §S13▪7. The assessment of underestimation is certainly plausible, and is supported by the consequent constancy of the ‘extrapolation’ method correction factor as 2.5. Therefore it has been used to ensure a consistent basis for comparison throughout §7▪4▪5. (An alternative approach would have been to assume that all of the estimates obtained from ‘permeability’ runs are correct, and hence apply different correction factors for the ‘extrapolation’ estimates — namely 2.5 at moderate pH and 4.5 at high pH.) However the reader should note well that n o scalings have been applied to estimates of R outside of this context.

7▪4▪5

Principal results

Figure 7-15 and Figure 7-16 are the master plots of py(φ) and R(φ) for the control, sheared,

and conditioned sludges. It is important to note that a l l o f t h e s e h i g h - p H R ( φ ) c u r v e s h a v e b e e n s h i f t e d . While all of the estimates of R obtained using the extrapolation method were found to be too high by a factor of 2.5, the estimates obtained from the usual steppedpressure ‘permeability’ method were too low by a factor of ~4.5 / 2.5 = 1.8 for the high-pH sludges.

This was validated by re-predicting experimental filtration h(t) profiles (see

§7▪4▪4▪3).


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D. I. VERRELLI

In both graphs the relative i n s e n s i t i v i t y of sludge dewatering behaviour to shearing or conditioning (after settling) is evident.

While some variation does exist, and will be

discussed below, the degree is smaller than that caused by pH or coagulant changes (see §5). Furthermore, the difficulty in characterising the conditioned sludges means that the experimental uncertainty for these samples is greater. Based on extensive validation work (see §7▪4▪4▪3) the filtration data for the conditioned sludges is believed to be of similar accuracy to the other samples. However quantifying the settling characteristics remained problematic.

This is a surprising result. Certainly, the materials a s l o a d e d appeared different. It must be concluded that at the high solidosities pertaining to filtration e q u i l i b r i u m , any dewaterability enhancement has been removed — if not marginally reversed. From these results it seems probable that any improvement in the dewaterability parameters py(φ) and R(φ) must be occurring at lower values of φ. The above does n o t imply that conditioning (or shearing) will not affect filtration behaviour, as the filtration kinetics will depend on dewatering properties for solidosities in the complete range from φ0 to φ∞, i.e. below those reported here. This emphasises the need (see also §S10, §S13▪7) to obtain further dewaterability information at intermediate φ, such as by centrifugation.

Examining the compressive yield stress data of Figure 7-15 in greater detail, it appears that there may be a marginal deterioration in dewaterability at large φ due to the high-shear processing, which is not evident in the conditioned sludge (even though this material was exposed to the same shear schedule). The shifts are small, albeit consistent, and it is not certain from these two tests if it is a universal result, or instead a coincidence due to minor experimental error. Conversely, there is a p p a r e n t l y a significant increase in the gel point (at small φ) for all of the processed sludges. Two curves are presented for the high-pH sheared sludge and for the low-pH Zetag sludge. In the former case, the settling h(t) profile plateaued at about 20d, but then underwent a

426



sharp drop commencing around day 70. The curve to the left is obtained by excluding this suspicious long-time data, which might be due to some physical knock *. In the latter case two settling experiments were run (see §7▪4▪1▪3, p. 407). The direct-filled run yields the curve to the right, attributable to the greater φ0. The experimental uncertainty implicit in the results for this pair of sludges suggests that the increase in φg for the processed sludges is at least partly overestimated.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3

80mg(Al)/L, pH 8.9 "80/8.9" + sheared ... + 40mg/L Zetag 7623 80mg(Al)/L, pH 5.9 "80/5.9" + sheared ... + 40mg/L Zetag 7623 ... + 90mg/L M'floc 338

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

Solidosity, φ [–] Figure 7-15: Compressive yield stress curves for high-alum-dose WTP sludges at moderate and high pH — coagulated only, sheared, and conditioned cases.

*

It could not be matched chronologically with any other artefacts in companion settling tests, which thus argues against an ambient vibration effect.


427

D. I. VERRELLI

2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08

80mg(Al)/L, pH 8.9 "80/8.9" + sheared ... + 40mg/L Zetag 7623 80mg(Al)/L, pH 5.9 "80/5.9" + sheared ... + 40mg/L Zetag 7623 ... + 90mg/L M'floc 338

1.E+07 1.E+06 1.E-4

1.E-3

1.E-2

1.E-1

Solidosity, φ [–] Figure 7-16: Hindered settling function curves for high-alum-dose WTP sludges at moderate and high pH — coagulated only, sheared, and conditioned cases.

High-pH curves have been

appropriately shifted (see text), and are not directly comparable with results presented elsewhere.

Looking in detail at Figure 7-16, there is a similar marginal deterioration in dewaterability shown for the processed sludges at large φ. These are consistent with the shifts in py(φ). The difference is clearer for the sheared samples, for which the comparison is also more precise, as the same methodology was used for the sheared and control samples. At small φ there is a p p a r e n t l y a significant decrease in R for the processed sludges. This is better understood as a shift to greater φ, consistent with the apparent increase in φg. Again two curves are presented for the abovementioned sludges, showing some variation.

428



It should also be noted that two of the conditioned sludges exhibited ‘considerable’ induction times prior to settling. Amazingly, the direct-filled pH 5.9 Zetag sample did not settle at all for 3 days, and then entered a normal settling mode. The pH 8.9 Zetag sample did not settle at all for 117 days (aside from an artefact due to minor evaporation losses), and settling could only be induced by inverting the cylinder so as to impose gentle shear and break up the evidently strong network formed. This resulted in only a small degree of settling (from which it may be concluded that φ0 was too high). The low-φ value of R for this particular sample may thus be regarded as more indicative of the measurement conditions than of the true material properties. Induction time phenomena are discussed more fully in §9▪1. Despite the experimental uncertainty, the consistent tendency of the processed samples to exhibit lower R(φ) curves supports the proposition that a real effect exists, albeit of uncertain magnitude.

7▪4▪6

Discussion

Earlier in this section it was suggested that some experimental problems arose because supernatant was partly separating from flocs prior to and upon loading, and that a portion was able to freely drain through the flocs with little resistance. The schematic of Figure 7-17 illustrates why liquid may be able to drain more readily from conditioned systems. The dewatering analysis assumes that the mixture is homogenous on a macroscopic scale; violations of this assumption, such as where channelling occurs, render the analysis invalid, because the analysis works on the basis that liquid is flowing through the mixture of (uniform) average solidosity. If instead the fluid is flowing a r o u n d larger lumps, then inconsistent results will be obtained. Of course, systems such as those depicted on the left of Figure 7-17 may occur in practice. The problem of how to deal with them lies in the specification of the two key dewatering parameters as simple functions of solidosity only, that is py(φ) and R(φ).

Whereas the

conditioned system suggests that φ itself could be expressed as the product of two volume fractions, viz.


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D. I. VERRELLI

 V φ =  flocs  Vsystem 

  Vsolids    = (φ ) (φfloc ) .   Vflocs  

[7-2]

So for conditioned systems it would be more appropriate to write py(φ, φfloc) and R(φ, φfloc). Or, alternatively, py(φ, φ) and R(φ, φ). (VAN DE VEN & HUNTER [1069] effectively correlated the shear properties of coagulated systems with both φ and φagg ≅ φfloc.) This system, in which the flocs better retain their distinct identities even upon formation of a network, is observed with other materials too, for example cheese curd in whey [1030]. It is different again to either fractal or multilevel i n t e r n a l aggregate structures discussed in Appendix R1▪5 and especially §R1▪5▪7▪4.

Conditioned case

Coagulated case

Supernatant (clear)

Supernatant (with small particles)

Floc

Weak association of particles/aggregates

Figure 7-17:

Schematic of the macroscopic structural differences between conditioned and

coagulated materials as loaded into a filtration cell.

A similar concept was proposed by CHANNELL, MILLER & ZUKOSKI [241] based on their observation that systems containing large clumps of previously-consolidated material dewatered further than a homogeneous system of the same initial (overall) solidosity. RUTH [882] also discussed the concept of a non-participating fraction of the pores.

430



Even in 1916 FREE [375] had emphasised the role of pore s i z e and c o n t i n u i t y (cf. tortuosity) in determining permeability — i.e. the r a t e of dewatering — rather than φ , which is a measure of the e x t e n t of dewatering. (Pore size is only implied from φ if the corresponding particle size and arrangement are known [375];

pore continuity and

tortuosity relies on aggregate structure, along with an implicit assumption regarding floc packing — usually random — at a given φ.)

To summarise these findings, there has not been any major improvement (or deterioration) in dewaterability identified as a consequence of shear or conditioning after settling. A marginal deterioration is observed at high solidosity, while a moderate enhancement is calculated at low solidosity. Examination of the curves in Figure 7-15 and Figure 7-16 suggests that high shear is not sufficient to make a pH 6 sludge behave like a pH 9 sludge, and nor is conditioning able to make a pH 9 sludge behave like a pH 6 sludge — at the same high dose of coagulant. (The only possible exception to this is in terms of R at low φ, which unfortunately coincides with the greatest experimental uncertainty.) This is a surprising result, given the attention paid to flocculation and conditioning in the water treatment industry, not to mention anecdotal evidence for the detrimental effects of high shear.

It may imply that the coagulation dose and pH determine the microscale

structure, which determines behaviour of the compressed material, while shear and conditioning change the macroscale structure, which only affects dewatering at low solidosities — in the region of φg or lower.

7▪4▪7

Conclusions

Characterisation of conditioned sludges was found to be highly problematic, necessitating the use of the end-point extrapolation method for estimating D (φ∞), and hence R(φ∞). Attempts to validate this technique for similar materials indicated that R was being overestimated. This overestimation was consistent for the three sludges examined, and could not be explained by the subjectivity of sub-set selection or by model fitting uncertainty. In the absence of an alternative, the results were scaled by a constant factor of 2.5. Use of this


431

D. I. VERRELLI

factor itself requires further validation. The usual stepped-pressure ‘permeability’ method appears have underestimated R, by a factor of about 4.5 / 2.5 = 1.8, for the high-pH sludges. When the dewaterability of the sheared and conditioned sludges was compared, no major changes could be identified.

There was a marginal decrease in permeability and

compressibility associated with shearing the samples. There was no clear difference for the conditioned sludges, aside from moderate improvement in the kinetics at low φ. There was also quite good agreement of sludge produced under nominally the same conditions, but from different raw waters a couple of years apart (tapwater versus raw water). An important feature of polymer-conditioned sludges — and arguably flocculated sludges too — is the ‘multilevel’ structure of the system, in terms of m a c r o s c a l e heterogeneity of aggregate arrangement. This is responsible for the difficulties encountered in characterising those sludges, and also explains the improved dewaterability observed at the lowest solidosities (at which floc formation occurred).

Ideally a fundamental study of these

materials would consider the separate influences of φ and φagg (or φ) upon py and R.

432


8.

EFFECT OF UNUSUAL TREATMENTS

This chapter examines what have loosely been termed ‘unusual treatments’, namely sludge ageing, freeze–thaw conditioning, and addition of powdered activated carbon (PAC). In general these are ‘unusual’ in the sense that they are relevant to a minority of WTP’s. More specifically, these processes constitute ‘unusual treatments’ in that when they do occur it is not always intentionally or with the objective of improving dewaterability.

8▪1

Ageing

The discussion in this section focusses on ageing prior to characterisation. For a discussion of the influence of ageing during characterisation, or ‘intra-experimental’ ageing, see §9▪3.

When a sample is stored for a long period of time between experiments, there is a possibility that the sample properties may change, be it due to chemical changes, or physical rearrangements and further consolidation of settled material. This can be called ‘interexperimental’ ageing. There is already some anecdotal evidence to suggest that ageing of sludges can lead to a large increase in dewaterability. The observations were made on ferric wastewater sludges that were stored for several months in large drums prior to shipment from Antarctica to Australia. Although freeze–thaw conditioning would have led to a dramatic enhancement of dewatering, for those sludges freeze–thaw conditioning was ruled out as a mechanism due to the attention paid to their storage (and also, presumably, to the appearance and behaviour of the sludges).

8▪1▪1

Reported effects

The important mechanisms of WTP sludge ageing generally fit into one of four categories: • bond strengthening; • densification — i.e. redistribution of the aggregate mass; 433

D. I. VERRELLI

• phase transformation of the metal (oxy)hydroxide to a more stable form; or • biological activity of bacteria, algæ, or other microscopic life.

In numerous colloidal systems interparticle bonds have been found to become more rigid with ageing, postulated to be caused by a gradual decrease of the interparticle gap after collision and initial bond formation [143] and an increase in the contact area [814], or ‘sintering’ [261, 773, 842] (see also p. 938). This should lead to stronger, but more brittle, aggregates. It can also promote synæresis [261, cf. 842] (see §R2▪1), leading to aggregate densification.

Densification of q u i e s c e n t aggregates is envisaged to occur through a

process of spontaneous ‘sintering’ upon ageing [347, 842]: see §9▪1▪1▪1(b).

A more crystalline aluminium (oxy)hydroxide phase has been associated with higher pore water contents (i.e. lower solidosities) upon centrifugation, and thus a structure that is “more resistant to the mechanical forces in action [during] centrifugation” [870]. (The crystallinity of the aluminium phase was not *, however, found to resist capillary forces [870].) FRANÇOIS [367] claimed that “filterability increases strongly with the degree of crystallinity of the flocs”, although no evidence was presented to support this. Formation of such crystalline phases was found to be favoured under more alkaline conditions and upon ageing of the wet sludge [870], and proceeds more rapidly under certain conditions [see 367].

WANG et alia [1098] reported increasing shear strength of alum and ferric WTP sludges upon ageing over a timescale of weeks to months in “sealed [...] plastic bags”. It was suggested that network strengthening would be greatest at intermediate solidosities, where particles are sufficiently close to experience strong interactions, yet their rearrangement is not significantly hindered by steric or volume-exclusion effects [1098].

The dewatering behaviour of algæ-containing WTP sludges has also been found to be greatly affected by ageing: an initial improvement (in rate) sometimes occurs — attributed to ‘bio-

*

434

A study by VISHNYAKOVA et alia (1970) published the opposite statement [870].

Chapter 8 : Effect of Unusual Treatments


flocculation’ by polymers exuded by the algæ — followed by a significant deterioration [811, 827].

Alum WTP sludges are generally found to dewater more readily after ageing for a period of months, except for sludges generated from raw water containing high proportions of ‘active’ biological matter (which produced smaller, slower settling aggregates, and led to anaerobic conditions), which maintain a high resistance [480] [see also 1139]. CALKINS & NOVAK [227] found that the dewaterability of both alum- and ferric-based WTP sludges changed upon ageing, with a timescale of order months. There are only slight changes after several weeks ageing [811].

Whereas the compressibility improved

(concentrations increased by around 20 to 60% for settled solids, and by 10% for filtered solids), the specific resistance to filtration deteriorated by a factor of 1.4 to 2.1 [227]. Ageing of sludges from three sites was investigated, and the two ferric sludges exhibited greater changes in both equilibrium and kinetic parameters upon ageing than did the alum sludge [227]. NICHOLSON & GOLDBACH [780] reported that aged alum WTP sludge had a lower polymer demand, which may have been due to a reduction in (available) surface area [223, 815]. DILLON [315] described a potential deterioration in dewatering “performance” if thickened sludge is stored for more than 3 days (which seems rather short), with allusion to anaerobic conditions due to algæ.

8▪1▪2

Experimental methods

Experiments were carried out on a number of sludges where sufficient material remained after characterisation of the fresh material.

These samples were generally aged under

ambient laboratory conditions, in glass beakers sealed with poly(methylene) wrap, in the open but out of direct sunlight.

As an exception, the aged ferric sludge sample was

refrigerated for much of the time; as this sample was not characterised prior to ageing, it is compared with fresh samples subsequently collected from the same plant.

8▪1 : Ageing

435

436


Note:

Age a

a

84 6.1 2.76 Ambient

" " " Ambient 1.5 and 2.6

0.24

"

9.9

1

2004-02-13

"

"

Tapwater

As at left

14.9

Ambient

"

"

"

"

"

"

As at left

Intermediate pH lab. alum

0.5

Ambient

2.47

4.8

80

0.83

12

2004-06-02

Winneke

13.1

Ambient

"

"

"

"

"

"

As at left

Low pH lab. alum

0.1

Ambient

2.84

6.1

80

0.57

9

2004-09-15

17.3 (settling)

14.8 (filtr’n)

Ambient

"

"

"

"

"

"

As at left

Lab. ferric Winneke

Refers to the storage time until filtration, unless otherwise indicated, as this was typically commenced after gravity batch settling.

[months] 0.7 and 0.8

Ambient

3.15


Storage

8.6

80

0.87

[–]

[mg(M)/L]

Dose

pH

[10/m]

A254nm

[mg/L Pt units]

14

2004-05-21

and date

True colour

Winneke

High pH lab. alum

Raw water source

Sample

D. I. VERRELLI

Table 8-1: (a) Experimental conditions for fresh and aged laboratory sludge samples.


Table 8-1:

(b)

Experimental conditions for fresh and aged dMIEX laboratory alum sludge

samples.

Sample

Low pH lab. alum — dMIEX

Raw water source

Winneke + 1.25%V dMIEX

As at left

2004-07-05

"

37

"

and date True colour

[mg/L Pt units]

A254nm

[10/m]

Dose

[mg(Al)/L]

80

"

pH

[–]

4.8

"

Hydrolysis ratio

[–]

2.47

"

Ambient

Ambient

1.3 and 1.4

8.0

Storage Age a Note:

[months] a

2.40

Refers to the storage time until filtration, as this was typically commenced after settling.

Table 8-1: (c) Experimental conditions for fresh and aged plant ferric sludge samples.

Sample

Plant ferric (1)

Plant ferric (2)

Plant ferric (3)

Raw water source

Macarthur

Macarthur

Macarthur

and date

2005-03-23

2005-09-21

2003-08-21

8

12

11

[mg(Fe)/L]

1.5

2.2

1.1

[–]

9.0

8.7

8.8

Polymer

Yes

Yes

Yes

Storage

Ambient

Ambient

Mostly refrigerated

0.4

0.5 and 0.8

~15.7 (refrigerated)

True colour [mg/L Pt units a] Dose pH

Age b

[months]

~0.1c and 2.1d (ambient) Notes:

a

Recorded as Hazen units.

b

Refers to the storage time until filtration, as this was typically commenced after settling.

c

Gravity batch settling and first filtration run.

d

Second filtration run only.

8▪1 : Ageing

437

D. I. VERRELLI

In this work filtration tests completed within about one month of sample generation and settling tests commenced within about two weeks of sample generation are taken as characteristic of the “fresh” material. As in the present work, KNOCKE & TRAHERN [579] did not observe significant changes in dewaterability of alum or ferric WTP sludges over a one month period.

Details of the aged sludges characterised herein are presented in Table 8-1. Of all these sets of sludges, centrifugation was only carried out for the two fresh ferric sludges. Although the centrifugation data is plotted, it cannot be directly compared with the other data (see discussion in §3▪5▪2▪2(b)).

The hindered settling function was obtained for only three of the aged sludges, and only two include settling test data (Figure 8-2 and Figure 8-5). This is chiefly due to sample volume constraints, but another important issue is the quality of data that can be obtained from settling tests with φ0 [ φg — or, more precisely, with ι(φ0) ≈ 1 (see §2▪4▪5▪3(a)) — as is often the case with aged samples.

Attempts to dilute these samples are liable to lead to

unrepresentative macroscopic heterogeneity (cf. p. 421), so the best course of action is to remove a portion of sludge from the top of the aged sample, to achieve a satisfactorily low φ0. (Generally the aged samples did not appear to have stratified, so it is assumed that the only difference between different layers in the sample is their solidosity.)

8▪1▪3

Results

Results for alum sludges are shown in Figure 8-1 and Figure 8-2. Results for the dMIEX alum sludges are shown in Figure 8-3. Results for ferric sludges are shown in Figure 8-4 and Figure 8-5.

With regard to the compressive yield stress, all of the sludges show a ‘potential’ for improvement in dewaterability upon ageing. The change is greatest for the high-pH alum sludge.

438




1.E+3

1.E+2

1.E+1 Lab. alum pH 8.6 ... aged 10mo Lab. alum pH 6.1 ... aged 15mo Lab. alum pH 4.8 ... aged 13mo

1.E+0 1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-1: Compressive yield stresses for three pairs of fresh and aged laboratory alum sludges.

It is not clear what the magnitude of enhancement might be for the plant ferric sludge, as the aged sample was not characterised fresh. It is probable that the aged material has undergone either a significant or a negligible improvement in dewatering, based on the other pairs of sludges and the fresh plant ferric sludges, although this cannot be stated with certainty. For the other sludges the changes are slight, but always with a tendency toward improved dewatering. While the high-pH alum sludge suggests diverging behaviour for the fresh and aged material as φ increases, the laboratory ferric sludge suggests the opposite, with a greater divergence at low φ. Due to sample volume constraints, gravity batch settling was only carried out for these two aged sludges. 8▪1 : Ageing

439

D. I. VERRELLI

2


1.E+15

1.E+14

Lab. alum pH 4.8 ... aged 13mo

1.E+13 1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-2: Hindered settling function for one pair of fresh and aged laboratory alum sludges.

440




1.E+3

1.E+2

1.E+1

dMIEX 80 mg(Al)/L, pH 4.8 ... aged 8mo

1.E+0 1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-3: Compressive yield stresses for a pair of fresh and aged laboratory alum sludges prepared from raw water spiked with dMIEX.

8▪1 : Ageing

441

D. I. VERRELLI


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 Lab. ferric pH 6.1 ... aged 15mo Plant ferric (1) Plant ferric (2) " " (3) aged 17±1mo

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-4: Compressive yield stresses for two sets of fresh and aged ferric sludges.

With regard to R (Figure 8-2 and Figure 8-5), again all of the sludges show a ‘potential’ for improvement in dewaterability upon ageing. At high solidosity a change is only observed for the (low-pH) alum sludge. At low solidosity a significant improvement is found for the laboratory ferric sludge, and either a significant or a negligible improvement for the plant ferric sludge (depending on the ‘baseline’ chosen). For the laboratory ferric sludge a large part of the improvement in R is likely due to the shifting of the gel point evident from the compressive yield stress curve. No low-solidosity data was available for the alum sludges.

442



2


1.E+15 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 Lab. ferric pH 6.1 ... aged 15mo Plant ferric (1) Plant ferric (2) " " (3) aged 17±1mo

1.E+09 1.E+08 1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-5: Hindered settling function for two sets of fresh and aged ferric sludges.

8▪1▪4

Discussion

It is not clear why there is a difference in the enhancements attained. However, it does not seem to be associated with the ageing time. Aside from chemical changes, mechanical stresses applied to the sludges are likely candidates for the observed dewaterability enhancement. In the first instance, the slow and continual consolidation of these materials (certainly leading into a creep regime at these long times — see §9▪3▪2, §R2▪2 and §R2▪3▪2) leads to a reduction in the spacing between the aggregates that might seem to favour gradual and progressive densification. Although the

8▪1 : Ageing

443

D. I. VERRELLI

velocities are very low, the times (and concentrations) are very high (cf. the dimensional analysis for BROWNian motion in §R1▪5▪6▪4(a)). Thus it is hypothesised that aggregates in concentrated sludges are more prone to breakage upon exposure to shear due to handling than aggregates in less concentrated sludges, because of the increased transmission of forces at an increased number of contact points throughout the networked gel structure.

The c o n v e r g e n c e of the laboratory ferric sludge dewaterabilities with increasing φ suggests an ageing mechanism that principally affects the l a r g e r lengthscales of the aggregate or network structure.

The most likely candidate would be a p h y s i c a l l y

motivated densification, due to imposed forces from collisions, ‘solids pressure’ gradients, and hydrodynamic shear. On the other hand, the apparent d i v e r g e n c e of the high-pH alum sludge dewaterabilities with increasing φ suggests an ageing mechanism that principally affects the s m a l l e r lengthscales of the aggregate or network structure.

A plausible candidate would be a

c h e m i c a l l y derived change, such as crystallisation or some other solid phase change.

It is assumed in the present work that a fairly stable material is available approximately one day after generation. Another possibility is that the changes upon ageing are very fast (of order hours or days). In any case it is not possible experimentally to fully characterise sludge dewaterability on a timescale shorter than days. It appears unlikely that changes are occurring on a timescale of days, because: • duplicate characterisation of the same ‘fresh’ sample weeks apart shows no significant changes (see §3▪5▪4); • crystallinity changes appear to be very slow (see §4▪2▪2); • creep (as a possible sympathetic effect) is observed only at long times (see §9▪3▪2); and • the differences upon ageing do not appear to be correlated with the age of the nominally fresh sludge when characterised.

444



Biological effects are unlikely to have been important for the laboratory sludges. Even for the plant (ferric) sludge biological activity did not appear to be significant (note that this sample had been refrigerated for a long period).

8▪1▪5

Conclusions

Ageing of sludge samples has the potential to induce improvements in dewaterability. However, consistent trends in the manifestation of the changes could not be determined: • the degree of these changes varies from marginal to highly significant; • effects may be seen in both py and R; • enhancement is sometimes greater at low φ, sometimes at high φ. Enhancements that are manifest principally at only low or only high φ could imply the lengthscale upon which changes in the aggregate or network have occurred, from which a mechanism might be inferred.

8▪2

Freeze–thaw conditioning

It is well known that freezing a sludge sample completely will result in a great amount of dewatering upon thawing. The material will transform from a gel made up of loose, fluffy aggregates of very small particles, to a mixture of supernatant and large (say 1 to 2mm) hard, compact particles.

8▪2▪1

Background

When sludge is subjected to a freeze–thaw conditioning process, the structure of the aggregates is modified such that water can more readily escape [854].

The effect was

reported for simple sols by LYUBAVIN in 1889, and for coagulated metal hydroxides by HEPBURN in 1926 [1149].

The change in properties is so dramatic that VOZNESENSKII

suggested that the conditioned material be renamed as “ z o t ” [1149]. The zot has the appearance of wet coffee grounds or wet iron filings.

8▪2 : Freeze–thaw conditioning

445

D. I. VERRELLI

Freezing a sludge compresses the solids into “large discrete conglomerates” surrounded by frozen water [879]. The compactness of the zots means that capillary forces between zots are much lower than inside (or between) fluffy flocs [1079]. Drainage is facilitated through cracks in the frozen mass as thawing takes place, as well as through the large pores and channels that are created in the new colloid structure [351, 879]. Water is able to drain almost instantaneously as it melts [879, 1079].

Many benefits can be derived with this process [137]: • it is clean, efficient, and capable of automation; • it yields a massive improvement in dewaterability, greatly reducing the amount of solid waste to be disposed of; and • it produces a safe, stable [cf. 721], non-odorous product that can be conveniently disposed of or recycled for metal oxide recovery. While the literature reports a clear supernatant developing from settled freeze–thaw WTP sludges [1079], the present work found that the supernatant following freeze–thaw was less clear than the original supernatant.

8▪2▪1▪1

Mechanism

An important component of the sludge freezing mechanism involves migration of aggregates ahead of a freezing front (i.e. the interface between ice and liquid water), where they are ‘rejected’ by the interface [824, 1081, 1149].

This has been described as the dominant

mechanism for dewaterability enhancement [507]. The concentration of particles is much higher immediately ahead of the freeze front [1088], analogously to filtration. The aggregates are partially dewatered as water diffuses out of their volume, and they densify to some extent [1088]. Water from the unfrozen bulk, beyond the vicinity of the freeze front, also diffuses to the freeze front between and through the aggregates built up in that interfacial zone [1088].

Both the continual accumulation of

aggregates at the freeze front as it advances and their collapse cause the permeability of the layer to decrease [1088]. As the resistance grows, and diffusion of water is hindered [823, cf. 1081, 1089], the water in the bulk may become supercooled (~2 to 5°C [1089]), soon resulting in the formation of ice 446



crystallisation nuclei ahead of the freeze front [1088]. Eventually ice will grow through the layer of accumulated aggregates, connecting the freeze front with these crystallisation nuclei [1088]. The particles are then pushed into compact layers between ice crystals [824, 1149], as dendrites and needles of ice penetrate the aggregates [1090], while beyond this zone the freeze front continues as it did previously [1088]. The solids thus tend to concentrate along grain (or sub-crystalline) boundaries [824]. This process is cyclic — rejection of aggregates, accumulation of a concentrated layer ahead of the freeze front, decrease in permeability, engulfment of the layer by the ice — while the freeze front advances steadily, which results in ‘rhythmic banding’, i.e. distribution of entrapped solids in bands [823] [cf. 958]. When the ice finally encloses (partially-collapsed) aggregates, the water within the fractal structures is ‘pulled’ to the freeze front (by film diffusion [1081, 1089] or ‘cryosuction’ [820]), and the solid primary particles making up the aggregate are ‘pushed’ back in further away from the front in order to accommodate its growth, so that the overall effect is for the flocs to be (further) ‘dehydrated’ [1079, cf. 1090]. Ice can also nucleate within the aggregates if sufficiently large pores exist, which accelerates the freezing process [1089]. The aggregate dehydration is irreversible * [704, 1088, 1089]. As the solidosity and freezing rate are increased, aggregates will be more readily ‘entrapped’ by the interface [822, 824, 1088]. Entrapment and aggregate dewatering may also be affected by the presence of high concentrations of dissolved impurities, which cause freezing point depression [cf. 1088]. If φ0 is low, and the freezing is fast, then the particles may be entrapped singly, rather than combining to form large zots [cf. 507].

Another mechanism, which may work in combination with the above process, is the hypothesis that as the primary particles making up the aggregates are pushed closer and closer together by the encroaching ice fronts, eventually they will be sufficiently close that attractive surface forces take over, effectively bonding the particles to one another [820, 1079, cf. 1149]. The bonds may be stronger than before [820], or the increased zot strength may be *

PARKER & COLLINS [820] stated that “sonication destroyed the zots and reverted them to their original form”; however no supporting information was provided.


447

D. I. VERRELLI

due simply to an increased bond density. These attractive forces are sufficient to hold the large zots together after thawing [1079], and avoid re-hydration. Other researchers [398] concluded that only small agglomerates could form upon freezing, and that the main network collapse and particle aggregation occurred upon thawing. (Indeed s e p a r a t i o n of particle “chains” upon freezing was asserted [398].) TRONC et alii [1053] attributed this to a loss of the structured layer of solvated water (and ions) [see 538] from the particle surfaces upon solvent crystallisation, which is not recovered upon thawing.

The expansion of water upon solidification has regularly been considered as a candidate mechanism for freeze–thaw conditioning [e.g. 1090] — either through tension arising from freezing inside the aggregate, or compression due to freezing outside the aggregate [1088]. The volume expansion of water as it freezes was rejected as the main mechanism for dewatering by VESILIND & MARTEL [1079] based on the work of VOL'KHIN & PONOMAREV [1088], who achieved essentially the same effect using organic fluids [see also 209]. However, such organic fluids would undergo significant volume c o n t r a c t i o n s , so large pressure force differentials would still arise. Furthermore, VOL'KHIN & PONOMAREV [1088] decided: The possibility is not excluded that the pressure exerted by the expansion of water during crystallization may have a positive influence on [dehydration of the coagulates].

BRANDT & TOMASHCHIK [190] investigated the freezing behaviour of mixtures of ethanol and water (which are completely miscible [662, 1106]).

They reported the influence of

composition of the mixture, at up to 35% ethanol, on the change in volume upon freezing, the freezing temperature (i.e. melting point), and the pressure obtained when the mixture was frozen at constant volume. The maximum pressure (~170MPa) and volume change (~8.0%) was observed for pure water *; increasing the proportion of ethanol in the sample yielded ever smaller pressures and volume changes [190].

The volume change tended

towards zero, being just 1.6% for a 35% ethanol mixture; based on the shape of the curve, it may be expected that a mixture of ~40% ethanol would yield zero volume change [190].

*

The expected volume change is ≤9.1%, given water solid and liquid densities at 0°C of 916.7 and 999.8kg/m3, respectively [662].

448



However, interestingly, the pressure increase upon isometric freezing was recorded as zero for considerably lower ethanol concentrations: for rapid freezing this occurred at an ethanol concentration of 25%, while for slow freezing the pressure developed was zero for ethanol concentrations above 15% [190]. There was no reported preferential partitioning of the components into the solid or liquid phase while freezing, and rather the mixture was described as exerting a more ‘homogeneous’ pressure than pure water [190]. This media suggests itself as a means of confirming the independence of the freeze–thaw conditioning effect from pressures arising from volume changes upon freezing.

The solid phase densities of an activated biological sludge before and after freeze–thaw conditioning showed no significant differences [238]. The same constancy would seem to apply to ‘inorganic’ WTP sludges (see §4▪2▪2▪2(a) and §4▪3▪2▪2).

8▪2▪1▪2

Operational parameters

Several factors that may influence the outcome of freeze–thaw conditioning have been investigated by various researchers. These are summarised below: • D i r e c t i o n a l i t y . Freezing in the field is essentially unidirectional, giving rise to uniformly aligned ice crystals. Results indicate that (slow) directional freezing at most slightly enhances the conditioning effect [824, 1088]. • G e o m e t r y . The geometry of the vessel holding the sludge may be important in that it will affect the directionality but also, more critically, the freezing rate [cf. 507]. • Freezing speed.

The freezing rate has been identified as the most important

freeze–thaw conditioning parameter by many researchers [1079]. A higher freezing rate is associated with more favourable economics, as space requirements are reduced. Unfortunately the desired migration of aggregates is optimised by low freezing rates [107, 507, 824, 1139], whereas more rapid freezing encourages nucleation of smaller ice crystals, which have less of an effect on the aggregates [1090]. Maximum freezing speeds of 5 to 18μm/s have been recommended [1079]. PARKER et alii [822] identified three regimes of sludge freezing: o S l o w freezing (<7μm/s [cf. 351]), in which aggregates are free to migrate ahead

of a planar freeze front, in which a few round air bubbles are incorporated. At 8▪2 : Freeze–thaw conditioning

449

D. I. VERRELLI

high solidosities the aggregates are partially dewatered ahead of the freeze front, and water diffuses to the ice interface. o I n t e r m e d i a t e freezing (7 to ~14μm/s), in which aggregates mostly migrate

ahead of a bumpy (quasi-cellular [351]) freeze front, in which several air bubbles — elongated in the direction of advance — are incorporated.

Fragments were

broken off some aggregates, and these were ‘captured’ by the freeze front. These fragments may have been pierced and held by dendrites too small to see: dendrite radii of order 10‒1nm have been reported [821]. o F a s t freezing (>14μm/s), in which knife-like dendrites shoot ahead of the rough

‘macro’ freeze front at rates of 100μm/s or more. These dendrites both pierce and confine the aggregates, so that they are unable to migrate. The aggregate is then also fragmented. Additionally, some workers have experimented with o ‘ u l t r a - f a s t ’ freezing (up to 200μm/s [247]), variously finding negligible

dewatering benefit [cf. 821, 1079] or a reduced dewatering benefit [137, 247, 821, 822]. It is suggested that at the highest freezing rates, interstitial water in the flocs freezes (or ‘vitrifies’) where it is, without being removed [247, 1079], as the rate of freezing exceeds the rate at which water can diffuse [cf. 821].

By

extrapolation of the observations for fast freezing, no particle migration is expected; however significant (~50%) migration was observed by PARKER & COLLINS [821]. Given that the solids migrate to unfrozen ‘pockets’, and needles of ice tend to intrude from the ice front into the unfrozen sample, avoiding the formation of these ice needles should minimise the subdivision of unfrozen pockets, so increasing the size of concentrated zot ‘grains’ ultimately formed; presumably this could be accomplished by lowering the freezing rate [1079]. • F r e e z i n g t e m p e r a t u r e . In contrast, for ferric (oxy)hydroxide precipitates more compact conditioned sludges were obtained as the freezing temperature (with uncontrolled rate) was decreased from ‒1°C to ‒15°C [1149], and settleability improved slightly [721].

The largest, but weakest, zots were formed at the higher freezing

temperatures (‒1°C) [1149]. Experiments at low (bulk) ionic strength indicated that

450



pore water did not begin to freeze until ‒7°C, and that freezing was complete by ‒30°C [398]. • A g g r e g a t e s t r u c t u r e . VOL'KHIN, PONOMAREV & ZOLOTAVIN [1089] reported that ice can nucleate within the aggregates if sufficiently large pores exist — as for the (oxy)hydroxides of Mg and Cr, but not of Fe(III) or Mn, prepared by them. (JEAN et alii [528] ascribed this to differences in the chemical potential.) Intra-aggregate nucleation accelerates the freezing process: hence the mechanism of conditioning enhancement observed for a decrease in freezing temperature with Fe(III) and Mn precipitates is subordinated in the case of Mg and Cr precipitates, where instead a slight reduction in the benefit of conditioning results [1089]. On the other hand, if the solid particulates are “basically nonporous”, then negligible internal restructuring can occur [528] (although aggregation could still be promoted) [cf. 507]. • Completeness.

The principal dewaterability enhancements depend upon the

sample bulk freezing completely [107, 507, 528, 638, 721, 1079]. The settled volume of the thawed material decreases at first slowly and then more sharply as it approaches complete freezing; the further enhancement upon curing is minor for coagulated ferric [1149] and aluminium hydroxide sludges, but may be substantial for other metal hydroxide waste suspensions [638]. • C u r i n g t i m e . Curing refers to the exposure of the sample to freezing conditions after ‘complete’ freezing of the bulk. VESILIND & MARTEL [1079] found that longer curing times were associated with “better” dewaterability, as did PARKER et alii [823] for slow-frozen alum sludges and PARKER & COLLINS [821] for both slow- and fastfrozen alum sludges upon curing for up to 6h. MARTEL et aliæ [704] observed no benefit of curing for very slowly (<2.5μm/s) frozen alum WTP sludge. This may have been due to sample peculiarities (see e.g. Solidosity [cf. 823], Ionic strength). LAVROV, PONOMAREVA & ROZENTAL' [638] found significant enhancements for alum sludges frozen and cured at higher temperatures (~‒4°C) for up to 150h, but not at lower temperatures (~‒15°C). Similarly, CHEN et alia [247] observed improvements for an alum WTP sludge frozen at conventional speed, but the enhancement was marginal when frozen at ‘ultra-high’ rate. (This suggests that a threshold rearrangement of the aggregate structure during the initial freezing may be required for curing to be


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D. I. VERRELLI

effective. Alternatively, the cryogenic temperatures commonly employed in ‘ultra-fast’ rate freezing may be able to freeze salty ‘surface water’ almost instantly, whereas the process is slower at higher temperatures. The zots formed by ‘ultra-fast’ freezing are smaller, so the distance for water to diffuse is also shorter, suggesting shorter times [cf. 821].) VESILIND & MARTEL [1079] attribute the curing effect to the gradual freezing of ‘surface water’. Hence, curing may take longer for larger, fractal aggregates of small primary particles [528]. ZOLOTAVIN, VOL'KHIN & REZVUSHKIN [1149] found that at relatively high temperatures (say > ‒10°C), increases in curing time were associated with further densification of the sample (measured by settled volume), approaching the concentrations achieved much more rapidly by samples frozen at colder temperatures, for which an extended curing time had negligible effect. • C u r i n g t e m p e r a t u r e . Usually the freezing temperature is adjusted to control the freezing speed and is the same as the curing temperature. VESILIND & MARTEL [1079] experimented with curing temperatures independent of the freezing temperature, and found that lower curing temperatures were associated with an improvement in dewaterability (as CST) for wastewater sludges. They related this to the purported freezing temperature of ‘surface water’ of about ‒30°C [1079]. ZOLOTAVIN, VOL'KHIN & REZVUSHKIN [1149] reported the same phenomenon, and likewise proposed a mechanism due to the different properties of bound surface water, oriented nearsurface water, and free bulk water. The quantity of bound water was expected to be higher for more hydrophilic solids [1090]. Other researchers suggested that capillary water would exhibit analogous differences (namely freezing point depression) [1149]. Lower curing temperatures also avoid effects due to freezing point depression by salts (see Ionic strength). Such effects will be magnified near the surface of the particles, due to the need for aqueous counter-ions to concentrate in that region to balance particle surface charge. • P a r t i c u l a t e s i z e . Freeze–thaw conditioning is reported to be more effective with smaller particles (and so, perhaps, with ‘fresher’ sludges) [1079]. It has been suggested that colloidal particles of less than about 10μm will readily migrate ahead of the freeze front, while large particles (say >100μm [see also 638]) will be trapped in the ice front

452



[1079]. It is likely that this is due to the greater mobility of the smaller particles that enables them to better ‘avoid’ capture by the freezing front. • Ionic strength.

It is presumed that freeze-concentration of salts and other

dissolved species in the liquid phase does not directly affect dewatering. However, indirect mechanisms may be important.

Reports of both improvement and

deterioration in dewaterability have been published [1090, 1148], as well as the absence of any effect [528, 1081]. Deteriorations were seen for salt concentrations T 0.1M, while enhancements can be obtained at lower concentrations (( 0.01M) [1148]. A plausible mechanism for a deterioration in dewaterability is freezing point depression by salts that do not form cryohydrates at the given temperature [1090, 1148]. (Even low initial salt levels may be significant, because the salt concentration will rise due to inability of water to form a solid solution [1090] [cf. 638, 704].) In such cases the solids would be confined in narrow, unfrozen layers between ice crystals — some consolidation still takes place, but the zot size is smaller [1148]. This suggests that lower freezing and curing temperatures would avoid this problem [1090]. However experimental observation shows that at very low temperatures (< ‒70°C), although the salts would all form solid cryohydrates [cf. 351], they also act as nucleation sites for ice crystal formation, so the eutectic freezes quickly into small crystals [1148]: small crystals dispersed throughout the volume were less effective in conditioning the sludge [1090]. Where the temperature is not low enough to form cryohydrates, it is possible that enhanced conditioning could result from ‘colloid’ destabilisation by the concentrated salt [1090], particularly for multivalent cations [1148]. The formation of cryohydrates may be disrupted by the presence of solids in suspension, whose presence tends to increase ordering of water molecules [528]. I.e. the aggregates may depress the eutectic temperature. A final possible mechanism for reduced effectiveness is the reduced ice crystal interface stability when the solute concentration (gradient) is high, such that the maximum freezing rate for ‘slow’ freezing is depressed [351] (see Freezing speed). • S o l i d o s i t y . Dewatering (alum) sludge prior to freeze–thaw conditioning was found to be beneficial in terms of enhancing the zot dewaterability and reducing the


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D. I. VERRELLI

operating cost [137, 704, 721, 821]. Progressively larger zot particles (and narrower size distribution) were observed as the initial concentration was increased from that typical of clarifier output (≤1%m) to that typical of a belt press filter cake (~12%m) [704]. The mechanism behind this positive correlation is believed to be entrapment of multiple (networked) aggregates in the same cavity, so that they are dewatered together to form a single zot [821]. Note that the local solidosity ahead of a slowly-moving freeze front will be elevated due to aggregate migration [821]. • Thawing

temperature/speed.

No effect unambiguously attributable to

changing of the thawing temperature or speed was observed [1149].

Superior

dewatering was observed for thawing at low (~1°C) and high (50°C) temperatures, compared to room temperature thawing, but only in some cases [1149]. Enhancements at very low thawing temperatures may be due to the longer effective curing time [1149]. Higher thawing temperatures may accelerate a post-thaw ageing mechanism [1149]. • P o s t - t h a w a g e i n g . The dewaterability of the zot was found to improve if the sample was held for some time (of order 102h) at room temperature after thawing, especially for higher freezing temperatures [1149].

Post-thaw ageing appears to

strengthen the zot, which is more significant for the weaker particles generated at higher temperatures [1149].

8▪2▪1▪3

Improvements to dewaterability

Improvements in settled sludge (or zot) volume of 15 to 25-fold [1149] and 40-fold or more [1089] have been reported for various metal hydroxide aggregates, with 100-fold improvements in settling rate [1149]. Under typical English weather conditions, zots drain and weather to about 60 to 70%m solids [137]. Freeze–thaw conditioning was able to achieve 1000-fold enhancements of filtration rate [1149]. In filtration, the resistance was said to be due to a ‘self blockage’ mechanism, where the surfaces of the zot particles degrade and fill in channels (i.e. fluid pathways), rather than blockage from particles entrained in the suspension flowing into and filling the pores [1149].

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8▪2▪1▪4

Industrial application

The procedure is suited to climates in which water will freeze naturally each winter under ambient conditions in a lagoon [823] [cf. 880], where sludge is periodically spread in a layer, once the previous layer has completely frozen [879]. Depending upon local conditions, freezing of sludge held in lagoons or beds might occur only in the top ~0.10m, with this frozen layer (and any fallen snow) ‘insulating’ the mass beneath — a benefit may be derived by mechanically breaking up and mixing such partially frozen beds [880].

In more

favourable conditions bulk freezing to over 1m depth is reasonable [282]. Aside from a suitable climate, natural freezing requires large land areas and significant sludge storage facilities [880, 1079]. More recent research has looked into the economics of ‘mechanical’ freezing, and optimisation of such processes [824]. In 1990 VESILIND & MARTEL [1079] wrote that “the only successful freeze–thaw systems depend on natural freezing” [see also 107].

Mechanical freezers can be grouped according to the freezing volume and method of heat transfer. In l a y e r f r e e z e r s the sludge is transported on conveyor belts, or forms a ‘film’ inside heat-exchanger tubes or outside a rotating drum [704]. Freezing of these thin layers is the most efficient configuration, but large floor space is required and only pilot scale units have been run [704]. F r e e z e c r y s t a l l i s a t i o n (or freeze concentration) works by continually stirring a volume of sludge below its freezing temperature [704], e.g. in a scraped-surface exchanger [649]. In such freezing operations crystals are suspended as a more or less dilute slurry [649, 704]. Such configurations have generally been rejected as too inefficient for water treatment sludges [289]. Furthermore, freeze crystallisation has even been found to worsen sludge dewaterability in some cases [704], perhaps related to the failure to freeze the entire bulk. D i r e c t - f r e e z i n g processes in which refrigerant is injected into the sludge [579] or sludge is sprayed into a refrigerant [e.g. 209, 351] appear less efficacious for sludge conditioning, albeit perhaps more energy-efficient [cf. 107]. The only devices known to have entered full-scale service for WTP sludge conditioning are b u l k f r e e z e r s , which have operated in the U.K., Germany, and Japan, pioneered around


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D. I. VERRELLI

Lancashire (England) in the 1960’s [137, 315, 557, 704, 1139].

These units commonly

consisted of large, reinforced tanks fitted with heat-transfer fluid piping for freezing and thawing [137]. Reliability issues were experienced at some plants [315]. To avoid tank rupture, the English designs relied on foam rubber curtains or brine-filled bladders, which would yield to the expanding ice [137]. Partial freezing of the bulk (~40%) has also been practised [704], although this would seriously reduce the achievable improvement in dewaterability. The drained zots cannot be pumped, although they are suitable for ‘manual’ handling. A convenient means of zot transport in the plant is to use the melted supernatant as a carrier fluid for pumping; zot does not sediment in the pipes provided appropriate minimum flow velocities (>1m/s) are maintained in the pipework [137].

In discussion of their 1969 paper, BENN & DOE [137] stated that filter pressing of WTP sludge was aided tremendously by the advent of commercial synthetic polymer flocculants [see also 797, 1139].

Hence it may be read that mechanical freeze–thaw conditioning is a good

technology whose advantages were overtaken by the development of alternatives that became more cost effective. Of course, the cost–benefit calculation may change again.

8▪2▪2

Experimental methods

Both alum and ferric plant sludges were subjected to freeze–thaw conditioning, as summarised in Table 8-2. Aside from the two samples characterised for dewaterability, a further two samples were conditioned for estimation of ρS (see §4▪3▪2▪2). One sample was also used for XRD analysis (§4▪2▪2▪2(a)).

Sludge samples were placed in 2L plastic beakers of approximately 180mm height and diameter tapering from about 135 to 120mm. The top was covered with plastic film, and the whole was stored in a domestic freezer unit at approximately ‒12 to ‒18°C for a period of 15 days (alum sludge) to 24 days (ferric sludge) — the bulk was frozen in a much shorter time. The samples were loaded after settling for some time, and so were at solidosities at or

456



slightly above φg. As shown in the previous section, ageing effects are unlikely to have affected the freeze–thaw conditioning process. The samples were thawed overnight. This was conveniently achieved by slightly elevating the beakers above the bench top and placing them in the draught of a fume cupboard.

Table 8-2: Overview of freeze–thaw conditioned sludges.

Sample

Plant alum

Pilot plant alum

Plant ferric A

Plant ferric B

Winneke

Happy Valley

Macarthur

Macarthur

and date a

2005-07-01

2005-05-23

2005-03-23

2005-09-21

Measurements

py, R, XRD

ρS

py, R

ρS

Freezing date

2005-07-04

2005-10-14

2005-05-09

2005-10-14

Thawing date

2005-07-19

2005-10-24

2005-06-02

2005-10-24

Table 3-14(b)

Table 5-3

Table 5-4

Table 5-4

Raw water source

Further information

Table 4-10 Note

a

Sample collection date may be equated to the sludge generation date.

8▪2▪3

Experimental results

The freeze–thaw conditioned samples clearly showed the effects of particle exclusion from the freeze front, with clear ice surrounding a frozen core of concentrated sludge.

Figure 8-6 shows the mechanism of freeze–thaw conditioning schematically.

For ferric

sludge A the particle-free zone extended about 5mm in from the sides and base, but about 20mm down from the top — the difference is presumably due to gravity settling interaction. In contrast, for ferric sludge B the zones extended 3mm in from the sides, 5mm up from the base, and 10mm down from the top. For the plant alum sludge the zones were 5 to 15mm from the sides, 15mm from the base, and 25mm from the top.


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Supernatant

Air bubble

Sludge Beaker

Direction of movement

Figure 8-6: Schematic of the progressive exclusion of particulates by a moving freeze front. The outer material is nearly pure supernatant or water, while the inner core is concentrated sludge. Air bubbles elongated in the direction of freeze front movement were visible in the ice.

These measurements indicate that the particle-free shell makes up about 15 to 55%V of the total. In an approximately self-similar feature, the particle-rich core in turn comprises very dense zots surrounded by ice.

As the aqueous phase froze, it also expanded, and some large cracks were observed in the top of the frozen sample, as it pushed its way out of the confining beaker, giving the appearance of a crusty roll or loaf of bread. The direction of progression of the freeze front was evident from the displacement of the (now concentrated) particulates from their original locations, as well as from the elongation of air bubbles in the ice. The elongations suggest an intermediate freezing rate (see p. 450), which would imply complete freezing of the bulk within about 3h, faster than expected.

458




1.E+3 1.E+2

Original plant alum Original plant ferric Alum freeze–thaw Ferric freeze–thaw

1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0


Figure 8-7: Compressive yield stress of sludges subjected to freeze–thaw conditioning. The thinner curves at left illustrate behaviour of the unconditioned sludges.

Particle sizes in the approximate range 0.1 to 5mm were observed. Although banding of the particles could not be observed through the ice, banding was evident in the air bubble features.

Preliminary measurements on the plant alum sludge conditioned in this way indicated that the solidosity rose from a typical 0.6%V for the original sludge, to around 12%V for the thawed material, corresponding to about a 20-fold increase.


The material d r a i n s so

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D. I. VERRELLI

readily, that the solidosity of the conditioned sample was perhaps a slight overestimate of what could be obtained by (say) settling alone, in which drainage is impossible.

2


1.E+15 1.E+14

Original plant alum Original plant ferric Alum freeze–thaw Ferric freeze–thaw

1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 1.E+05 1.E-3

1.E-2

1.E-1

1.E+0


Figure 8-8: Hindered settling function of sludges subjected to freeze–thaw conditioning. The thinner curves at top and left illustrate behaviour of the unconditioned sludges.

More rigorous data is presented in Figure 8-7 and Figure 8-8. The main conclusion is confirmation and quantification of the massive enhancement of dewatering that may be gained through freeze–thaw conditioning.

460



Aside from this, it seems that the ferric sludge has attained the most readily dewaterable state, although the precise advantage is dependent upon the accuracy of the solid phase density used.

For the zots it is possible to make an independent order-of-magnitude estimate of R(0). Unlike settling flocs, advection through these particulates is certainly negligible, and their size is much less ambiguous (albeit polydisperse). From §2▪4▪5▪1(b) R → λ / Vp as φ → 0, and for a sphere R(0) = 18 ηL / d2.

To a first

approximation ηL ≈ 0.001Pa.s and d ≈ 0.0005 to 0.001m, which yields R(0) ~ 104 to 105Pa.s/m2. This is consistent with the data of Figure 8-8. In future work it would be possible to improve this estimate by characterising the zots in more detail, such as the precise size distribution, average sphericity, and actual settling rates of individual particles.

8▪2▪4


It is fascinating to observe the full hindered settling function curve for the conditioned alum sludge, which exhibits a clear point of inflexion at around the gel point. The gel point can be estimated from Figure 8-7 to be a little under 10%V. Through the collection of settling data close to the gel point (both above and below), it is obvious from the curve (Figure 8-8) that in the free settling and hindered settling regimes R is r e l a t i v e l y constant, increasing by perhaps a couple of orders of magnitude. At the gel point R increases by around 6 orders of magnitude almost instantaneously! Then, beyond this, a further region of r e l a t i v e l y constant R is established, increasing by perhaps an order of magnitude with φ. (The gel point behaviour of R for the alum sludge is not characterised as well.)

While the dewaterability of the freeze–thaw sludges differs greatly from the unconditioned sludges over the entire range probed here, consideration of the highest py data suggests that the behaviour of the sample pairs may each converge at higher pressures and solidosities. This exhorts further experimentation at pressures at least an order of magnitude greater.


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Clearly the altered dewatering behaviour upon freeze–thaw conditioning must be due to major structural rearrangement of the particles. If a region for convergence of the py(φ) curves — and, by implication, the R(φ) curves — could be found, then it would be especially interesting to associate this (perhaps the threshold φ) with the lengthscale at which the aggregates were not rearranged [cf. 241]. (It may be that the lengthscale is as small as the ‘primary particles’ themselves [cf. 416]!)

Freeze–thaw conditioned sludges exhibit the greatest dewaterability enhancement that has been observed, and the effect has been quantified in terms of py and R for the first time. These results could be used to produce arrays of dewaterability data that could be used for preliminary assessment of the benefit of employing freeze–thaw conditioning. In order to increase accuracy and confidence in the results it would be recommended that additional freeze–thaw conditioned samples were characterised. It is also of interest to quantify the effect of φ0 on the conditioning.

8▪3

Powdered activated carbon (PAC)

Activated carbon may be added in water treatment due to its excellent adsorptive properties. At Happy Valley WFP activated carbon is added as needed to manage taste and odour problems associated with algal blooms [57].

Activated carbon is generally classed as

granular (GAC) or powdered (PAC), depending upon particle size.

8▪3▪1

Reported effects

PAC addition has been reported to result in increases in the solids concentration of both alum and ferric sludges [797, 854]. This is consistent with the concept of PAC acting as inert, incompressible ‘ballast’ (see discussion in §8▪3▪5). Although activated carbons can contain pores in the range <2 to >50nm, they have much greater solidosities [949], φ, and mass fractal dimensions, Df, than the WTP sludge aggregates — especially for the desirable products containing primarily the smallest pores [949].

462



Measurements on WTP sludges incorporating various proportions of PAC yielded estimates of Df in the range of typical values for coagulation without PAC — although this is a very wide range [478].

8▪3▪2

Equipment

A series of graded fine mesh stainless steel laboratory test sieves (Endecotts, London) were used for wet sieving analysis: these were classed as allowing passage of particles of sizes 180, 90, 53, and 25μm.

8▪3▪3

Materials

An alum sludge sample was obtained from the pilot plant at Happy Valley (see §3▪2▪6▪3). This sample was nominally algal; however it was established that a significant proportion of PAC had been added. The coagulant was alum, added at 13mg(Al)/L. The PAC was added 100s (1.7min) after coagulant addition.

After a further 5.1min a

polymer flocculant, Magnafloc LT-22, was added at 0.07mg/L (for the other pilot plant sludges the dose was 0.11mg/L — see §5▪6▪2). The particular PAC added was expected to have an average diameter of approximately 20μm. However the adsorption properties observed on the pilot plant seemed to be around 5 times worse than expected in this case, leading to some speculation that the particle size may have been somewhat larger (yielding a less favourable ratio of surface area to mass). Nevertheless, wet sieving analysis indicated that the average particle size (including sorbed material) was indeed of order 20μm, as shown in Table 8-3. Hence the poor adsorption observed may rather have been due to, say, kinetic factors or interference by the coagulant [949].

8▪3 : Powdered activated carbon (PAC)

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D. I. VERRELLI

Table 8-3: Size distribution of suspended solids in Happy Valley PAC sludge.

Particle size range [μm]

Retained fraction [%m] Drying at 60°C

Drying at 100°C

> 180

0.2

0.2

90 to 180

1.6

1.5

53 to 90

11.6

11.9

25 to 53

20.5

20.7

< 25

66.0

65.7

It may be seen that there is generally good agreement between results for solids dried at 60 and 100°C, in each case indicating particle sizes predominantly less than 25μm. The results are compatible with a typical commercial PAC having been used (i.e. between 65 and 95% passing a 44μm sieve [189, 949]) [289] [cf. 478, 778]. The material in the smallest size range naturally includes also precipitated coagulant and material removed from the raw water. However the PAC is expected to dominate the mass even in this range, considering qualitative observation (e.g. colour) and the estimated ρS (see §4▪3▪2▪2).

8▪3▪4

Experimental results

The dewatering properties of the PAC-laden alum sludge are presented in Figure 8-9 (compressive yield stress) and Figure 8-10 (hindered settling function). For comparison similar sludges produced at the same pilot plant are also displayed. Although the new sludge was initially described as “algal”, it is likely that the dewatering properties were dominated by the large PAC dose that was added. As far as is known, there were no other significant differences in the processing conditions.

It is clear that the PAC sludge lies considerably apart from the other three (non-PAC) sludges; indeed, it lies furthest from that non-PAC sludge of the same coagulant dose (13mg(Al)/L).

464



The compressive yield stress shows an order of magnitude improvement at intermediate to high solidosities, and for the hindered settling function the improvement is almost one order of magnitude. Results of both py and R are comparable to those estimated from the data of KOS & ADRIAN [598] for a PAC-dosed alum WTP sludge — see Figure 9-20 and Figure 9-21.


1.E+3 1.E+2 1.E+1 1.E+0 1.E-1 1.E-2 1.E-3 19 mg(Al)/L , pH ~ 6.1 13 mg(Al)/L , pH ~ 6.4 6 mg(Al)/L , pH ~ 7.0 13 mg(Al)/L ; dosed with PAC

1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0


Figure 8-9: Compressive yield stress for alum pilot plant sludges of varying coagulant dose compared to a pilot plant sludge of intermediate coagulant dose but containing some algæ and a high PAC load (pH assumed to be comparable).


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D. I. VERRELLI

2


1.E+15

1.E+14

1.E+13

1.E+12

1.E+11

1.E+10

19 mg(Al)/L , pH ~ 6.1 13 mg(Al)/L , pH ~ 6.4 6 mg(Al)/L , pH ~ 7.0 13 mg(Al)/L ; dosed with PAC

1.E+09 1.E-3

1.E-2

1.E-1

1.E+0

Solidosity, φ [–] Figure 8-10: Hindered settling function for alum pilot plant sludges of varying coagulant dose compared to a pilot plant sludge of intermediate coagulant dose but containing some algæ and a high PAC load (pH assumed to be comparable).

8▪3▪5


Water treatment plant sludges containing high loadings of PAC exhibit markedly improved dewatering characteristics compared to equivalent sludges without PAC, both in terms of kinetics (R(φ)) and in terms of the equilibrium condition (py(φ)).

In both cases the

enhancement factors are of order 101. Although this conclusion is based on the characterisation of a single alum pilot plant sludge, it is expected to be general across all sludge production scales, and a wide range of coagulant

466



doses and coagulation pH values, provided that there is ‘sufficient’ loading of PAC. The conclusion is also expected to be valid in qualitative terms for ferric sludges and even sludges in which similar ‘ballast’ is present. These huge enhancements of the dewatering properties suggest that PAC (or something similar) c o u l d be added to aid dewatering [cf. 431]. However, it must be remembered that to have a significant effect, a considerable amount of PAC (or equivalent) must be added, and this will quickly increase the mass of dry solids to be dewatered. Thus, although the sludge may dewater 5 times faster (say), and to a fivefold greater concentration (say), the mass of dry solids may have increased tenfold — or by 100-fold. This is a relationship that would need to be checked before adding such ‘ballast’ purely as a dewatering aid. Further considerations are the additional operating cost of dosing PAC, and the possible adsorption of contaminant species (desirable) and treatment chemicals such as chlorine (undesirable) [189]. Nevertheless, where PAC and similar materials (e.g. bentonite clay [28, 115, 171, 431], ~100μm quartz [52, 171, 431, 518, 827, 896], 1 to 10μm magnetite [171, 431, 827], fly ash [431], et cetera [cf. 28, 107]) are added for treatment purposes, the results presented show that the sludges produced are very different from ‘conventional’ non-PAC water treatment plant sludges. This will need to be accounted for in plant design and operation.


467

9.

UNUSUAL MATERIAL BEHAVIOUR

In analysing experimental observations, and in modelling dewatering behaviour, it is usual to make a number of simplifying assumptions.

Some key assumptions that can be

mentioned are: • microscopic homogeneity; • no ‘boundary’ effects (cross-sectional uniformity, one-dimensional behaviour); and • material stability — no appearance, disappearance, or transformation of any phase.

While assumptions can permit us to characterise the controlling mechanism, if used wantonly they can end up obscuring important phenomena. With this in mind, this chapter discusses unusual material behaviour that does not fit into the common set of assumptions.

9▪1

Induction time

The induction time refers to the period of nil o r very slow settling prior to commencement of relatively rapid settling. These phenomena can often be understood as arising from metastability o r from the formation of features that promote dewatering by the dewatering process itself (respectively). Examples of this were alluded to in §7▪4▪5; see also §9▪3▪2▪2.

9▪1▪1

Published observations and theories

Two topics from the literature that give insight into induction times are observations of delayed settling and research into chaotic behaviour. In fact, their relevance is even broader than this, as they can help to understand other ‘threshold’ or ‘critical’ phenomena that have been observed (see §9▪3▪2▪2). Further useful background material is discussed in the review of fibre bundle models (§R2▪3▪3) and other material in Appendices R2▪2 and R2▪3.

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D. I. VERRELLI

9▪1▪1▪1

Delayed settling

In a range of particle or gel systems a ‘waiting’, ‘latency’, or ‘induction’ time has been observed before the occurrence of perceptible settling or before the onset of relatively rapid settling [213, 246, 248, 298, 401, 411, 435, 450, 567, 628, 698, 840, 841, 842, 969, 1035, 1092] (also in filtration [926] and constant-stress shear rheometry [412]). (Rapid drainage from the corners of the meniscus is considered an artefact [842] * — it can be readily avoided by working with hydrophobised glassware (see §9▪2▪2).)

These latency times vary in

magnitude, up to more than 10h [211, 401, 567, 842, 969] (years, even [212] [cf. 841]), depending upon the system.

The magnitude has been associated with the strength of

interparticle attraction [347] and the solidosity [211, 567]. The network during the induction period may be classified as being in a metastable state. In certain circumstances the sample may ‘cascade’ through multiple metastable states throughout the settling [cf. 246, 401, 840].

Some possible causes of an ‘induction time’ before settling reaches its maximum rate include: • The simple requirement for acceleration of the particles (and liquid) from a nominal zero initial velocity. Analysis of dynamic STOKES flow suggests this is unlikely to be a practical constraint for WTP aggregates. • Circulation currents induced by the filling of a sample into the settling cylinder [cf. 308, 856, 869], and by repeatedly gently inverting the cylinder — or similar [e.g. 363] — to improve homogeneity. • Breakage of the particulate structure upon loading, without provision for a “stable” structure to be reformed prior to sedimentation [435]. • Air bubbles introduced by vigorously agitating the sample prior to settling [401] [cf. 411, 842], or possibly by in situ evolution [cf. 246] or earlier dissolution [cf. 298]. • Generic ‘wall effects’ [840, 842].

*

However, it may reduce the settling induction time by encouraging material to “slip” from the top corners and then “detach” entirely from the meniscus, “removing any support [on the network] from above” due to depletion forces [969]. For certain materials the corners do not drain, and the bed retains the meniscus’s profile as it settles [1107].

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Chapter 9 : Unusual Material Behaviour


• Bond breakage: o Sudden ‘slipping’ of individual bonds (after a period of creep) [386, 814]. See

also §R2▪3▪3, §R2▪3▪4 and §R2▪3▪5. o A chemical mechanism may inhibit the (re)formation of strong bonds between

‘aged’ precipitate surfaces [1141]. o If a system is only “weakly flocculated”, then although initially the structure has

many cross-links (ι(φ0) ≡ py(φ0) / Δρ g φ0 h0 > 1), after ‘ageing’ the yield stress may weaken (ι(φ0) < 1) [628].

The ageing mechanism may be a structural

rearrangement in a dynamic quasi-equilibrium — see also bulk viscosity (§9▪3▪2▪4(a)). • Densification or compactification of aggregates by thermally-activated processes (particle ‘hopping’) reduces the network’s ability to ‘heal’ following bond rupture and thereby maintain a dynamic quasi-equilibrium [211, 213, 347, 411, 412, 567, 841, 842]. o Evolution toward an equilibrium ‘colloidal crystal’ (plus fluid) state [841].

• The formation of macrostructural features [246, 273, 401]: o Formation [133, 945, 1035] — or rather reformation [338, 950] — of larger

aggregates. o Formation of large voids [e.g. 261, 314, 362, 450, 1078]. This may be initiated by

aggregate densification.

(See also synæresis, §R2▪1.)

They might also form

randomly as a result of dynamic instabilities [cf. 362].

9▪1▪1▪1(a)

Delay due to channelling

Formation of macroscopic voids, and especially channels, is of most interest, and has been widely observed.

Channels are conventionally considered to be much wider than the

particle dimension, so that fluid in the channels is ‘short-circuiting’ the particulate matrix [1078]. In fact liquid flow relative to the solids in dewatering operations could never be uniform over the cross-section, apart from the case of ordered (e.g. close-packed) particle beds. The chaotic occurrence of slightly larger interparticle gaps could be interpreted as the absence of channelling, or as ‘dynamic’ channelling; however, even where such ‘ m i c r o c h a n n e l s ’ are more stable and persistent, they are conventionally viewed as an i n h e r e n t f e a t u r e of the m a t e r i a l . 9▪1 : Induction time

471

D. I. VERRELLI

Channel formation may be promoted in moderately dilute systems with strong particle interactions [cf. 401] — including hydrodynamic interactions [cf. 86].

Channels can be

formed by the rise or fall of foreign ‘inclusions’ such as air bubbles or large particles [218, 450, 951]. The effect of channels is to greatly enhance fluid escape rates [1078].

In the present work macroscopic voids have been observed at the edge of settling cylinders, often not too far from the surface of the bed (where particle pressures are lower), and are proposed to be due to ‘edge effects’ where the wall is acting as a support that is not balanced locally. (Similar horizontal rolls of coherent flocs were observed at the cylinder walls in settling of activated sludge at low φ0, although these were in the un-networked ‘suspension’, rather than the networked bed [246].)

Other workers, researching different systems, have observed the formation of vertical channels [401, 842, 969], as well as horizontal “fissures” (sometimes connected by minute vertical tears) [401, 950, 969]. The channels enable the liquid to escape the bed with minimal resistance, and often carry small amounts of entrained particles [950, 951], which “erupt” at the surface [842], resulting in the formation of ‘volcanoes’ [218, 246, 362, 401, 450, 969, 1078]. Fissures have been observed to commonly propagate inward from the walls [969]. Channel stability depends on both particle and fluid properties, and is reported to be enhanced at higher initial solidosities [401]. Dark field imaging experiments revealed not only c h a n n e l s carrying escaping fluid u p to the drainage surface, but also so-called “ s t r e a m e r s ” apparently carrying dense “blobs” back d o w n into the bed [842].

It was proposed that the streamers form when the

accumulated “debris” at the mouth of a ‘volcano’ becomes too heavy to be supported by the gel beneath and sinks back into the bed [cf. 401], “often along channels opened up earlier” [842, 969]. (Aside from transport of dense ‘blobs’ to the top of the bed by circulation currents, they may also form ‘in situ’ through densification by aggregation or as a by-product of channel formation [401].)

The ‘blobs’ displace lighter material as they sink, causing

additional circulation [401] (cf. ‘aggregative’ and ‘nonhomogeneous’ sedimentation [86]). The blobs may also sink faster due to their larger effective diameter [86].

472



It was only after the development and transport of these channels and streamers that rapid sedimentation commenced [842, 969]. Transport of solid material to the top of the column promotes network failure by two s y n e r g i s t i c effects: removal of particles from within the bed w e a k e n s the structure at that location, while deposition of the particles at the top of the bed increases the l o a d on the bed for all horizons above the particle’s original position. Delayed settling was observed for depletion-flocculated systems with ‘moderate’ interaction energies, of order (4 to 8) kB T [347]. In more-strongly attracting systems, the induction time is so long that the suspension ‘creeps’ slowly to its equilibrium state before any effects can manifest; in less-strongly interacting systems the induction time vanishes to zero [cf. 347] — in these two limits the induction time ceases to have physical meaning.

VESILIND & JONES [1078] investigated channel formation in calcium carbonate slurries. The channels were relatively short compared to the column and bed heights [1078]. Their results show that the channels occur around the top of the networked bed, which rises as more sediment is deposited [1078]. At the same time the suspension is falling, and so eventually the bed–suspension and suspension–supernatant interfaces meet, at which time the channels are no longer supported and mostly c o l l a p s e [1078]. This time may correspond to sudden dips in the h(t) settling profiles.

Remnants remain as cavities within the bed and as

‘volcanoes’ at the surface [1078]. The solidosity in the region around the channels is not sensitive to φ0 [1078]; the local solidosity is probably both the ‘cause’ and the ‘result’ of channel formation. The channel length would be limited below by the maximum particle pressure that can be withstood by the rapidly-flowing liquid, and limited above by the distance the plume can rise into the suspension before it is sufficiently dispersed laterally that the velocity is insufficient to maintain a clear flow path. The reported experimental results indicate that the bottom of the channels approximately coincides with the gel point [1078]. (FITCH [363] likewise stated: “Channelling is observed only in a band at the top of the compression zone in batch tests”. He also indicated that ‘short-circuiting’ commences above a threshold solidosity [362].) It was concluded that vertical channels must therefore arise due to “buoyant instability caused by the reduced solids concentration in the region just above the compression zone” [1078].

9▪1 : Induction time

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D. I. VERRELLI

The channel zone, and hence the top of the bed, was claimed to rise at a constant rate, independent of initial (suspension) solidosity, contrary to conventional theory [1078]. Moreover, the s u s p e n s i o n solidosity does not remain constant (as in conventional zone settling), but rather progressively decreases [1078]. This latter effect is explained by the release of liquor from the consolidating bed into the suspension faster than it can permeate through the suspension [1078]. The two effects can be synthesised using a mass-balance argument that the presence of channels causes solid mass to be added to the bed more quickly than it can be supplied by the falling suspension (at φ0) [cf. 205].

TORY & SHANNON [1050] had earlier suggested that channelling was more likely to occur in tall columns of uniform (intermediate) solidosity. This might be interpreted as relating to columns in which the suspension or network is far from equilibrium.

CHEN et alia [246] proposed that the mechanism of transition from the latency period to a constant-rate period was controlled by the volume fraction of (activated sludge) f l o c s in their system, φ.

It was explained that — given negligible permeability of the flocs

themselves — permeability would be a strong function of φ, and approaching a certain limiting value the resistance would rise greatly, and sufficiently for the hydrodynamics to induce channel formation [246].

BATCHELOR & JANSE VAN RENSBURG [131] studied the stability and instability of b i d i s p e r s e particle systems experimentally, and analysed their results in terms of the theoretical framework discussed in §2▪4▪3▪2. Their focus was on the settling (or creaming) of hard-sphere particles at low to moderate total solidosity, at low REYNOLDS numbers (Re < 1) [131]. In agreement with prior research [e.g. 1108], they observed the spontaneous formation of a number of macroscopic structures in unstable systems, principally ‘blobs’ (superficially similar to bubbles in fluidisation applications, although there Re > 1) and ‘streaming columns’ (i.e. vertical channels) [131]. Importantly, the vertical features were preceded by the appearance of grain- or drop-like regions of localised concentration in one component, and depletion in the other, implying that the streaming columns are caused by “bulk-buoyancy effects” [131].

474



Aside from channelling, these bidisperse-system phenomena can also be compared to ‘fingering’ effects [cf. 1108]. Unstable systems with high total solidosities tended to form blobs, while those with lower total solidosities formed vertical streams or columns [131]. Where proportions of the species are significantly different, the columns and blobs contain the minor component, and have more globular features [131]. Where the proportions of the species are similar, the structures are more elongated [131]. The clarity of each of the observed macroscopic structures varied in different systems; greater visual contrast between regions rich and poor in a given component implies greater separation or ‘partitioning’ [131]. As a general rule, contrast between regions was increased as the level of ‘instability’ increased [131]. For example, in a system where one species creamed and the other sedimented, contrast between regions was increased as the total solidosity rose [131, 1108]. In another system, with fixed total solidosity, instability and contrast were increased as the particle sizes became more similar, and as the ratio of free settling velocities of the two species was reduced (with negative values allowed) [131, cf. 1108]. This separation was attributed to the particle interactions [see also 1108], rather than convective motion arising from macroscopic inhomogeneity * [131]. Bulk convection was important to the behaviour of the more unstable systems, in which clear blob-like features were observed (although convection developed sooner in systems that formed columns) [131].

In the remaining systems, the dimension of the macroscopic

structures was found to be relatively constant, in the range 10 to 15 particle diameters (d0) [131]. (Blob dimensions were up to 34 d0 before even reaching steady state [131].) Earlier research by WEILAND, FESSAS & RAMARAO [1108] suggests that notwithstanding the ‘unstable’ character of systems with streaming columns, the columns tend to evolve from initially large diameters to smaller, ‘more stable’ diameters [131].

Uniquely, EGOLF & MCCABE [338] reported that channelling occurred when sedimentation was “almost complete”. However no effects from such channelling were obvious in the numerous h(t) profiles published [338]. *

The contrast between regions was quite steady, suggesting that separation occurred initially, and was not affected by convection, which simply t r a n s p o r t e d these regions [131].


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D. I. VERRELLI

One more-developed model proposes that initially the fluid flows through long, tortuous paths, with many contractions, and that through s y n e r g i s t i c * effects the flow paths tend to straighten out into wider and more nearly vertical channels [742, 842]. This is a positive feedback loop, as the increasing permeability permits greater fluid flow, which is better able to break off fragments from the channel walls [218, 842, 969]. Alternatively, the annular interface between the cylinder wall and the suspension can act as a path of least resistance for upward liquid flow (causing the material at the top of the bed near the wall to “fold over” away from the wall): this effect was found to be increasingly significant as cylinder diameter is reduced † below 37mm [950]. See wall effects: §9▪1▪1▪1(c) and §9▪2.

It may be briefly mentioned here that indirect evidence of channelling has also been reported in filtration when the sample partly sediments so that eventually a pure supernatant is filtered through a formed bed [cf. 608]. In contrast to a homogenous suspension, where incipient channel formation may be counteracted through blockage by particles carried in the bulk flow, supernatant permeation is much more compatible with the idea of synergistic effects as increased flowrate creates wider channels and so on (as above).

9▪1▪1▪1(b)

Delay due to densification

Latency times in systems subjected to prolonged, g e n t l e tumbling prior to settling were reproducible within ±20% [842]. It was suggested that when tumbling ceased, and settling would be expected to commence, cluster–cluster aggregation could continue [842] (with the break-up rate now negligible). At this time the sample network was sufficiently robust that

*

Flow restrictions engender higher velocities and greater shear forces, and thus it is at precisely these locations that the fluid most readily overcomes the yield stress of the solid structure and smooths out the restriction [742]. Alternatively, the increase of channel width encourages fluid to flow by this route as a ‘path of least resistance’, breaking further material from its walls [969].

†

A different mechanism was claimed to result in an enhancement in settling rate for the same system (containing phosphatic slime particulates smaller than 37μm), as the cylinder diameter was increased above 47mm [950].

476



settling was not promoted by moving a 5mm steel ball up and down inside the 10mm (square) cuvette [842]. This is consistent with the requirement for relatively direct channels to be formed prior to settling, which would not be formed by this action. Indeed, such channels could be destroyed by the local shear caused by movement of the ball, although no increase in latency time was reported [842]. Uniform shearing of a sample held between rotating concentric cylinders ( with Pé ~ 3) w a s able to significantly r e d u c e the latency time above a threshold shear stress [842]. However, in all cases quite massive strains, of order 101, were created d u r i n g the latency period, including those samples sheared below the threshold stress that did exhibit a reduced latency time [842]. These massive strains “must have broken the network many times over” [842] [cf. 243]. (Early experiments by VESILIND (1968) indicated that channelling can still occur in stirred cylinders, but the channels are then “twisted in the direction of the stirring” [1078] [cf. 1056].) A further example — seen in the present work — of a network’s ability to ‘recover’ from significant shear forces is the observation that pouring a gel into another vessel with moderate care does not prompt significant dewatering [347]. It was proposed that the network is normally able to “heal itself” by forming new bonds between disrupted clusters following the action of some external stress [347, 842]. It may then be reasoned that the settling that finally occurs must be due to a loss of this “healing” ability (or “going off”) [347, 842]. Looking at the problem from a dynamic point of view, it is more accurate to argue that the end of the latency period corresponds to a transition to a regime where the bonds are being broken faster than they can reform [cf. 347] — somewhat evocative of (e.g.) fibre bundle models (§R2▪3▪3). Densification, in which the aggregates become more compact, could reduce the aggregates’ bond forming ability [347, 411, 842]. Densification is envisaged to occur through a process of spontaneous ‘sintering’ upon ageing [347, 411, 842].

For the reported experiments a

s u r f a c e d i f f u s i o n mechanism was considered more likely, in which the diameter of the aggregate remains u n c h a n g e d (until the evolution is almost complete *), and only the

*

Although a mathematically rigorous treatment predicts rupture of the aggregate into individual densified clusters [800], in practice most of these would probably reattach rather quickly.


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D. I. VERRELLI

more tenuous tendrils ‘draw back’ [347, 800, 842] — somewhat like OSTWALD ripening * (§R1▪2▪4▪5) [cf. 773]. Aggregates in certain systems, such as those with large interparticle pair potentials, may ‘sinter’ by a “ v i s c o u s f l o w ” mechanism, where the diameter of the aggregate s h r i n k s considerably [347, 800]. For both mechanisms the driving ‘force’ is surface energy (hence area) minimisation [347, 550]. If the network were not subject to gravity, then the localised densification would presumably continue far enough to break up the network [842] — in a similar way to the formation of cracks in physically constrained samples undergoing synæresis (§R2▪1▪2▪3). Stress is transmitted through a network via conceptual cluster and aggregate ‘backbones’ that are interconnected [347, 813]. Although the unconnected tendrils do not participate in the stress transmission, their form (and location and number density) control how quickly the material is able to ‘heal’ by forming new inter-aggregate and inter-cluster connections [347]. Under the action of gravity the densification acts to increase separation between aggregates or clusters, so that when a bond ruptures (through a combination of kinetic fluctuations and gravitational stresses) the cluster or aggregate can move more readily and moves further before encountering another cluster with which to bond [cf. 347]. Alternatively, this can be described as a growing imbalance in the initial dynamic quasi-equilibrium between bond rupture and re-formation, as the frequency (or probability) of bond re-formation decreases [347] — see also §9▪3▪2▪4(a) and §9▪3▪2▪4(b).

A summary of mechanisms is proposed here: • In unsheared settling, the breakage of network bonds occurs due to self-weight and densification, but bonds are able to dynamically reform fast enough to maintain the macroscopic structure until a certain degree of ageing (densification or sintering) has

*

In

principle

other

sintering

mechanisms,

e.g.

‘evaporation–condensation’

[cf.

188]

(or

“evaporation/deposition” [800]; for aqueous suspensions better termed ‘dissolution–re-precipitation’ [221, 280]), can also act [550, 571]. Evaporation–condensation corresponds more closely to surface diffusion, except that matter is transported through the fluid [550].

Theoretically only those modes involving

material transport from either the particle bulk (i.e. viscous flow) or the compressed contact area (e.g. “grain boundary diffusion”) can lead to macroscopic network shrinkage [550, 571].

478



occurred. The settling is both accelerated by and accelerates the formation of channels through which fluid escapes. • For samples subjected to a macroscopic shear field: o below a threshold stress, the bonds may reform faster than they are broken;

channel formation may be disrupted, but the microscopic sintering will not be affected — as in the case of the steel ball. o above the threshold stress, bonds are broken faster than they can reform, and the

consequent ‘fluidisation’ or liquefaction [286] of the mixture effectively ‘lubricates’ the dewatering process — i.e. reduces the resistance. Alternatively, the higher stresses may be sufficient to break up more tenuous small-scale structures, resulting in an alternative route to densification.

In this process

channels may not be needed. “Migration” of particles away from the walls [cf. 1015], producing a relatively large zone of improved-permeability drainage routes — with only short drainage paths to the walls — is one possible alternative, but by no means confirmed *.

9▪1▪1▪1(c)

Delay due to wall effects

The other aspect of interest in the list presented on p. 470 is the question of wall effects. Decreasing the cuvette w i d t h was found to increase the induction time [401, 840, 969]. The induction time also appears to increase for small sample h e i g h t s [840, 969]. From a statistical perspective, smaller sample dimensions decrease the probability that a major structural ‘flaw’ will form in the network [151]: the ‘failure’ time thus increases on average, but the variance of repeated measurements increases too [cf. 969]. In contrast, larger sample dimensions increase the probability of a major structural flaw to near certain, with corresponding asymptotic decrease in ‘failure’ time and variance [cf. 969].

*

Typical investigations into this phenomenon are done using hard spheres, rather than aggregates: roughness, solidosity, ‘close packing’ solidosity, and a number of other factors can alter the magnitude of particle migration effects [e.g. 1015], and these would all be very different for aggregates. The particle migration profile develops slowly, and even at equilibrium the [ a z i m u t h a l m e a n ] minimum solidosity may not be greatly depressed below the mean [1015].


479

D. I. VERRELLI

Alternatively, if there is an optimum stable floc size for a given system, then container dimensions smaller than this imply that the floc spans the space (in that direction), whereas the weaker inter-floc interactions increasingly dominate for larger container dimensions. While they did not report an induction time, SENIS & ALLAIN [918] predicted that networks would not settle if the column’s height or width were too small, and observed experimentally that the equilibrium dewatering became independent of h0 when friction controlled.

9▪1▪1▪2

Deterministic chaos:

self-organised criticality

and periodicity The settling phenomena that arise in ‘real’ systems are also encountered in observations and simulation results in other fields.

BLUE & ADLER [164, 165] developed models of pedestrian traffic by treating individual pedestrians as cellular automata. They found that pedestrians could self-organise into more favourable configurations *, principally d y n a m i c m u l t i p l e l a n e (DML) formation in bidirectional (opposing) traffic, and ‘mode locking’, where pedestrians become oriented into bands perpendicular to the direction of travel and do not move laterally (they march in ‘lock step’) [164, 165]. DML flows are analogous to channelling [cf. 1108], in that a virtuous circle is set up whereby it is more favourable to follow a fellow pedestrian (particle) travelling in the same direction than to remain in the path of an oncoming pedestrian (fluid). Periodic patterns can emerge from mode locking behaviour [164, cf. 1108]. In both cases overall flow tends to increase, although mode locking can also lead to reduced flow [165]. DML is frequently observed in empirical pedestrian studies, and is a (dynamically) stable state † [165]. Mode locking is less commonly observed, although it can occur in situations *

On the other hand, the separate endeavours of each automaton to maximise their own speed can also combine to slow the o v e r a l l traffic speed in some situations [165].

†

The two other main types of pedestrian flow [cf. 165] can also be related to particle dynamics: i n t e r s p e r s e d f l o w corresponds to the idealised conception of settling and is metastable; s e p a r a t e d f l o w s are stable, and are analogous to situations where the solids move as a slug [cf. 86] or wall effects are dominant.

480



such as oriented movement of a swarm [163]. In these real situations mode locking is a metastable state that will not be persistent, but rather will dynamically emerge and dissipate [165]. Mode locking is encouraged by monodispersity of automaton (i.e. particle, pedestrian, ...) properties *, as well as systems where lateral movement is discouraged † [165].

Cellular automata (CA) modelling can also give rise to self-similarity (i.e. fractal) properties [906]. BAK, TANG & WIESENFELD [119, 120] identified the possibility for entities to arrange themselves into critical states [906]. This is referred to as ‘self-organisation’, as the systems evolve towards the critical state without being sensitive to changes in the initial conditions or the system parameters (i.e. rule set, in CA simulation) [119, 120] [cf. 958]. The conventional illustration of this is the ‘avalanches’ that occur on the side of a steep pile of sand as the slope exceeds the critical value for stability [119, 906] — e.g. by drying the pile, adding sand [120], or tilting the base. If the sandpile has locally non-steep surfaces, then avalanches from the steeper parts will tend to increase the slope there, until the entire surface of the sandpile is at the critical condition [cf. 906], where each grain is providing the maximum support possible to its neighbours [120]. At this point, further perturbation results in a cascade of self-similar avalanches across the lengthscales [120, 906]. Such cascades are evocative of physical processes as diverse as the fibre bundle models (§R2▪3▪3), the spring–block earthquake models (§R2▪3▪5), and KOLMOGOROV’s [593] turbulence model [cf. 119, 120, 381, 650, 964], along with observed settling behaviour. Cascades on the microscale are also evoked by KAPUR’s description of network failure, paraphrased by DE KRETSER et alii [605]: following reduction of the interparticle spacing, due to local heterogeneities and the directions of forces acting on the particles, the network becomes unstable and particles slip past one another into adjacent interstices to reach a new equilibrium state.

Most relevant to the present work, cascades have been identified in the yielding of particulate suspensions down an inclined plane [286]. The mechanism was described as a

*

Which suggests it may be more frequently encountered in laboratory studies on ‘real’ model systems.

†

For particle systems this may be affected by solidosity or velocity.


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D. I. VERRELLI

positive feedback loop where an initial (‘metastable’) balance between microstructure destruction due to shear and “restructuration” upon ageing (i.e. ‘healing’) is upset and the initial yielding damages the structure such that further yielding occurs, and so on [286]. BOTET & CABANE [175] discussed the irreversible response of a network, i.e. plastic deformation, in terms of “avalanches of complex events involving [bond] rupture, reordering, and creation, until mechanical equilibrium is reached.” This would apply to filtration as much as any other dewatering operation.

Such behaviour was classed as

“fragile” (rather than “plastic”), and is predicted when the applied elastic energy is n o t stored uniformly along the resistant particle chain, but is localised into a small domain — possibly containing some ‘defect’ [175]. It is easy to accept that the percolated chains formed chaotically in real systems could contain defects that would result in this ‘fragile’ behaviour. Fragile behaviour is expected to dominate where individual bonds can store more energy when compressed than they can under tension (before breaking) [175]. Other workers [e.g. 210, 263, 452, 772, 798] have identified cascades of stress ‘avalanches’, after a load has built up.

9▪1▪2

Practical relevance and analysis

In the first instance, investigations into delayed settling provide insight into the physical processes occurring on the scale of particles and aggregates. This provides an important context for broader studies into the optimisation of clarification and thickening operations.

An interesting question is how these observations might apply to c o n t i n u o u s thickening processes, given that laboratory studies have been carried out in batch mode. A continuous process cannot manifest the same ‘induction time’ feature as a batch process; upon reaching steady state, at each elevation within a continuous thickener the material is supposed to be at a stable condition with respect to time (i.e. constant in an EULERian sense). Nevertheless, the kinetics in question could be observed as a near step-change in the steady-state solidosity profile as the flowrate (and hence residence time) in the thickener is gradually changed. Thus study of this phenomenon has relevance to continuous industrial systems.

482



Besides the above motivations, it is essential to be mindful of any induction time effects due to the danger of introducing errors if these are not appropriately accounted for in analysis of experimental settling data. In the present work the B-SAMS program (§3▪5▪1▪1) includes an algorithm to effectively identify the rapid, post-induction settling velocity as the expected constant-rate phase of the h(t) curve. Apart from this provision no other ‘corrections’ are made, but this is not of concern in the present work, because very few samples exhibited an induction time, and for those that did the temporal bias was typically small (i.e. negligible). Furthermore, present protocols do not readily allow the d e w a t e r a b i l i t y information contained within induction time dynamics to be extracted and presented. As alluded to herein, the effects are time-dependent, and perhaps ‘stress-path-dependent’; at best such data would then be presented in the form of py(φ, t) and R(φ, t), but in general it is very difficult to decouple the influence of φ and t on the material. The problems are analogous to those encountered in analysing long-time data exhibiting ‘creep’ effects (9▪3▪2). Delayed settling phenomena may be more amenable to analysis by other approaches, such as micromechanical (§2▪4▪7) or stochastic (§2▪4▪8) modelling with embedded densification (§9▪1▪1▪1(b)) algorithms.

The literature reviewed in §9▪1▪1 dealt primarily with model systems, and so §9▪1▪3 presents experimental observations of delayed settling with WTP sludges.

9▪1▪3

Experimental findings

It was observed that a few samples exhibited a significant induction time during gravity batch settling. The times ranged from seconds to hours. Plots of h(t) for batch gravity settling experiments given in Figure 9-1 and Figure 9-2 illustrate the induction time phenomena. Details of the sludges are given in Table 7-3 and Table 7-4.

§7▪4▪1▪3 also explains the distinction between directly and indirectly filled

cylinders.


483

Height, h [mm]

D. I. VERRELLI

270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90

h = –16.0 ln(t ) + 284 R2 = 0.9987 h = 294t –0.0731 R2 = 0.9992

Loaded directly Loaded indirectly

1E-04 0.001 0.01

0.1

1

10

100

1000

Time, t [days]

Figure 9-1: Gravity batch settling of alum sludge (80mg(Al)/L, pH 5.9) conditioned with Zetag 7623. Directly filled test carried out in a 500mL cylinder with φ0 ≈ 0.0026; indirectly filled test

Height, h [mm]

carried out in a 100mL cylinder with φ0 ≈ 0.0010.

270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90

h = 239t –0.0202 R2 = 0.9955 h = –4.60 ln(t ) + 239 R2 = 0.9957

Filled directly Gently shaken

1E-04 0.001 0.01

0.1

1

10

100

1000

Time, t [days]

Figure 9-2: Gravity batch settling of alum sludge (80mg(Al)/L, pH 8.9) conditioned with Zetag 7623. The directly-filled cylinder was inverted a number of times after about 177 days, yielding the “gently shaken” data. Tests carried out in a 500mL cylinder with φ0 ≈ 0.0016.

484



In Figure 9-1 the directly-filled sample shows negligible settling for 3 days! At this point, the settling slowly commenced. No induction time was seen, however, for the indirectly filled test. Evidently this was not simply due to wall effects, as the first test actually had the larger cylinder diameter (49 versus 26mm). Instead the key factors were the initial solidosity relative to φg, and the shear history of the sample — which could alter φg. Between the day-3 and day-7 readings the samples were inadvertently exposed to low-level vibration due to the operation of a mixer on an abutting bench for a short time. It is likely that this small additional oscillating stress was sufficient to irreversibly disrupt the (meta)stable structure that was originally established [107, 375, 450, 580, 923] [cf. 951]. A key feature is that even upon removal of the external vibration stress, the sample continued to consolidate in a creep-like mode (see §9▪3▪2). The indirectly loaded sample (cylinder filled from material collected in a beaker) shows no clear response to the vibration: it continues to consolidate after 7 days, however this was not preceded by any long-lived metastable state that could have been disrupted.

The characteristics of Figure 9-2 support the above analysis. Here a sample was loaded directly into a wide cylinder (50mm), but didn’t settle until the existing structure was disrupted. Settling and consolidation, or creep, then proceeded. (Note, the second run commenced at a slightly lower height, and greater φ0, due to evaporation through the seal.) After unloading this sample from the cylinder, it was observed that a residue of flocs remained adhered to the walls. This adhesion may have been enhanced by the added polymer.

While it may seem unacceptable to classify a period curtailed by externally-imposed stress as representing an induction time, it is essentially impossible to entirely eliminate such stresses, if thermal fluctuations are included in our definition of ‘vibration’.


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D. I. VERRELLI

9▪2

Wall effects

Wall effects are the most visible of the boundary effects present in the systems investigated. Wall effects become increasingly important in geometries where more of the sample is exposed to (or close to) a wall, parallel to which it wants to move. Of lesser importance, although still present, are end effects associated with the upper and lower cross-section of the sample. A surprising example where end-effects were observed was in the settling of the Magnafloc-conditioned laboratory sludge, where strands of flocculated clusters spanned 15mm from the air–supernatant interface to the supernatant– bed interface in the first few hours of settling. This occurred in the centre of the column, not at the wall (cf. 9▪3▪1▪1)!

9▪2▪1

Cylinder diameter

A common assumption made in dewatering models is that the system can be treated as onedimensional.

This is usually a fair assumption.

In geometries where the phases flow

between walls with very narrow spacing, relative to the aggregate size, wall effects become important, and the one-dimensional assumption is invalid. (Further complications arise in industrial devices, where material enters at a central location, say, and is assumed to then be uniformly distributed over the entire cavity or chamber cross-section.) It is worth emphasising that the effect is expected to depend on the gap dimension with respect to aggregate diameter. Polymer conditioning was shown in §7▪4 to result in the formation of large flocs; freeze–thaw conditioning likewise resulted in the formation of large zots (§8▪2). However, something different happens when the solidosity surpasses the gel point, and the material forms a network. A true mathematical fractal network has no characteristic lengthscale [906]. Our system, however, is constrained by the dimension of the cylinder and the size of the primary particles. It is also not necessarily true that the aggregates or flocs will arrange themselves in a self-similar manner (cf. Figure 7-17, the last part of §R1▪5▪3, and the note on percolation following Table R1-13).

That is, the fractal character might not extend beyond the

(erstwhile) limits of a given aggregate [cf. 386, 844, 845, 967] — or might be of a different nature. 486



Under a mild pressure, the clusters from which the aggregates or flocs were built may be sufficiently robust to be treated as effectively the largest integral particles in the system. Under progressively higher pressures the network would eventually rupture to the extent that primary particles would lose their identity as constituents of a parent aggregate or cluster, so that the characteristic particulate size would reduce to d0.

9▪2▪1▪1

Previous recommendations

ZHAO [1145] found that 100mL cylinders (30mm diameter) gave identical settling to larger cylinders for unprocessed samples of WTP sludge, but slightly retarded the settling of polymer-conditioned sludges. This can conceptually be related to the formation of large flocs following polymer conditioning.

Various researchers suggested that wall effects could be neglected for ratios of cylinder to mean particle diameter, D / (dagg)50, of >50 to 100 [in 1145] or >200 to 1000 [246], where (dagg)50 represents the median aggregate size.

Other results suggest the cylinder diameter must be greater than 10mm to neglect wall effects (depletion-flocculated 0.4μm PMMA spheres) [347, 969]. COE & CLEVENGER [273] recommended D > 50mm. FITCH [363] made a general recommendation for diameters of D T 100mm (with h0 T 1m). KAMMERMEYER (1941) found D ≥ 40mm (CaCO3, BaSO4 and SiO2) to be acceptable [133]. AUZERAIS et alia [102] reported nil wall effects for settling of monodisperse silica systems of 0.27 to 0.94μm size, both dispersed and weakly aggregated, with a cylinder diameter of order 36mm.

SOMASUNDARAN, SMITH & HARRIS [951] found significant sensitivity for D ( 50mm (with h0 = 178mm), but continued influence all the way up to D = 300mm, for fine phosphate rock slimes that exhibit channelling. The greatest deviations were observed at intermediate times [951].

BERGSTRÖM [140] derived a simple relation between h∞ and D, such that for a given material and fixed φ0 and h0 the wall shear stress could be obtained from the gradient of 1 / h∞ versus 9▪2 : Wall effects

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D. I. VERRELLI

1 / D.

The derivation was based on incompressible sediments, ignoring the solidosity

variation of the true profile, and also the axial variation of the compressive stress [140]. SENIS & ALLAIN [918] proposed a more complicated dependence of h∞ on both D and φ, and allowed for compressible sediments using a simple power-law expression for py(φ). Both derivations [140, 918] estimated the wall stress as the product of the axial particle stress, namely py, the stress analogue of POISSON’s ratio (i.e. the ratio of lateral to axial stresses), say н, and AMONTONS’s ‘friction coefficient’, μ [see also 905, 1012]. The friction coefficient is generally specified in terms of the a p p a r e n t contact area, and thus the apparent normal stress [see 195]. py is affected inter alia by aggregate size and solidosity. Both publications [140, 918] treated н and μ as constant; although true for a simple solid, for a particulate network they may depend upon local solidosity, the network stress, or indeed the history of compaction [918], and dynamics, along with the configuration of the testing device (wall material and lubrication, geometry, piston velocity, et cetera) [661, 984, 1012] [see also references following equation 9-10b]. For clayey sludge TERZAGHI [1012] reported μ ≈ 0.12 for ‘static’ interaction with steel, μ ~ 0.20 for glass, and μ ~ 0.25 internally. For 40nm ferric oxide powder at ~10MPa STRIJBOS et alia [984] reported μ ~ 0.3 to 0.4 (lubricated) and μ ~ 0.5 to 0.6 (unlubricated) for ‘dynamic’ interaction with steel walls; for the lubricated case ‘static’ values were estimated as ~ 0.2 to 0.3. For BERGSTRÖM’s [140] system of sterically-modified ~0.2μm alumina particles the wall stress was estimated to be of order 5Pa, introducing an error of circa 4% for D = 57mm. In SENIS & ALLAIN’s [918] system of neutrally-charged 70nm calcium carbonate significant wall effects were seen at larger diameters as solidosity increased: up to D of order 15mm near the gel point.

9▪2▪1▪1(a)

Torpid matter

EVANS & STARRS [347] proposed that each gel has a characteristic macroscopic stress transmission lengthscale [690, 969].

488

This can be more evocatively described as a zero-



frequency * stress or momentum “screening length”, or a characteristic stress (or elastic energy) d i s s i p a t i o n l e n g t h [347] [690]. The principle is that the network of particles has a “finite elastic memory” [347].

The observed settling behaviour (or indeed physical

response to any stress) then depends upon the ratio of the smallest sample (or container) dimension, Dmin, to this characteristic lengthscale, ξ [347] [cf. 690, 918].

For example,

supposing Dmin to be the diameter [347]: • Dmin [ 2 ξ — settling is uniform at the hindered terminal velocity, i.e. ‘plug flow’, resisted only by hydrodynamic drag; • Dmin > 2 ξ — the centre is in plug flow, while the material near the walls undergoes shear; • Dmin / 2 ξ — the settling assumes a parabolic POISEUILLE-flow-like profile (see bulk viscosity: §9▪3▪2▪4(a)). In thinking about this behaviour it is helpful to draw a distinction between a network defined by its r i g i d i t y and a network defined by its c o n n e c t i v i t y [see 681]. For ease of measurement and direct interpretation in terms of py the former definition has been adopted for φg in the present work, although it is tacitly assumed that the two approaches do not differ greatly (see §2▪1▪2). A corollary of the above model is that a particulate system may form a network or gel, in which pairwise particle interactions percolate the entire space, without being able to transmit a stress between its boundaries — i.e. the yield stress of the bulk may remain zero until some solidosity a b o v e the gel point. The behaviour was considered sufficiently novel for a new class of material to be proposed to describe it, namely “torpid matter” [347]. It is unclear precisely what varieties of material might fit into the class of ‘torpid matter’, but it is indicated that the (shear) yield stress — as the (elastic) storage modulus, G′, at zero frequency — must equal zero [347], and so this classification may be theoretically justified for dispersions, suspensions or even ‘ p h y s i c a l l y -bonded’ gels, but not ‘ c h e m i c a l l y bonded’ gels [346] [690].

*

Although all materials are ‘lossy’ at non-zero frequencies [347] (e.g. high-frequency sound carries only for a short distance), the unusual quality of ‘torpid matter’ is that even zero-frequency stresses dissipate [346].

9▪2 : Wall effects

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D. I. VERRELLI

The principles can be illustrated through the following theoretical example [cf. 347]. Consider an assemblage of aggregates. Each aggregate is rigid, and transmits stresses across its body. Each aggregate in turn interacts with other aggregates; while a proportion of these interactions occur through rigid connections (i.e. with a yield stress), the majority occur by floppy modes. In this scenario it can readily be seen that macroscopic stresses will decay on a lengthscale related to the size of the aggregates and the fraction of rigid interaggregate bonds [cf. 347]. (Moreover, py becomes a function of lengthscale!) This is a probabilistic interpretation of a feasible microscopic mechanism. In contrast, the mathematical development of EVANS & STARRS [347] deals strictly with macroscopic conditions, and derives an e x p o n e n t i a l d e c a y pattern. Thus the torpid matter theory is a m a c r o s c o p i c model. Indeed, it may be possible to explain the same observations using other models. The existence of torpid matter has not been confirmed, and certain aspects are yet to be studied (e.g. dependence of ξ upon applied stress). Furthermore, by the nature of the definition it is only possible to identify a material as ‘torpid matter’ if its behaviour has been observed on a sufficiently large lengthscale (T ξ, say). Hence the usual ‘rules’ of physics (viz. GALILEan invariance) can be expected to apply in the limit of small lengthscales — even when the system size is large.

9▪2▪1▪2 9▪2▪1▪2(a)

Present findings Settling

A number of samples of a plant alum sludge (2005-04-05, see Table 5-1(a)) were loaded to the same height, h0, into cylinders of varying capacity and diameter. The h(t) gravity settling profiles are presented in Figure 9-3. For most of the time there is no discernable difference between the three larger cylinders, indicating that there is no benefit to be gained in using sizes larger than 250mL (37mm diameter) for typical WTP sludges.

The smallest cylinder, with a diameter of 26mm,

appeared to exhibit slightly retarded settling, suggesting that the walls have tended to provide extra support to the network (cf. ‘arching’), rather than acting as channels for supernatant to escape (cf. ‘short-circuiting’) [308, 1075].

490



At long times, >10d, there appears to be divergence in h(t) among the three larger cylinders, with the material in the larger cylinder approaching a lower final height.

This is also

suggestive of the cylinder walls providing support to the particle network. An alternative explanation is that the walls of the cylinders taper inward slightly toward the base, and the base itself is not perfectly planar. Such errors would be expected to become more evident as the heights of material in the cylinders decreased, as is the case here.

240 100mL : 26mm 250mL : 37mm 500mL : 49mm 1000mL : 61mm

230 220 210

Height, h [mm]

200 190 180 170 160 150 140 130 120 110 100 90 80 0.001

0.01

0.1

1

10

100

Time, t [days] Figure 9-3: Gravity batch settling of an alum sludge in cylinders of varying capacity and diameter (as indicated in the legend). All were filled to the same initial height, h0, within a range of 1.5mm.


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D. I. VERRELLI

Given that the differences in long-time transient behaviour do not affect our estimate of R(φ), and will only have a minor effect on the estimated gel point, it is concluded that use of 250mL cylinders is acceptable.

This conclusion cannot automatically be extended to the conditioned sludge samples, where considerably larger floc sizes were obtained.

Settling here was carried out in larger

cylinders. It is unfortunate that no samples exhibiting either an induction time (§9▪1) or ‘false’ equilibrium height (§9▪3▪2▪2) were assessed in the investigation of wall effects.

9▪2▪1▪2(b)

Filtration

The present work has not included a systematic study of wall effects in filtration.

It is notable that the samples studied generally have compressed to relatively thin cakes. The filtration results have also exhibited good reproducibility. Agreement was obtained despite variation in initial solidosity and initial height, although it must be recognised that the range of feasible variations was rather constrained due to practical experimental considerations: namely, an ability to load a homogeneous sample without air bubbles and to finally obtain a sufficiently thick cake.

In order to investigate further possible variations from one-dimensionality, a series of experiments commend themselves, in which the material at a certain horizon is somehow marked upon loading the sample. If one-dimensional ‘plug flow’ occurs, then this marker substance will maintain a plane form throughout the dewatering operation. This could be assessed by dissecting the filter cake at the end — or indeed any intermediate stage. The marker substance could be chosen to dye the liquid phase or the solid phase (or both), or it could be a solid object.

Candidate solids are superfine powders and permeable

membranes. The two key criteria for choosing the marker substance are that it not interfere with the dewatering properties of the sample and that it be readily detectable.

(More

sophisticated studies might use markers that are detected radiologically or magnetically, say — cf. §2▪4▪5▪3(d).) 492



A preliminary experiment utilising calmagite indicator dye to colour the sample was inconclusive. A laboratory alum sludge was compressed at 10kPa in order to ensure a sufficiently thick cake for analysis. The chosen protocol was to load half of the sludge sample, drip in a more-or-less uniform film of dye, and then load the remaining half of the sludge sample. It was found that loading the second portion of sludge caused the material already present to swirl, so that the dye was mixed through much of the upper portion, and part of the lower portion, before filtration even commenced.

While one-dimensional

behaviour was not proven in this experiment, neither were any obvious two-dimensional effects identified. This technique could be a promising means of investigating the importance of twodimensional dewatering effects, provided that the loading technique can be refined.

9▪2▪2

Cylinder surface properties

It has been reported that coating a filtration cell with poly(difluoromethylene) reduced adherence of the sample [926]. In the present work the inner surface of a number of glass measuring cylinders was rendered hydrophobic to examine any influence of the walls on gravity batch settling.

9▪2▪2▪1

Experimental

Glassware surfaces may be rendered more hydrophobic by a process of silanisation (or silylation), in which a chlorosilane is reacted at the surface, where the glass is assumed to consist largely of SiO2. Chlorotrimethylsilane (“CTMS”), (CH3)3SiCl, was used, as this has been identified as a more ‘robust’ treatment [987]. Background material and the adopted procedure is presented in §S16.

The sludge sample selected was the low-alum-dose pilot plant sludge described in §5▪6▪2. This was assessed as being relatively biologically active, in that vegetation grew and was visible after a couple of weeks.


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9▪2▪2▪2


Results of sample settling in treated and untreated cylinders are presented in Figure 9-4. Both samples loaded for settling were assumed to be the same, although the initial heights were very slightly different. While the sample in the control cylinder starts and finishes with a similar offset to the sample in the hydrophobised cylinder, for short to intermediate times (say up to about 0.1 days) the control sample appeared to settle slightly slower than the sample in the modified cylinder. At longer times the expected offset was re-established. Although the differences are small, they are consistent with the concept that floc particles will adhere more strongly to ordinary hydrophilic glass surfaces than to modified hydrophobic surfaces. The fact that the control sample eventually settled to an equilibrium height in proportion to the settling undergone by the other sample may suggest that either: • the hydrophobic modification is not long-lasting; or • the sticking effect is only important during free (and hindered) settling. The first option seems quite plausible, as it was observed after the settling was complete that the inside glass surface of the cylinder remained hydrophobic (by inspection of water droplets) above the sample water line, but had lost most of its hydrophobicity throughout the area below the (initial) sample level. The suggestion that sticking is more important for the more dilute material seems counterintuitive, due to the expectation that wall effects would be more important in concentrated systems that might form relatively stable ‘arches’. However it is also possible that the dependency may be due to the changing kinetics: sticking is a transient phenomenon, that may hold long enough to disturb the rapid dewatering occurring during free (and hindered) settling, but which releases on a timescale smaller than that which would be significant for the final consolidation.

Figure 9-4 indicates a marginal influence of wall hydrophobicity upon sample settling. To

test whether this is a general result, the comparison was repeated using plant alum sludge (Winneke 2005-07-01) and plant ferric sludge (Macarthur 2005-09-21). Both exhibited even less discrepancy between settling in control and silylated cylinders.

494


240 230 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 0.001

100000

h = -836.75t + 231.57 R2 = 0.9996

10000

1000

100

10

h : Silylated h : Control –dh/dt : Silylated –dh/dt : Control

0.01

0.1

1

0.1 1

10

Settling rate, –dh /dt [nm/s]

Height, h [mm]


100

Time, t [days] Figure 9-4: Comparison of settling of plant alum sludge with silylated glass walls against settling in an unmodified glass cylinder.

Overall it must be concluded that the effect of silylation upon settling kinetics is negligible, and arguably within experimental errors. However, a benefit is obtained in the fact that rendering the surface suitably hydrophobic can practically eliminate the meniscus, as observed experimentally here (Figure 9-5). This is useful in improving the achievable measurement precision at the start in the free settling period (where the initial height is difficult to determine) [cf. 842]. Along with this there is less tendency for an uneven bed surface to arise * in the consolidation phase (where small changes in height occur over long period of time), cf. §9▪3▪1▪2.

*

This is attributed in part to the improved initial interface evenness and in part to a decreased strength of adhesion of sludge particulates to the wall. There is, however, an increased likelihood of air bubbles adhering to the treated walls!


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D. I. VERRELLI

Despite the usefulness of a more planar meniscus, it can create other experimental problems with certain samples. In particular, for samples where strong depletion forces exist the network may ‘stick’ to the air interface (cf. Figure 9-7), gain extra support against consolidation, and manifest an increased induction time [969]. This applies irrespective of whether the interface curvature is reduced by hydrophobising or by increasing the vessel’s width [cf. 969].

Figure 9-5: Meniscus of untreated surface (left) and of surface treated with CTMS (right).

9▪2▪3

Conclusions

Sample settling is marginally dependent upon cylinder diameter and hydrophobicity. Provided 250mL cylinders or larger are used, wall effects can be neglected for most water treatment sludges. Polymer-conditioned sludges are the exception, due to the very large lengthscale of their structure — of order millimetres. For these samples the largest diameter cylinder available should be used. For samples where wall effects are suspected, it is beneficial to conduct settling tests in different cylinders in order to obtain an estimate of the error involved [see 308]. Although silylation appeared not to affect the settling directly, by rendering the meniscus more planar it improves the accuracy of height readings.

496



9▪3

Long-time dewatering behaviour

Several effects have been observed in the process of characterising drinking water sludge dewaterability that were not expected in view of the LANDMAN–WHITE phenomenological model. Examples of such behaviour include: • the apparent attainment of (metastable) equilibrium by settling sludges followed by an increase in the settling rate, and • the difficulty of fitting the long-time settling (and filtration) data in order to obtain a finite, positive estimate of the final (equilibrium) bed height. These effects seem to be independent of each other, and may occur together.

The significance of these effects lies in the accuracy of the model that will be used for predicting dewatering. It is possible that material changes occur naturally over the course of time, and this is important experimentally, in order to ensure that representative samples are being characterised. It is also pertinent to the behaviour of sludges in lagoons and drying ponds. It is also possible that a different dewatering mechanism becomes significant, or even dominant, as high concentrations are reached, and the rate of dewatering according to mechanisms modelled by LANDMAN & WHITE slow and approach zero as equilibrium in those transfer mechanisms is neared. If effects such as ageing or competing dewatering mechanisms are present and significant, then this can, for example, affect the dewaterability parameters obtained from the characterisation and analysis. For example, although a sludge on site may not be subjected to more than even one day’s dewatering, the phenomenological model uses an equilibrium value of the solids volume fraction as a parameter (very roughly akin to a driving force parameter) that can affect the predictions for even short-time dewatering.

9▪3 : Long-time dewatering behaviour

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D. I. VERRELLI

9▪3▪1

Ageing and biological activity during experiment

Quite distinct from the ageing that occurs when a sample is stored for a long period of time, for characterisations that take a long time to perform there is a chance that the material may even change its properties in the course of the characterisation. Intra-experimental ageing is considerably more difficult to identify and analyse than interexperimental ageing. Analysis can proceed by: • decreasing characterisation times — although this may come at the expense of accuracy; • developing new theoretical models — although this is quite difficult. Despite, and because of, these difficulties, intra-experimental ageing should not be ignored.

9▪3▪1▪1

Observed biological activity

One potential cause of unexpected behaviour may be the natural organic materials that are present in WTP sludges. At very long times a small amount of ‘vegetation’, possibly algæ, had grown in a minority of samples and was visible on the surface of the settled bed, with a tendency to be oriented toward the sun. In a few instances strands of vegetation adhered to the wall slightly above the level of the bed: see Figure 9-6. Given the typical caldera-like topology of the interface between the settled bed and the supernatant for all sludges (e.g. Figure 9-8), these strands give the impression of acting as ‘guys’ to ‘anchor’ the bed, limiting

further consolidation (or synæresis). The most remarkable manifestation of this occurred uniquely in a surplus sample of plant ferric sludge that had been set aside under ambient laboratory conditions for ~1½ years. In this sample a ‘biomembrane’ formed around the circumference, running between the crown of the shrunken bed and the beaker wall, as high as the supernatant–air interface (Figure 9-7).

The observations suggest that the

biocompounds are only able to attach to the glass wall when the bed is almost stationary. In general, growths were not observed below the surface of the bed, or at intermediate times, although it is possible that very small growths formed that could not be seen.

498



Figure 9-6: Strands of vegetation adhering to cylinder wall for laboratory alum sludge [Winneke raw water 2004-05-11 coagulated with 1.5mg(Al)/L at pH 6.0 (2004-08-19)] (left), and plant alum sludge [Winneke WTP sludge 2005-04-05 (on 2005-06-17)] (right).

Figure 9-7:

Macarthur WFP plant ferric sludge 2005-09-21 (on 2007-02-02).

Images of

‘synæresed’ sludge and ‘biomembrane’ under tension between liquid meniscus and ‘crown’ of shrunken sludge bed.

9▪3▪1▪2

Development of large-scale morphology

The topology typified in Figure 9-8 is distinct from that described in §9▪1▪1▪1(a), as the craters or depressions form in the centre of the top surface of the bed, on the cylinder lengthscale. This topology is similar to the form observed by WEEKS, VAN DUIJNEVELDT & 9▪3 : Long-time dewatering behaviour

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D. I. VERRELLI

VINCENT [1107], who performed settling experiments on suspensions of 80nm silica particles in thin glass cuvettes. The form attained by those materials was apparently due to attractive forces pulling the network in upon itself — i.e. synæresis — and was amplified by the high meniscus curvature in the thin cells [1107]. High wall friction [see 347] might also be capable of producing such an interfacial profile. SHEN, RUSSEL & AUZERAIS’s [926] work on gas-driven filtration of ~130nm silica sphere gels also resulted in the formation of interfaces depressed at the centre and in the immediate vicinity of the walls, as in Figure 9-8, although the mechanism may be different in several ways, given that the solid and liquid phases move in the same direction in filtration, and in view of the ‘chaotic’ boundary condition at the top interface. The “catastrophic” separation at the walls was apparently favoured by the consequent relief of the radial stress gradient; synæresis was held not to be responsible [926].

Figure 9-8: Central depression, vegetation, and material rolled against (or down) the walls, in sludge from Winneke raw water 2004-07-05 with dMIEX, 5mg(Al)/L, pH 6.0 (2005-01-07). Largescale features of the interface are shown schematically at right in cross-section.

500



Figure 9-9:

Batch settling of Macarthur WFP ferric sludge 2005-03-23.

Photograph (taken

2005-06-17) and schematic cross-section. At long times extensive stratification developed: the lower (charcoal-coloured) layer underwent synæresis, and supports a ‘plug’ of well-packed white material, with ‘fluffy’ rust-coloured flocs on top — some flocs from the top layer have fallen past the ‘plug’ into the gap created by the shrinkage. Several cracks are also apparent.

Several other observations are illustrated in Figure 9-8 and Figure 9-9: • Cracking, both vertically and horizontally. • Drawing in of the gel from the sides of the container, suggesting synæresis (see §R2▪1), but possibly due to bioactivity. • Stratification — this seemed to become evident only after the bed had been formed for quite some time, and so n o t obviously due to different free-settling rates [cf. 131, 416]. • Other wall effects, such as the formation of rolls [cf. 246].

All of these phenomena make the task of reading the settled bed height more difficult. However it must be emphasised that for the great majority of samples these phenomena were negligible.

9▪3▪1▪3

Exposure to light

The foregoing observations led to the idea of altering the conditions to prevent, or minimise, adhesion to the walls. Two possibilities were investigated both individually and in concert, namely modification of the cylinder surfaces to render them more hydrophobic and


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D. I. VERRELLI

shielding the contents from the light. The former is more general, and was treated in §9▪2; the latter is associated more definitely with biological activity. To investigate this second effect, another set of experiments was carried out in which samples of the same material were settled in cylinders that were either silanised or unmodified, and kept in ambient light (night and day) or in continual darkness.

Samples have been settled in cylinders that were kept in continual darkness by covering them with cylinders made of black card (apart from occasional removal to take readings). The samples used were a plant alum sludge (Winneke 2005-07-01) and a plant ferric sludge (Macarthur 2005-09-21).

No significant effect of exposure to light on the settling rate could be identified. The selected plant ferric sludge turned out to manifest little biological activity, even in the light-exposed cylinders.

In contrast, the plant alum sludge eventually (~3 months)

developed biological growths, which differed between the light and dark cases (but not between hydrophilic and hydrophobic cylinders). The samples kept in the dark developed a number of black mould-like spots over the sides and top of the sludge bed, while those exposed to light developed a layer of green ‘fuzz’ on the top surface only. Both sludges stratified.

9▪3▪1▪4

Conclusions

Although growth of vegetation was evident in some samples at long times — especially in the plant samples — it was not possible to determine whether this could be restricted by either adjusting the wall hydrophobicity or limiting exposure to light. (A further variable of interest is dissolved oxygen, which is as much a function of biological activity as a determinant of it.) Observed biological activity was commonly restricted to a light growth at the top of the bed, although occasionally more ‘structural’ configurations were seen that may have supported the sludge against further consolidation. Nevertheless, generally the biological activity did not appear to interfere with sample dewatering. The growth was only significant in a small number of samples, and that at long

502



times, so that the characterisation was still essentially complete from the short- and mediumterm data. Naturally the possibility remains that microscopic biological growth occurred in all samples. Such an eventuality could more justifiably be regarded as characteristic of the material. In any case, as this was not observed it is not possible to account for it here.

9▪3▪2

Creep and long-time metastability

9▪3▪2▪1

Postulated behaviour

The mechanism of the dewatering behaviour of the sludges at long times is contentious. It has been suggested that this long-time behaviour is due to changes in the constitution of the flocs themselves, based on the theory that the gel point is shifting to higher values at long time. While the gel point may shift, experimental results presented earlier (§4▪2) are not indicative of phase changes (i.e. rearrangement at the atomic level), suggesting that a physical mechanism (perhaps influenced by electrostatics), operating on larger lengthscales, is responsible. Understanding of this long-time behaviour, and an ability to model it, would confer two benefits: 1.

A greater insight into the mechanism of consolidation — i.e. network failure.

2.

An ability to more accurately estimate the equilibrium condition — i.e. prediction of φ∞, h∞, V∞, et cetera by extrapolation of ‘truncated’ time-series.

It should be noted that the equilibrium data is also used to determine short-time behaviour.

The main theoretical tool for analysing long-time behaviour is the analytical solution separately derived to describe the limiting behaviour in settling (§2▪4▪5▪3(g)) and filtration (§2▪4▪5▪6), which predicts e x p o n e n t i a l decay of h: h = exp[(E1 ‒ t) / E2] + h∞ .

[9-1]

This exponential decay is consistent with the asymptotic long-time behaviour predicted by the consolidation model of SHIRATO et alii [933] (§R2▪3▪2).


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D. I. VERRELLI

The other key tool is the l o g a r i t h m i c behaviour empirically associated with primary creep (§R2▪2▪3▪2), exemplified by equation R2-25.

However other relations have been suggested too, principally various power laws (cf. §R2▪2▪3▪2, §S3). The true form may well be a function that has not been investigated. One such form is the ‘ s t r e t c h e d ’ or ‘ c o m p r e s s e d ’ e x p o n e n t i a l [e.g. 214, 248, 582, 666], for which agreement with theoretical prediction [e.g. 263, 567, 599, 636, 693, 902, 908] and experimental observation [e.g. 259, 261, 262, 263, 599, 636, 690, 697, 927] of various ‘relaxation’ processes has been found (cf. §9▪3▪2▪5). (Some of these long-time relaxations have been called “ultraslow”, and the characteristic timescale itself increases with ageing [263].) ‘Stretching’ or ‘compressing’ of otherwise exponential decay can be ascribed to the presence of a “wide distribution” of characteristic relaxation times for the elementary components of the material behaviour [263, 902] [cf. 636] [see also 243], with each potentially associated with fluctuations on a particular lengthscale within a (fractal) colloidal aggregate or gel [599] [cf. 697].

9▪3▪2▪2

Settling

In several of the batch settling experiments the sediment interface appeared to be approaching an equilibrium value, but then continued to settle for an apparently indefinite period of time (Figure 9-10). It is probable that this behaviour is present at all solidosities above the gel point — it is not usually observed in filtration runs, however, due to the configuration of the stoppage criterion algorithm, which limits the experimental run time.

Another good example of this complicated behaviour is presented by a plant ferric sludge obtained from Macarthur WFP. Figure 9-11 shows that the settling would appear to be slowing * to a final height at around 1.5 days, yet later data shows no equilibrium condition. The pre-equilibrium plateaus could then be characterised as ‘metastable’ states.

*

Plots on logarithmic co-ordinates can sometimes deceive the eye. The trends identified here have been confirmed on linear co-ordinates.

504


250

250

230

230

210

210

190

190 Height, h [mm]

Height, h [mm]


170 150 130 Expected asymptote?

110

170 150 130 Expected asymptote?

110

90

90

70

70

–0.1198

h = 112.1t 2 R = 0.9973

h = –9.53 ln(t ) + 108.1 2 R = 0.9977

50

50 0

24

48

72

0.001

96 120 144 168 192 216 240

0.01

0.1

1

10

100

1000

Time, t [days]

Time, t [hours]; Time, t [days]

Figure 9-10: Continuation of settling after asymptote appeared to have been reached. The sample was laboratory ferric sludge at 160mg(Fe)/L and pH ≈ 5.1 (see Table 5-4).

260 240 220 Height, h [mm]

200 180 160 140 120 100 80 60 40 0.001

0.01

0.1

1

10

100

Time, t [days]

Figure 9-11: Batch settling of plant ferric sludge [Macarthur WFP, 2005-03-23 (see Table 5-4)]. Arrows indicate the end of a height ‘plateau’.


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D. I. VERRELLI

The slowing and subsequent acceleration of the settling rate may have a precedent in the concept of fibre bundle models discussed in §R2▪3▪3. The mechanism could be due to gradual slipping of the particles or aggregates cascading into a sudden structural failure towards a new, more stable (macroscopic) state (cf. §R2▪3▪4, §R2▪3▪5). Another potential underlying cause of the ‘sudden’ drops in h(t) is the collapse of macroscopic voids that formed earlier in the settling process [cf. 1078] (see §9▪1▪1). However this is not a satisfying explanation here, given the relatively large heights and times involved, and the failure to reach an obvious equilibrium. The last nine or so points are fairly well fitted by either a logarithmic or a power-law curve. This suggests an analogy with the conventional logarithmic model of primary creep, equation R2-25, used in soil mechanics (see §R2▪2▪3▪2). Both fibre bundle models and soil mechanics analyses also allow for constant and increasing consolidation rates (secondary creep and tertiary creep, respectively), when the ‘strength’ of the material is exceeded.

These can be considered in assessing the disruption of the

metastable states, but are not of major benefit. Conceptually, given the physical limitation on consolidation, it must be assumed that if the imposed load exceeds the material strength such that tertiary creep occurs, then eventually this regime must be terminated by the transition to a new (more compact) network structure with a greater strength.

Additional data in support of the logarithmic model approximation of primary creep is presented in Figure 9-12(a) and (b), which show batch settling data for two ferric sludges. It is seen that power-law curves also provide quite good fits. It is not clear why there might be two regions with slightly different settling behaviour.

506



Interface height, h [mm]

140

120

h = –9.70 ln(t ) + 109.2 R2 = 0.9974

100

80

h = 102.2 t –0.0742 R2 = 0.9971 h = –5.73 ln(t ) + 99.0 R2 = 0.9953

60 0.01

0.1

1

10

100

1000

Time, t [days]

Figure 9-12(a): Batch settling of a ferric sludge, 80mg(Fe)/L and pH ≈ 6.1, showing tendencies toward logarithmic-type primary creep at long times in two regions.

Interface height, h [mm]

80

70 h = 63.0 t –0.0768 R2 = 0.9967 60

50 h = –4.14 ln(t ) + 62.8 R2 = 0.9983 40 0.01

0.1

1

10

100

1000

Time, t [days]

Figure 9-12(b): Batch settling of a ferric sludge, 80mg(Fe)/L and pH ≈ 5.6, showing tendencies toward logarithmic-type primary creep at long times in one region.


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D. I. VERRELLI

An example of curve-fitting batch settling data to generate a prediction of the equilibrium sediment height is shown in Figure 9-13. Here three different curves have been fitted to the nine points at the end after excluding the last two. The exponential fit has furthermore been fitted in a ‘rolling’ or ‘moving’ fashion over sub-sets of seven data points over the entire domain of the data, so the predictions are thus those obtained using only the last seven data points up to the given time. Unbiased coefficients of determination, R2, associated with each h∞ prediction curve are also plotted in line with the last time in the sub-set. The three forms of equation used to fit the data at the end of the curve are given with the graph, in addition to their fitting coefficients and (unbiased) R2 values.

Fitting these

equations over the last nine points (excluding the last two) resulted in good fits in all cases, shown as the example plots in Figure 9-13. When the number of points was increased to 13, the power and logarithmic fits remained good, while the exponential fit began to appear unsatisfactory, as in Table 9-1, below. As can be seen, the power and logarithmic fits tend to be on a par with or superior to the exponential fit, except that unfortunately their predictions are not physical!

Table 9-1: Long-time batch settling data curve fits (h and h∞ in mm, t in days).

Equation

Fitting over 9 points

Fitting over 13 points

R²

Predicted h∞

R²

Predicted h∞

h = a t‒b

0.9986

0

0.9961

0

h = a ln(t) + b

0.9993

‒∞

0.9987

‒∞

h = exp(a t + b) + h∞

0.9989

110.6

0.9883

113.4

508


Height, h [mm]; Predicted final height, h ∞ [mm]


280 270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110 100

1.00 R² 0.99 0.98 Sediment height Example sub-set Example exp. fit Predicted h∞ (exp. fit) R² (exp. fit) Example power fit Example log. fit

h = 172.7t –0.0806 2 R = 0.9986

0.96 0.95 0.94 0.93

h = -9.8482 ln(t ) + 164.5 R2 = 0.9993

0.92

h = exp{3.3518 – 0.01205t } + 110.6 R² = 0.9989

0.01

0.97

0.91 0.90

0.1

1

10

100

1000

Time, t [days] Figure 9-13: End-point prediction for a laboratory alum sludge at 80mg(Al)/L and pH ≈ 4.8 (see Table 5-1(b)). The crosses labelled “Predicted h∞ (exp. fit)” represent the prediction based on applying the exponential fit over seven data points up to that time; here “R2” represents the coefficient of determination.

Even after more than 100 days worth of settling, the exponential fit remains sensitive to the number of points included in (or excluded from) the analysis. However the greater problem with the prediction can be seen from examination of Figure 9-13. It is quite clear that, with a suitable density of data points, the exponential curve fit could have been applied after (say) 40 days of settling to yield a significantly overestimated final height prediction despite the reassuringly large value of R2. Thus it must be concluded that so far prediction of experimental settling data before completion of the experiment, i.e. “end point prediction” is not yet feasible.


Yet an

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D. I. VERRELLI

analogous method is occasionally utilised for the estimation of R(φ∞) in the filtration of certain WTP sludges — see §7▪4▪4▪3 — and routinely for biological sludges, where the only alternative is a tedious iterative re-prediction procedure (cf. §3▪5▪2▪2, §S10▪3). This conclusion is reinforced by the common ability to fit various curves quite well through most sections of the data, as illustrated in Figure 9-14, where the only curve fit with a clear theoretical basis is the linear form fitted to the initial, free-settling phase.

280

h = –2163t + 287.4 R2 = 0.9985

260 240

Height, h [mm]

220 200 180 160 140 120 100

h = –6.237 ln(t ) + 75.3 R2 = 0.9937

h = 81.39t –0.2685 R2 = 0.9995

80

h = 81.24t –0.1214 R2 = 0.9862

60 40 0.001

0.01

0.1

1

10

100

1000

Time, t [days]

Figure 9-14: Curves fitted to batch settling data for a dMIEX alum sludge at 5mg(Al)/L and pH ≈ 6.0 (see Table 6-2). Only the linear fit over the first section has a clear theoretical basis.

The ultimate aim of batch settling analyses such as those in the preceding discussion will depend upon whether the long-time settling data is perceived as being relevant to the dewatering behaviour of the material as originally loaded, or whether the material is ageing and/or creep or ‘synæresis’ processes are beginning to dominate. In that case the aim must be either to predict what final sediment height would be reached subsequent to the last observed point, or to identify a nominal ‘final’ height within the range of sediment heights actually observed, and not equal to the last observed height.

510



It has been shown in the foregoing that prediction of a final height beyond the domain of observed values is problematical. Although a detailed analysis has not been presented here, it is likewise unclear as to the ‘triggers’ that may be invoked to truncate a set of observed h(t) data and so declare a nominal value of h∞.

9▪3▪2▪3

Filtration

As noted earlier, it may be expected that ageing effects will be present in filtration as well as settling, albeit perhaps somewhat more difficult to identify.

Approximately-linear asymptotes for d(V 2)/dt have been observed experimentally, as given in Figure 9-15. The sample used was 92mg(Al)/L alum sludge at pH 8.6 (see Table 3-14(a)). Applying the standard LANDMAN–WHITE approximation to the limiting long-time behaviour (equation 2-125b), a closely-linear fit of t as a function of ln(E3 ‒ V ) can be obtained from the last 41 data points, but a poor fit results when more (141) points are used — see Figure 9-16 (“default fit”, LW). The goodness of fit is reflected in the prediction of the tail end of the filtration: compare the LW predictions of V 2 in Figure 9-17 and Figure 9-18. Evidently the LW fits of dV 2/dt in these two Figures leaves room for improvement; one notable feature is the higher curvature of the predicted derivatives compared to the experimental values. It may be hypothesised that choosing E1 and E2 differently — e.g. by optimising both dV 2/dt and V 2 — could improve the overall closeness of the fits in Figure 9-17 and Figure 9-18. These alternative fits, denoted LW', turn out not to be able to significantly improve the derivative predictions while maintaining reasonable approximations of V 2.

Again a

curvature is introduced in dV 2/dt that is not present in the original data. The problem is complicated by the varying density of data points (sparsity increases at long times), however the primary constraint is the functional form dictated by equation 2-125b.

A further

disadvantage is that the derivation may also lose its theoretical validity: see the alternative fit for the long data set in Figure 9-16. Overall these alternative estimates do not possess an advantage over the standard LANDMAN–WHITE parameter estimation.


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D. I. VERRELLI

V² dt/dV² (40-pt. mov. ave.) dt/dV² (2-pt. central diff.) linear fits

8.0E-3

3.0E+9

2.5E+9 R2 = 0.9809

2.0E+9

2

7.5E-3

1/Slope, dt /dV [s/m²]


8.5E-3

1.5E+9 7.0E-3

R2 = 0.9607

R2 = 0.9838

6.5E-3

1.0E+9

5.0E+8

6.0E-3

0.0E+0 0

50000

100000

150000

Time, t [s] Figure 9-15:

Linear regression on dt/dV 2 for three pressures in a stepped-pressure

compressibility run. The dashed curve is the 40-point prior moving average of dt/dV 2 typically considered (default output of Press-o-matic software); the points are obtained from a 2-point central moving average (that is, local Δt/ΔV 2) and are better estimates, albeit noisier.

512



80000

Time, t = E 1–E 2ln(E 3–V ) [s]

70000

R2 = 0.9970

R2 = 0.9342

60000 50000 40000 30000

Long data set Short data set

20000

Alt. fit long (LW') Alt. fit short (LW')

10000

Default fit long (LW) Default fit short (LW)

0 -15.0

-13.0

-11.0

-9.0

-7.0

-5.0

ln(E 3 – V ) [–]

Figure 9-16: Standard linear regressions of t against ln(E3 – V ) for long and short sets of data optimising R2, and alternative fits optimising the fit of V 2 and its slope against t.

Based now on the observations made in Figure 9-15, and following on from the ‘logarithmic creep’ analysis considered for batch settling (see §9▪3▪2▪2; also §R2▪2▪3▪2), it is of interest to assess the predictions resulting from the a s s u m p t i o n of a linear slope of V 2(t). These fits, denoted DIV, are presented in Figure 9-17 and Figure 9-18 for long and short sub-sets. The fits for a large sample of points are poor, as they are biased to data at intermediate filtration times, too far before the final asymptotic behaviour is manifest. Yet for a smaller sample of data points a good fit is obtained, seemingly superior to even the LANDMAN–WHITE fits (either LW or LW').

It is noteworthy that — as in the batch settling analysis — the

predictions of V∞ are u n b o u n d e d for this logarithmic behaviour.


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D. I. VERRELLI

1.80E+9 1.60E+9

7.15E-3

1.40E+9 1.20E+9

7.05E-3

1.00E+9

7.00E-3

8.00E+8 6.00E+8

6.95E-3

V² V² long — LW V² long — LW' V² long — DIV dt/dV² (central diff.) dt/dV² long — LW dt/dV² long — LW' dt/dV² long — DIV

6.90E-3 6.85E-3 10000

30000

50000

70000

2

7.10E-3



7.20E-3

4.00E+8 2.00E+8 0.00E+0

90000

Time, t [s] Figure 9-17: Long-time fits to V 2 and dt/dV 2 over the last 141 points using equation 2-125b with standard (LW) and modified (LW') parameter estimation, and using an assumption of linear behaviour in dt/dV 2 (DIV).

514



1.8E+9 1.6E+9

7.15E-3

1.4E+9 1.2E+9

7.05E-3

1.0E+9

7.00E-3

8.0E+8 6.0E+8

6.95E-3

V² V² short — LW V² short — LW' V² short — DIV dt/dV² (central diff.) dt/dV² short — LW dt/dV² short — LW' dt/dV² short — DIV

6.90E-3 6.85E-3 10000

30000

50000

70000

2

7.10E-3



7.20E-3

4.0E+8 2.0E+8 0.0E+0

90000

Time, t [s] Figure 9-18: Long-time fits to V 2 and dt/dV 2 over the last 41 points using equation 2-125b with standard (LW) and modified (LW') parameter estimation, and using an assumption of linear behaviour in dt/dV 2 (DIV).

9▪3▪2▪4

Discussion

BERGSTRÖM [140] reported experimental work on weakly-flocculated particulate systems, which showed creeping behaviour at long times, only approaching an “assumed” steady state after circa 6 months!

It was suggested that this represented a thermodynamic

‘diffusion’ regime (cf. §9▪3▪2▪4(a), §S17, §S18). Similar observations had been made earlier by BUSCALL, PARTRIDGE, GOODWIN and others [see 211]. GOPALAKRISHNAN, SCHWEIZER & ZUKOSKI [411] claimed that persistent slow settling meant that it was “impossible” to measure a true final sediment height in their system.


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D. I. VERRELLI

SHEN, RUSSEL & AUZERAIS [926] reported possible “stress-induced creep” in the filtration of weakly-interacting suspensions of 0.1 and 0.3μm silica sphere gels; they concluded that “syneresis” or another “thermodynamic” mechanism was not responsible.

At present it does not seem possible to reconcile the long-time logarithmic (or power-law) consolidation behaviour with the LANDMAN–WHITE model of filtration, specifically the asymptotic analytical solution that predicts exponential decay of h(t) at long times. It should be recalled that this asymptotic solution ultimately rests on the assumption that the consolidation rate is governed by the viscous drainage of fluid from between the particles and that this drainage is very fast (§2▪4▪5▪1(c)). If the restructuring kinetics begin to control the consolidation rate at long times, then the LANDMAN–WHITE dewatering model becomes formally inapplicable, as no suitable constitutive equation can be formulated [630]. Rigorous analysis of such a condition is beyond the scope of the present work, but is suggested as an avenue of future research. The most fruitful avenue of investigation is likely to be in filtration at constant applied pressure, due to the greater uniformity of stress (pS) throughout the material, and uniformity of φ → φ∞ at long times. The limiting case would be if there were a massive shift in control over the kinetics as φ → φ∞, so that py → pS. In this case the cake would dewater according to the LANDMAN– WHITE model until the entire cake were at a solidosity just below φ∞, with the remaining consolidation controlled by (say) the restructuring rate. This suggests that in that limiting case the entire material would ‘relax’ as a homogeneous ‘solid’ as t → ∞.

Another possible mechanism relies on the microscopic heterogeneity of the material. Although it is expedient to simplistically treat the solid phase as regularly distributed [e.g. 213], this is likely to be approached only in the random packing of fully dispersed (i.e. noninteracting) particles [cf. 753]. The microscopic heterogeneity of real suspensions and cakes comprised of (consolidated) fractal aggregates would spread the local compressive yield stress to a distribution, rather than a unique value (cf. §R2▪3▪3). This means that the material cannot behave as an ideally plastic material, except perhaps on very large lengthscales.

516



9▪3▪2▪4(a)

Bulk viscosity theory

An alternative means of incorporating material r e l a x a t i o n into the dewatering model is to include the effects of bulk viscosity. An early discussion of the balance between bulk viscous stresses and the interparticle network stress was presented by AUZERAIS, JACKSON & RUSSEL [101], in which a PÉCLET number was used to characterise the dominant consolidation mechanism. BÜRGER and colleagues [200, 207, 218] have also discussed solid-phase viscous stresses [1057]. POTANIN and co-workers [844, 845] developed a theory incorporating bulk viscosity that can be seen as an extension to the LANDMAN–WHITE model adopted throughout the present work. They proposed that a material may dewater by overcoming the s m a l l e r of the p l a s t i c compressive yield stress (σy) and the v i s c o u s stress due to the bulk viscosity (ηbulk). A characteristic relaxation time (trelax) provides an indication of the relevance of viscous processes to dewatering at practical timescales. Effectively the LANDMAN–WHITE model assumes that ηbulk and trelax approach infinity. The theory is presented in Appendix S17, along with a discussion of its properties and merits, and comparison with other formulations [175, 347]. A full discussion of the order-ofmagnitude estimates arising from this theory is also presented in Appendix S17, which is summarised below.

Key variables that arise in estimating the parameters σy, ηbulk, and trelax include the particle– particle interaction potential (‒U), the mean co-ordination number (z), particle size (d0) and separation (δ), aggregate fractal dimension (Df), and system solidosity (φ). Each of these variables has some associated uncertainty.

Unfortunately formulæ for

estimating ηbulk, and trelax contain an exponential function which greatly amplifies these uncertainties. It was found that suitable choice of the physical properties provided reasonable estimates of the compressive yield stress. Estimates of ηbulk, and trelax varied over more than twenty orders of magnitude, although many of these values were not physically realistic. The key results were that the majority of the estimates of trelax were considerably less than 107s (1y ≈ 3.2×107s)


517

D. I. VERRELLI

for φ = 0.005 (as in gravity settling), and estimates of ηbulk were correspondingly below about 106 to 107Pa.s.

Another approach for estimating the importance of bulk viscosity is to use (say) the extended gravity settling model to obtain parameter estimates which can be used to generate h(t) predictions to compare with observed settling profiles — with particular attention to longtime behaviour. The numerical application of this method is beyond the scope of the current work, but a rough approximation was presented to provide an order-of-magnitude indication of parameter values. The long-time h(t) data of Figure 9-10 indicate that the slowest observed interface settling rate, at ~100 days, was as small as h ~ O(10‒9)m/s, while still measurable (see also Figure 9-4). From this it was estimated that the slow long-time settling could be explained by a bulk viscosity as high as ηbulk ~ O(108)Pa.s, which is above most values predicted from the physical properties.

Although the analysis has not proved a significant influence of bulk viscosity effects on dewatering behaviour for the present system, the major conclusion is that their effects cannot be summarily dismissed.

9▪3▪2▪4(b)

Thermally-activated barrier hopping theory

Thermally-activated barrier-hopping models such as those developed by SCHWEIZER & colleagues [248, 582, 908] have been applied by GOPALAKRISHNAN et alia (and others) to describe particle rearrangements relevant to delayed settling [411] [cf. 248] and delayed flow [412] [cf. 582]. The approach could also be applied to more general creep modelling [cf. 582]. [See also 243.] Important aspects of this theory are outlined in Appendix S18. One of the fundamental features is that the system dynamics depend on a characteristic time, thop, that is defined differently to the relaxation time of §9▪3▪2▪4(a).

518



9▪3▪2▪5

Non-diffusive processes

Although a number of the long-time creep theories are derived from an assumption of thermally-activated diffusion, other processes may be responsible. CIPELLETTI et alia [263] found that, for four very different colloidal ‘gels’, relaxation of the dynamic structure factor proceeded initially in accordance with a thermally-activated diffusive or “subdiffusive”  q‒2) *, but at the longest times adopted a mechanism (‘stretched exponential’, with trelax 1 ∝  q‒1) that m a y not be different, “non-diffusive” decay (‘compressed exponential’, with trelax 2 ∝

thermally activated [cf. 261].

The approximately linear dependence of the long-time

characteristic decay timescale on distance suggests restructuring by a l o n g - r a n g e b a l l i s t i c transport mode [263] [cf. 690] (cf. §R1▪5▪6▪1). Such behaviour could be due to relaxation of endogenous network stresses — for which synæresis (§R2▪1) [263] (or, hypothetically, swelling) is a potential consequence. An interesting prospect is that local stress relaxation may induce stresses elsewhere in the material, producing a cascade, or avalanche, of “microcollapses” [263] [cf. 243] (§9▪1▪1▪2) †. Ultimately a dynamic equilibrium is attained [263] [cf. 690]. Despite commonality — perhaps universality — of the long-time relaxation dynamics, the fundamental microscopic mechanisms responsible may differ between systems [263] [cf. 690].

9▪3▪3

Conclusions

At long times sludges exhibit behaviour that is not considered in conventional dewatering analyses. Although chemical activity appears to be negligible (see §4▪2), in a number of samples significant biological activity was observed. This was most common in (pilot) plant sludges, presumably due to the greater proportion of NOM in the sludge at the low plant doses — possibly dominated by algæ in the raw water — in combination with the enhanced

*

The decays follow exp(‒tБ): a stretched exponential results for Б < 1, while a compressed exponential results for Б > 1 (cf. §9▪3▪2▪1).

q is the wavenumber, which is inversely proportional to the linear

dimension, d (see §R1▪5▪4▪2). †

The long-time decay correlation (and ballistic motion) is followed in a time-averaged sense; intermittencies are indicated in temporally-resolved measurements [690].


519

D. I. VERRELLI

cleanliness of the laboratory environment. Little effect was seen from shielding settling samples from light. A number of interesting features were observed, showing that these biological growths could form ‘tethers’ to the cylinder wall in batch settling, and stabilise the bed against further collapse. Synæresis-type effects were also seen, in which the sludge shrank in on itself, away from the cylinder walls. Nevertheless, such biological activity generally did not seem to interfere with characterisation of sludge dewaterability.

The dewatering characterisation methods are reasonably robust, but have difficulty predicting long-time behaviour of WTP sludges, which will affect the accuracy of both shorttime and long-time predictions. In both batch settling and filtration the long-time consolidation conformed closely to the logarithmic model of primary creep commonly applied in soil mechanics. This may indicate an additional mechanism that becomes important at long times, which would affect parameter estimation and dewatering predictions. A problem with this model is that the equilibrium consolidation is unbounded. Specification of a power-law model does little to resolve this problem. Analogies to the logarithmic model of primary creep commonly applied in soil mechanics may yield results useful for improving the accuracy of dewatering parameter estimation and performance prediction. The exponential decay predicted as the limiting behaviour by LANDMAN & WHITE’s analysis leads to physically-meaningful predictions of equilibrium consolidation. However, these predictions could be crudely described as saying that the equilibrium consolidation is ‘a little bit further’ than the final measured data point — no matter how long the experiment has run. This suggests that if we are only willing to wait long enough, then we will observe the bed or cake will consolidate beyond the current prediction of equilibrium. A further complication in analysing the transient dewatering profiles is the occurrence of ‘metastable’ states, where the consolidation appears to be practically at equilibrium, only for the dewatering rate to subsequently speed up. Such mechanical failure has a precedent in fibre bundle models, in the tertiary creep of soil mechanics, and in the self-organised

520



establishment of critical states. These precedents, unfortunately, are not compatible with the LANDMAN–WHITE approach to describing dewaterability, and do not serve as alternative routes to estimation of py(φ) and R(φ). An alternative possibility is that the long-time creep is governed by a strong negative correlation between the solidosity and the dynamic compressibility, κ, opposite to that previously assumed — see Appendix S17. An alternative means of incorporating creep-type effects into the dewatering model is to allow for dewatering by a viscous deformation mechanism, as described by POTANIN and coworkers [844, 845] and others [347]. Analysis of representative formulations of the theory in combination with estimated physical properties and experimental observations expose significant uncertainty but also establish a strong possibility that bond relaxation modelled as a bulk viscosity is important in the long-time settling behaviour. The analysis of multiple batch settling experiments presented in Appendix S10 further supports the existence of creep at long times. It must be recognised that the mechanism for speed-up in the settling rate at long time has not been ascertained. It would be of benefit for further work in this area to consider this mechanism further, and thus establish a range of validity for the LANDMAN–WHITE model of consolidation, including the possible importance of κ, the assumption of time invariant material properties, and the possible existence of a bulk viscosity. In some ways it is not surprising that the above effects prove difficult to model: analogous problems remain unresolved in the field of shear rheology [see e.g. 127, 1142].

9▪4

Reversibility: Elastic cake re-expansion

The dewatering model that has been used to both analyse experimental data and predict behaviour in industrial operation assumes that dewatering is irreversible. This assumption is commonly made in mathematical models dealing with dewatering. (On the other hand, LEE & WANG’s review [642] gave examples where the sludge cake dewatering was assumed to be entirely elastic [1137].) However the assumption is not necessarily strictly true. Certainly, it is easy to conceive of the dilution of a suspension from a solidosity, φ < φg to a lower value.

For example,

additional liquid phase may be ‘entrained’ with the flow of the escaping settled suspension

9▪4 : Reversibility: Elastic cake re-expansion

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D. I. VERRELLI

from a clarifier underflow. In such cases the reversal involves greater separation between already separate particles (or aggregates). However, the elastic expansion of compressed cakes upon reduction of the applied pressure is a different matter. For nominally ‘incompressible’ materials such as silica the compression phase is brief, involving some adjustment of the packing to the most stable and densest configuration (with an increasingly high density of contact points between particles) — only at extremes of pressure would significant particle fracture occur. On the other hand, ‘compressible’ materials such as the aggregates formed in drinking water treatment undergo significant structural rearrangement within each aggregate. In general the changes are so great that it is inconceivable that they could be entirely reversed. Nevertheless, it remains plausible that the aggregate deformation may comprise both an e l a s t i c component and a p l a s t i c component.

Indeed, some ‘recovery’ was been

suggested by measurements made in the batch centrifugation of WTP sludges in the present work.

80

70 Plant alum

Plant alum Lab. alum

70

60

Plant ferric

50

Height, h [mm]

Height, h [mm]

Lab. ferric

40

30

60

50

40

30

20

20

10 1

10

100

1000

10000

1

Cumulative centrifugation time, t [min]

10

100

1000

10000

Cumulative centrifugation time, t [min]

Figure 9-19: Preliminary indications of elastic cake re-expansion in batch centrifugation. Arrows indicate data points of interest, where h increased after leaving the sample to stand.

The centrifugation h(t) profiles are presented in Figure 9-19. In the left chart the arrow indicates the time at which the sample was left to stand overnight, before centrifugation was resumed. There is a re-expansion of 1.5mm recorded. 522



In the experiments conducted subsequently, more care was taken to avoid leaving the sample to stand. Nevertheless, the data in the right chart suggest that re-expansion occurred at about t = 50min, although the standing time could not have been much more than 1min. The feature is less likely to be measurement error, as it is present as increases in h for both plant sludges, and a higher-than-expected h for the laboratory ferric sludge. (The laboratory alum sludge is still settling significantly at this time, so there is possibly less elastic bed formed, and any elastic recovery is more likely to be overwhelmed by the magnitude of the prior compression.) These observations, while suggestive, were neither conclusive nor sufficiently quantitative, and so a more rigorous investigation was warranted.

9▪4▪1

Literature reports

SOMASUNDARAN, SMITH & HARRIS (1973) [950] observed expansion of phosphatic ‘slimes’ following centrifugation, which they described as due to “over-compression” — i.e. the φ achieved in the centrifuge exceeded the equilibrium condition attainable due to settling under gravity.

YEN & LEE [1137] commented on the plastic and elastic components of sludge cake compression, based on centrifugation experiments conducted on activated sludges. They arrived at the following conclusions [1137]: • most sludge cakes exhibited elastic recovery upon removal of the applied stress; • bed re-expansions varied from nil to about 30% (the recoveries in h varied from nil to about 20% of the original drop in height); • addition of polymer conditioner enhanced bed re-expansion, up to an optimal dose; • increasing centrifugation speed first enhances bed re-expansion, due to the increase in elastic energy stored, but then decreases bed re-expansion above a critical acceleration, due to (mechanical) degradation of the bed elasticity; and • the behaviour is complicated, and no simple, predictive correlations could be found.


523

D. I. VERRELLI

A critical feature of YEN & LEE’s [1137] work is that the re-expansion occurred essentially instantaneously, in the 10 seconds during which the centrifuge was decelerated to rest from 200 to 500rpm (8g to 50g m/s2); in the following 600s essentially no changes occurred. A question arises as to whether the deceleration contributes to the rebound in height. If this effect were important, then the variability in responses (e.g. with rotation rate) could be explained by the firmness and cohesiveness with which the sample formed a bed. The most obvious additional effect is for the material to want to bank up against the leading edge as the centrifuge is decelerated (or the trailing edge as it accelerates). Furthermore, experimental trials employing centrifuges with fixed-angle rotors have shown that “rapid” deceleration results in convective mixing of the tube contents due to the CORIOLIS effect [432, 496]. Additionally, BERMAN, BRADFORD & LUNDGREN [141] showed that liquid–liquid interfacial profiles in a centrifuge vary depending upon whether the rotational rate is increasing, constant, or decreasing.

Later centrifugation studies of activated wastewater sludges suggested that for some conditioned samples recovery continued for a couple of minutes after centrifugation ceased [646]. This is more supportive of a true relaxation of the structure, rather than a mechanical disturbance. The other characteristics seen in the earlier paper were confirmed [646].

ZHAO et alia [1144] and LEE et alia [646] presented evidence for the elastic recovery of consolidated filter cakes of activated wastewater sludge, which they termed “rebound” and “relaxation” — the latter term is more apposite. Cake re-expansions were of order 20 to 25% (recoveries in h varied from 5 to about 6% of the original drop in height) [646, 1144]. As distinct from the centrifugation results, in filtration the recovery was far more gradual, taking place on a timescale of hours [646, 1144]. Greater recoveries were seen in polymerconditioned samples, commensurate with the greater original compressions [646]. There were two differences in the experiments from the ideal case. Firstly, according to the authors, as the cake expanded it (partly [646]) took up air, rather than previously expelled filtrate [1144]. This premise is questionable, considering that the septum could be saturated with filtrate, and given that the magnitude of the recovery was only approximately 2mm. If air ingress was significant, then the resistance would be raised due to the capillary forces that

524



arise in desaturation. Secondly, equilibrium had generally not been reached prior to removal of the external stress [1144]. This would give rise to a significant variation in φ over the cake height, but does not greatly affect the conclusions drawn.

This faster elastic expansion of centrifuged samples compared to filtered samples is intuitively reasonable: • Generally the applied pressure in filtration is larger, leading to a higher mean final solidosity of the cake, with a correspondingly lower ‘average’ permeability. • The density of interparticle contacts would be greater in the filter cake, implying a greater resistance to structural rearrangement. • Centrifugation can be faster than filtration, because in centrifugation water always escapes the bed through the path of lowest solidosity, while it is forced through the path of greatest solidosity in filtration. Similarly, in elastic recovery the water re-enters the centrifuged bed at the top interface where φ ≈ φg (greatest permeability), whereas in filtration the water must pass through the most consolidated interface at the membrane face where φ ≈ φ∞ :Δp. (This is especially important where consolidation is incomplete [as in 646].) LEE et alia [646] concluded that the timescales of compaction and relaxation are similar for a given dewatering process.

The foregoing observations of elastic recovery were all made by the same research grouping and all on w a s t e w a t e r sludges.

Standard methods for one-dimensional soil consolidation [11, 37] (by double-ended, laterally-constrained filtration) anticipate significant rebound, or “swelling” (cf. §R2▪1▪2▪3), upon unloading [see also 361, 1014]. Upon final relief of the applied stress to the original ‘holding’ stress of ~5kPa, it is suggested that the swelling process may be sufficiently prolonged that the sample be left “overnight” before removal [37].

TERZAGHI’s [1012]

original experiments indicated that at least 4 days may be required for the full recovery.


525

D. I. VERRELLI

TERZAGHI, PECK & MESRI [1014] presented incremental loading–unloading curves for an illitic soil and four shales. By analogy to consolidation (§R2▪2▪1) a distinction was drawn between “primary rebound” and “secondary rebound” [1014]. MEETEN [737] recognised the possibility of elastic recovery of filter cakes — which he expected to be greatest for “swelling” clay materials — but was unable to detect it by checking for a mass increase due to filtrate uptake, after allowing for experimental uncertainty. He concluded that this could be explained by the filtrate ‘desorptivity’ being (at least) fivefold greater than the ‘absorptivity’ [see 737]. DIXON [317] pronounced that: “Especially for flocculated materials, the compression process is almost completely inelastic”. No justification was provided. A brief c o n c e p t u a l discussion of elasticity effects was presented by LANDMAN, SIRAKOFF & WHITE [625].

Only two sets of studies on W T P sludges have been published previously, namely those of KOS & ADRIAN (1975) [598] and of WANG and colleagues (1990’s) [880, 1098].

The first authors [598] concluded from experimental work on alum WTP sludges that elastic rebound was negligible: it reached up to 0.5 to 1.0% of the o r i g i n a l height for loads of 20 to 61kPa. While this seems small, it is arguably more meaningful to compare the recovery with the f i n a l height (prior to pressure relief): on this basis the maximal recovery at each pressure ranged from 2.5 to 6.9% [see 598]. In either basis the recovery was greatest as larger applied loads were relieved. ‘Rebound’ did not occur until the load was almost fully relieved (applied load of circa 5kPa) [598]. This was attributed to relaxation of the deformation of primary particles [598]. In the rig used it may be that the full load was never applied to the sample, due to frictional losses between the piston or shaft and the cell walls;

more importantly, the rig may have

maintained a high pressure on the sample (following compression to nominal equilibrium) due to static friction not being immediately overcome on partial pressure relief. It is unlikely that primary particles were deformed to the extent suggested. It should also be noted that the samples used were obtained from a WTP using PAC [598], which has been shown in the present work to alter the dewatering properties (see §8▪3).

526



100


Loading Unloading

10

1

0.1 0.01


Figure 9-20: Compressive loading and unloading curves for a PAC-dosed alum WTP sludge; data of KOS & ADRIAN [598]. Solid phase density taken as 2050kg/m3 (cf. Figure 9-21).

2500 kg/m³ 2000 kg/m³

2


1E+15

1E+14

1E+13 0.01

0.10

1.00


Figure 9-21: Hindered settling function estimated for a PAC-dosed alum WTP sludge; data of KOS & ADRIAN [598]. Solid phase densities as indicated.


527

D. I. VERRELLI

The raw data [598] have been transformed to the dewatering parameters used in the present work. For the compressive yield stress — Figure 9-20 — a single value of the solid phase density was assumed (for clarity), viz. 2050kg/m3, as for the PAC-laden Happy Valley sludge (see §4▪3▪2▪2). Pressures were not amended for possible friction losses. The unloading curves should be taken as guides only. Figure 9-21 presents estimates of R for two possible solid phase densities. These were

obtained by first estimating the DARCY permeability coefficient, KD, through the original data [598], and then applying the conversion formula, equation 2-121.

1000

Alum (#2) loading

Pressure, p [kPa]

Alum (#2) unloading

100

Alum (#3) loading Alum (#3) unloading Ferric (#1) loading Ferric (#1) unloading

10

1 0.01

0.10

1.00


Figure 9-22: Compressive loading and unloading curves for three WTP sludges; data of WANG et alia [1098]. The numbers in parentheses are those originally assigned: sludge #1 was taken from a lagoon, #2 after centrifugation, and #3 from a sand drying bed.

The second group of researchers [880, 1098] obtained slightly different results. Following laterally-restrained consolidation of both alum and ferric sludges, the applied pressure was relaxed and in all cases a degree of “swelling”, or elastic “rebound”, was observed [cf. 880, 1098]. The data is replotted as p(φ) in Figure 9-22. As shown, the ‘rebound’ occurred with the first increment of pressure relief [1098]. 528



It is implicit that on the loading curve p(φ) is essentially the compressive yield stress curve, py(φ∞);

the solidosities at low pressures, however, may be misleading due to the

uncontrolled and unknown loading history of the samples prior to testing.

9▪4▪2

Elasticity theory

In materials science it is conventional to discuss loads and material behaviour in terms of stresses and strains. A stress (intensity) is just the force acting per unit area *, and is called compressive or tensile if it acts ‘normal’ (at right angles) to the surface, or shear if it acts tangentially (parallel) to the surface [758];

the conventional symbols are σ and τ,

respectively. Stresses can be superposed — i.e. they are additive — and, conversely, forces that operate obliquely can be resolved into normal and tangential components [758]. A strain is a dimensionless measure of the resulting deformation of the material relative to its initial dimensions and geometry [758].

A given normal stress results in a tensile or

compressive strain given by ε ≡ ΔL / L0, where L is a linear dimension parallel to the stress [758]. Similarly, volumetric strains are computed as ΔV / V0, where V is the specimen volume [758].

A shear strain is measured by the angular displacement [758].

Strains are also

additive [758].

Under the action of a uniaxial compressive (or tensile) stress, it can be shown that a plane through the material oriented at an angle 0° < θ < 90° to the perpendicular experiences a nonzero component of shear stress [758]. In fact, at an angle of θ = 45° the tangential component is at a maximum, namely τmax =

1 2

|σuniaxial|, and equal in magnitude to the normal component

[753, 758, 1014]. Given that the shear strength is commonly less than half of the tensile (or compressive) strength for a given material (including published particulate networks: py / τy ~ ≤10 to 100 — see §2▪4▪7▪1), failure under u n i a x i a l normal stress is often due to a shear mechanism [386, 758, 794] — other mechanisms are discussed by BIKA, GENTZLER & MICHAELS [151], along with the often-overlooked tendency for τy to increase when samples are subjected to compression [see also 753, 984, 1014] [cf. 661, 912]. The angle of the failure

*

Sometimes this is taken as the i n i t i a l area [946]; in the present work the area is constant.


529

D. I. VERRELLI

plane from the perpendicular exceeds 45° by some (usually moderate) amount [e.g. 794, 1014, 1098], which is hypothesised to be due to ‘friction’ between the internal ‘surfaces’ that is directly proportional to the normal component of stress acting on that plane and that enhances the resistance to shear (NAVIER’s theory) [758] [see also 83] [cf. 904]. Hence the failure-plane angle is predicted to be θ = 45° + α/2, in which α is the ‘angle of (internal) friction’ or ‘angle of repose’ (the stable angle a pile of the material forms with a level surface [cf. 1012, 1013]) [758, 859, 1007, 1013, 1014]. If the axial load acts on a c o n f i n e d system so that a minor lateral stress is induced, then τmax =

1 2

namely

|σaxial ‒ σlateral| [242], which is now less than the normal stress on the same 45° plane, 1 2

|σaxial + σlateral| [243, 753, 758, 1014]. The lateral stress in such confined samples also

acts to increase θ [758]. Moreover, confined compression may imply a greater tendency for cracks to be closed up [cf. 83, 151, 1014], so the simple slip-plane model may not be accurate. On a particle lengthscale chain buckling (§2▪4▪5▪1(a)), leading to formation of shear bands [794], may be more representative. One can envisage a large number of localised slip or ‘avalanche’ events — on a range of small lengthscales, as in §9▪1▪1▪2 — occurring on transient slip failure surfaces throughout the body of a confined specimen. It must be cautioned that in rheology τy is conventionally evaluated without compressive loading [cf. 151, 243, 473, 661, 753, 876, 1014], which would generally increase the shear strength (given non-zero internal friction).

CHANNELL [243] performed experiments on

coagulated 1.3μm alumina which did manifest 8 to 19% increases in τy under increasing perpendicular normal load, σ⊥;

yet py / τy(σ⊥) ~ 100 even under load.

Although σ⊥ was

claimed to reach ~80% of py, the simplistic assumption of isotropic network stresses (or “pressure”) — i.e. equal orthogonal normal stresses — was implicit in the analysis and equipment design [243], so the true ratio σ⊥ / py could have been significantly less than ~0.80 (correction by a factor such as н of equation 9-10), suggesting that significantly lower values of py / τy(σ⊥) could be attainable for larger σ⊥. MOLERUS [753] indicates that for a c o h e s i v e p a r t i c u l a t e n e t w o r k the normal stress at a given plane also generates a proportional c o h e s i o n force (perpendicular to the plane) [cf. 904, 905], which — along with the coefficient of internal friction — should be related rather to the m a x i m u m stress experienced in the material’s history.

The introduction of this

cohesion force requires the use of an e f f e c t i v e angle of friction, α′, with α′ ≥ α [758].

530



Assuming the cohesion force is not greater than the normal component of the force acting on the plane gives α′ ‒ α < 20°; however, WANG et alia [1098] reported α′ ‒ α ≈ 24° (α ≈ 19°, α′ ≈ 43°) for three WTP sludges in undrained triaxial compression. A further corollary of the postulated cohesion force mechanism is that the magnitude of the cohesion forces will vary depending upon their orientation, just as the normal force on a given plane varies depending upon its orientation, and so a particulate network consolidated under a u n i a x i a l applied load c a n n o t be considered isotropic [753].

A uniaxial stress also usually gives rise to a lateral strain, which is related to the axial strain by POISSON’s ratio, ν [758]: ν ≡ ‒εlateral / εaxial

[9-2]

for an unconstrained system. Arguments of conservation of volume imply that ν = 1/2 exactly; however, experimentally a range of values between the limits ‒1 and +0.5 have been found for various isotropic materials, showing that volume need not be constant. Commonly values lie around 1/4 [758] to 1/3 [e.g. 753]. For soils ν approaches 0.5 for soft clays, but is about 0.3 for coarse sand or gravel [1033], and can be as low as ~0.1 [267]. POISSON’s ratio has been estimated as 0.474 to 0.497 for <5μm montmorillonite suspensions [738] and ~0.49 for 1.3μm alumina suspensions [242]. The first estimates [738] are dubious as they rely upon the strictly incorrect assumption of linear elastic behaviour up to yielding [605, 758] [cf. 681, 1007], implicitly assume that the sample fails in a shear mode even under compression * [cf. 435], and furthermore they overestimate both py and the effect of

*

At the compressive yield condition the maximum shear stress is τmax =

1 2

|σaxial ‒ σlateral| [242, 758], and

given equation 9-10 we may write |σaxial| / τmax = 2 (1 ‒ ν) / (1 ‒ 2 ν). Both MEETEN [738] and CHANNELL & ZUKOSKI [242] [cf. 243] then simply set ‒σaxial / τmax = py / τy. Given the derivation was carried out for the filtration configuration, py = ‒σaxial (even for σlateral ≠ 0); however τy > τmax is possible if the compressive failure mechanism does not rely on shear (cf. ν → 0.5) [cf. 984]. τy < τmax is possible in general (unlike compressive deformation, shear processes do not automatically foster ‘hardening’ upon yielding), but does not appear germane to filtration: e.g. shear ‘yielding’ could contribute to σlateral, in turn reducing τmax. Furthermore, generally shear failure would not occur in the plane of τmax, but rather in a plane offset by some angle depending on the internal ‘coefficient of friction’, where the local normal stress was smallest relative to τ [758]. Although generally τ < τmax at this plane, this cannot be directly compared with τy


531

D. I. VERRELLI

τmax *. The second set of estimates [242] are obtained from two methods: the former depends on the same assumptions of linear elasticity and shear failure, but the latter is based on the ratio of bulk modulus (see equation 9-4) to shear modulus [see 758] and appears to be reasonable. (The similarity of results from the two methods suggests that the assumptions of the former may not be unrealistic for that sample.)

LU, HUANG & HWANG [682] found the ratio of local lateral to axial stress — н in equation 9-10 — to be of order 0.4 to 0.5 for various 101μm-sized particulate networks compressed at 490kPa, implying that ν ~ 0.3 (neglecting sidewall friction). STRIJBOS et alia [984] reported н ~ 0.3 for powder compacts of 40nm ferric oxide at ~10MPa.

DIMILIA & REED [316]

estimated н ~ 0.4 for alumina powder compacts at 10 to 100MPa [cf. 140, 194, 195] (consistent with the known ν ~ 0.3 [194]). Earlier work by TILLER & LU [1038] gave similar estimates of н, namely ~0.35 (cellulose) to ~0.45 (~1mm sand) at ~680kPa. Also, for dry 1.1mm clover seeds н ≈ 0.35 for 100kPa [1121]. FEDA [361] cited a constant н ≈ 0.39 for a sand, and for a “collapsible” loess soil н increased from 0.29 to 0.53 upon failure of brittle cementation bonds. Several experiments gave н ≈ 0.49 for sand soils [1014]. Representative ranges of н for common soil types (including granular and clayey) have been quoted as 0.13 to 0.67, or 0.43 to 0.66 [1014] †. Somewhat higher values of н were reported by SOWERS & SOWERS (1961), viz. 0.4 (dense sand or gravel) to 1.0 (soft clays), with the latter corresponding to ν = 0.5 [1033], which is expected to be the maximum [661]. RUMPF [876] indicated н ~ 0.5 to be typical for particulate media. Early work on dry alkali metal halide salts (~0.5mm) indicated that н was roughly constant in the range 3 to 30MPa (taking values of 0.5 to 0.8), but ultimately increased to ~1.0 at ~100MPa, in some cases passing through a minimum at intermediate pressure [1125]. Similar behaviour was observed for organic pharmaceutical ingredients, except that for a

measured in conventional rheology as the stress field here is not pure shear. Furthermore, knowledge of the failure plane angle is required to estimate this τ. *

MEETEN [738] incorrectly sets τmax = |σaxial ‒ σlateral|. py is overestimated by assuming the full self-weight acts over the entire cake and also by neglecting the effect of the filter paper and support in potentially absorbing small quantities of filtrate at low loads [738, cf. 884].

†

532

TERZAGHI’s earliest estimates [1012] were н ≈ 0.42 for quartz and н ~ 0.73 for clay.



minority, composed of platy crystals, н ≈ 0.0 was found for pressures below 10MPa [1125]. In contrast, carbonate salts exhibited constant н ≈ 0.35 [1125]. The discrepancy between estimates for clays may be due to lateral variation of the axial stress (§3▪5▪3▪4(b)) [195, 661, 984, 1014].

Equation 9-10 neglects this variation:

strictly

speaking the parameter of interest is н :wall [195], but some investigators might report instead σlateral

wall

(

σaxial = н :wall σaxial

wall

)

σaxial [see 194, 661, 984, 1121] [cf. 316]. Further errors arise

if the decay in axial stress down the column (§3▪5▪3▪4(b)) is neglected [cf. 316, 984]. Much lower values of σlateral / σaxial, e.g. ~0.1, have been reported for systems whose interparticle contacts have very high rotational stiffness and where lateral dilation is allowed [794]. The definition of н requires that upon confinement (i.e. when the sample is transferred into the rigid-walled cell) the sample is in a state that is ‘stress-free’ relative to the subsequently applied load *. Later lateral expansion or contraction (e.g. producing ‘active’ or ‘passive’ plastic failure) does not satisfy this requirement, and can lead to a very different ratio of stresses [see 946, 1013, 1014].

Apparent values of н greater than unity have been also

reported where ‘residual’ lateral forces persist after the axial load is removed [661] [cf. 316] (including in situ ‘preconsolidation’ and ‘overconsolidation’ [850, 1014] [cf. 267]), which does not satisfy the above test. The two exceptions noted here are not relevant to the following analysis [1014].

A material may be said to behave e l a s t i c a l l y if it recovers completely from the strain induced by a given stress after that stress is removed, i.e. the strain reverts to zero [758]. For most materials a l i n e a r stress–strain response (i.e. HOOKE’s law) applies almost up to this elastic limit [605, 758] [cf. 681, 1007]. deformation [758].

Non-recoverable strain can be termed plastic

Following plastic deformation under load, a (predominantly) elastic

response can often be observed upon u n l o a d i n g (and reloading) [850]. The proportionality constant for pure tensile stresses is known as Y o u n g ’ s m o d u l u s , E — “in most materials [it has] practically the same value for compression” [758]. *

An

Otherwise the deformation is not strictly uniaxial. Analysis is easier if self-weight is negligible, but otherwise is still valid provided the sample is added appropriately: e.g. sand slowly poured in [1014] — thus the lateral constraint of each newly-laid-down layer is in the stress-free state.


533

D. I. VERRELLI

analogous constant is the b u l k m o d u l u s , B, which relates an isotropic stress to the ensuing volumetric strain [758]. (An isotropic stress can be considered the action of three mutually-perpendicular pairs of stresses of equal magnitude [758].) Thus: σ z = E εz ,

σx = σy = 0 ,

[9-3]

or σx = σy = σz = B

ΔV . V0

[9-4]

The two moduli are simply related according to [758, 1013] E = 3 B (1 ‒ 2 ν) .

[9-5]

POISSON’s ratio, ν, is typically ~1/3 ( E ~ B), but has been estimated as ~0.49 for ‘drained’ particulate networks ( BS [ ES). The descriptor ‘drained’ need not imply that the network contains no liquid, or that the liquid freely-drains under gravity: the meaning is that the liquid is able to readily flow out of (or into) the material under the influence of a stress, so that the liquid does not contribute to the material stresses resisting the externally applied load. (A promising means of estimating ν is to compare dewatering resulting from a standard uniaxial stress (e.g. approximated in filtration) with that resulting from osmotic consolidation [see 745], which could be arranged to be three-dimensional.

Some two-dimensionally

consolidated samples showed greater dewatering, indicating BS > ES (subscript for ‘drained’ particulate networks), while others indicated no difference. Further investigation would be required to confirm that other aspects, such as interparticle friction [745], are not affected by the change in driving force. Alternatively, osmotic consolidation could also be configured to operate in a uniaxial geometry.)

Evaluating E is straightforward for an unconstrained sample under known uniaxial stress, as is the evaluation of B for a known isotropic stress. In the case of a specimen under uniaxial a p p l i e d load c o n s t r a i n e d such that ε l a t e r a l = 0 , YOUNG’s modulus must be found by solving simultaneously the superposed principal strains [758]: εaxial, con. =

σaxial − 2 ν σ lateral , E

εlateral, con. = 0 =

534

(1 − ν) σ lateral − ν σaxial . E


[9-6a] [9-6b]


This yields [152, 758]  (1 − 2 ν) (1 + ν)  σaxial E= ,  1− ν εaxial, con.   

[9-7]

‘uncorrected’ E

where the factor in brackets is a ‘correction’ due to the lateral confinement. Clearly uncertainty in ν will lead to uncertainty in E. For the common case of ν ~ 1/3, E is ~2/3 of the ‘uncorrected’ value. On the other hand, if ν = 0.49, then E is only approximately 5.8% of the ‘uncorrected’ value — i.e. an order of magnitude difference. If ν = 1/2, then E cannot be determined by equation 9-7. Inserting equation 9-5 into equation 9-7 gives  1 + ν  σaxial B= .   3 (1 − ν)  εaxial, con.

[9-8]

If the stress is perfectly isotropic, so σlateral = σaxial — as for the (pseudo-uniaxial) application of stress to a constrained fluid — then recognising εaxial, con. as equal to ΔV / V0: σaxial

isotropic

B

=

εaxial, con.

.

[9-9]

The relationship between the confined axial and lateral stresses is obtained from equation 9-6b as [cf. 195, 242, 984, 1013] σlateral

confined

=

 ν     1 − ν  σaxial .  

[9-10a]

This proportionality encourages the definition of a stress analogue of POISSON’s ratio, say

σlateral

confined

=

н σaxial ,

[9-10b]

although н is not necessarily constant [cf. 140, 194, 195, 316, 361, 661, 682, 850, 859, 912, 918,

930, 946, 984, 1012, 1013, 1014, 1033, 1038, 1056, 1121, 1125]. (More generally the entire stress field might be assumed to scale with σaxial [83].) In soil mechanics н is called the ‘coefficient of (lateral) earth pressure at rest (in normally-consolidated, young deposits)’ [850, 876, 912, 946,

1013, 1014, 1033, 1038] [cf. 195, 316, 1012], or the ‘RANKINE constant’ [682] [cf. 859] [see also 1012] [cf. 661]; in granular mechanics it is also called the ‘JANSSEN constant’ [661] [cf. 194] or ‘WALKER coefficient’ [cf. 195]. Equation 9-10 shows that isotropic stress (н = 1) in a laterally-constrained solid would arise for ν = 1/2, and this yields εaxial, con. = 0 by equation 9-6a, as the compression (say) is exactly


535

D. I. VERRELLI

balanced by the increase in volume. Of course, ν = 1/2 implies an incompressible solid, for which B → ∞ *. (Note that even liquids and solids are not perfectly incompressible.) Equation 9-10 neglects the effects of axial shear forces due to friction at the walls [cf. 194, 195,

316, 661, 682, 1121].

For the purposes of the present discussion this is a reasonable

approximation, in view inter alia of the small aspect ratio of the filter cake [see 682] A rigorous analysis would require the geometry (known) and н or ν

(§3▪5▪3▪4(b)).

(unknown) and the coefficient of friction, μ, (unknown) be accounted for in a twodimensional model in which the largest principal stress would be slightly inclined from the cell axis [cf. 682].

As a practical measure for the following investigation, the ratio at the right-hand side of equation 9-9 will be computed and reported as the ‘drained’ bulk modulus of compressibility for the particulate network, BS. I.e., for the present discussion it shall be expediently defined that

BS ≡

σaxial εaxial, con.

.

[9-11]

This rather loose interpretation has a precedent in various applied disciplines, such as geomechanics. It should also be mentioned that for fluids and gases the compressive modulus (or reciprocal of the isothermal ‘compressibility’ described in §2▪4▪1▪1) is given by:

B∗ ≡ − V

∂p . ∂V

[9-12]

BS will differ from the true value (by equation 9-8) by a factor of 2/3 for ν = 1/3, or a factor of ~0.993 for ν ~ 0.49, and is exact as ν → 1/2. While these factors reflect residual uncertainty, the approximation is certainly sufficient for better than order-of-magnitude accuracy, in contrast to the much larger uncertainty in estimating E from the same data — given the unknown magnitude of the lateral stress [cf. 682, 930, 1033, 1038, 1143].

*

For fluids — with no static shear stress — it is more appropriate to interpret equation 9-5 as giving E → 0 for ν = 1/2, with B finite and non-zero.

536



A detailed investigation into the relative magnitude of the lateral stresses could proceed in at least two ways. The first approach would be to experimentally monitor the lateral stresses over the course of a filtration operation by means of specially-installed pressure transducers mounted in the side of the cell. The second avenue is to examine the properties of the final (or, indeed, intermediate) filter cake to identify any anisotropy. This might be achieved, for example, by carefully cutting cube- or cylinder-shaped forms from the cake and physically testing their mechanical strength in various orientations (cf. Figure 2-1).

9▪4▪3

Methodology

For this work the practice had been adopted to routinely employ a low final pressure for h i n d e r e d s e t t l i n g f u n c t i o n tests (for the purpose of yielding a sufficiently firm cake at the end of the run, without compressing to excessively small cake heights). Given that kinetics data were desired up to at least 300kPa, this necessitated a step-down in pressure. Uniquely, the decision was made to use this technique in a more measured way following a regular c o m p r e s s i v e y i e l d s t r e s s test in order to obtain a better appreciation for the significance of elastic expansion for WTP sludges.

Pressures were set as in Table 9-2. (From experience, the resistance to movement of the piston at the end of a run means that after compression at 300kPa the transducer pressure does not normally drop below 50kPa when the pneumatic cylinder is exhausted to atmosphere, even after many hours.)

Table 9-2: Pressure differentials employed in a ‘reversible compressibility’ test [kPa].

5

10

20

50

100

200

300

200

100

>50

The material which was tested was a laboratory-generated alum sludge coagulated at 80mg(Al)/L and pH ≈ 8.9 (see Table 7-3). These conditions typically have resulted in WTP sludges that cannot be readily compressed to high solidosities.


537

D. I. VERRELLI

Results 0.007

Cake height, h [m]

0.006

350

h Set Pressure Pressure

300

0.005

250

0.004

200

0.003

150

0.002

100

0.001

50

0.000

0

80000

85000

90000

Δp [kPa]

9▪4▪4

95000

Time, t [s] Figure 9-23(a): Expansion of a WTP sludge sample upon partial relief of the applied pressure. The initial height of material, h0, was 0.1079m.

Figure 9-23 shows that the stepped compression up to 300kPa is complete after about 91500 seconds, at which point the applied pressure is progressively relieved. The cake height, h, is clearly shown to undergo an overall increase in response to the drop in applied pressure. Although the change is negligible compared to the total change over the course of the experiment (see Table 9-3), it may be significant when compared to the changes in height measured at the highest pressures. (Note: although the filtration rig frame also physically expands and contracts in response to changes in the pneumatic cylinder pressure, these cannot account for the observed expansions. A full discussion is to be found in Appendix S19.)

538



0.0037

500 h Set Pressure Pressure Cylinder pressure

400

0.0035

300

0.0034

200

0.0033

100

0.0032

0

0.0031

–100

0.0030

–200

90500

91500

92500

93500

Δp [kPa]

Cake height, h [m]

0.0036

94500

Time, t [s] Figure 9-23(b): Detail of (a), with cylinder pressure added.

Table 9-3: Changes in cake height in response to increases and decreases in applied pressure. (a) Stepwise increasing pressure (read left to right). h0 = 0.1079m, h∞ = 0.00314m.

Δp [kPa] Overall Δh

[m] ‒0.1047

5–0

10 – 5

20 – 10

50 – 20

100 – 50 200 – 100 300 – 200

‒0.0899

‒0.0036

‒0.0031

‒0.0035

‒0.0021

‒0.0017

‒0.0008

(b) Stepwise decreasing pressure (read right to left). h∞ = 0.00314m, h∞+ = 0.00342m.

Δp [kPa] Overall Δh

>50 – 100 100 – 200 200 – 300

[m] +0.0003

+0.0001

+0.0001

+0.0001

BS [MPa]

<1.7

2.7

5.3

py(φ∞+) [kPa]

255

270

289

Note Δp = 10 – 5 = +5kPa represents a pressure i n c r e a s e .


539

D. I. VERRELLI

For example, in increasing the pressure from 50 to 300kPa, a change in height of ‒0.0045m was measured, while relieving the pressure to somewhere between 50 and 100kPa (the ‘set pressure’ of 50kPa could not be attained on the downward phase) resulted in a change of +0.0003m. This represents somewhere between a 6 and 11% recovery.

The recovery in height upon relief of the pressure can be used to estimate a modulus of elasticity, BS, as illustrated in §9▪4▪2. The order-of-magnitude accurate estimates shown in Table 9-3(b) are of quite low magnitude, at least 3 orders of magnitude lower than most pure solids or even liquids [see

665], but above most gases *. On the other hand, the values of BS may lie in the region typical of d r a i n e d bulk moduli of compression of plastic (soft) and stiff (medium) clays, which are at least 0.5 to 7.7MPa † [320]. This indicates that the e l a s t i c deformation of the particulate network, for a given pressure, is very large compared to most solids or liquids, although it is apparently small compared to its own p l a s t i c deformation for the same pressure (around 8%, judging by the present results).

The last row in Table 9-3 suggests that if the applied load could have been decreased from 300kPa to 0, then the cake would have expanded further, to roughly φ∞ :Δp ~ 225kPa (by extrapolation). This is a crude indication of the magnitude of the true (plastic) compressive yield stress.

*

Using the ideal gas law p V = n R T, one can derive simply B ≈ p for the isothermal case from equation 9-12, where the approximation is very good for most gases around ambient laboratory conditions [cf. 665] (cf. equation 2-27). The adiabatic case will not be greatly different, inflated only by the ratio of specific heats, which is ~1.

†

These values apparently include plastic deformation (more like the ‘coefficients of volume compressibility’ [cf. 946]) — greater estimates are obtained after cycling [320], whereby plastic deformation would no longer occur.

540



9▪4▪5


The most important immediate effect of these results is to cast some doubt over the accuracy of some experimental final solidosity measurements; ‘compressible’ materials.

especially those involving

The cause for concern can be illustrated by noting that the

magnitude of the expansion (+0.0003m) is significant relative to the final cake height before recovery (0.0031m): in this case the recovery is about 9% of the ‘true’ equilibrium height. The calculated final solidosity would n o t be significantly affected if the cake expands by drawing air into its structure. However it seems likely that at least some liquid would be drawn back into the structure upon recovery, as the membrane and sintered disk have generally been observed to still be damp upon unloading (even many hours after cessation of filtration — this is b y d e s i g n , to minimise drying of the cake; see §3▪5▪3▪3(a)). This would be expected to lead to underestimation of φ0. A mitigating factor in the present work is that the standard procedure involves duplicate measurement of the initial solidosity directly (upon loading) in addition to the measurement of final solidosity. Usually the duplicate measurements agree to within a couple of percent, while the initial and final measurements agree within about 5%.

Occasionally some

measurements cannot be made, or the values are inconsistent. In cases of inconsistency, the standard procedure adopted in the present work is to adopt the final measured value for compressive yield stress runs, and the initially measured value for permeability runs. This protocol is justified by the purpose of each experiment, although in future more care should perhaps be taken to minimise cake height recovery errors. In centrifugation it was possible to achieve this by simply conducting the measurements rapidly. In filtration the recovery is seen to be essentially complete within <10 minutes (for this sample), and so it is not likely to be practicable to unload and measure the sample before most of the elastic recovery occurs. Thus there are two ways that these errors might be avoided:

•

aim to finish with a cake at least 5mm thick, if possible; and

•

monitor the final height after pressure release by appropriate inputs to the Press-o-

matic rig control software.

Further investigation of elastic relaxation is recommended. This could be carried out in a stepped-pressure configuration by temporarily dropping the pressure after dewatering has


541

D. I. VERRELLI

approached equilibrium at a given set pressure. For example, a potential ‘compressibility’ run scheme is: 5, 10, 20, 10, 50, 10, 100, 20, 200, 30, 300, 40kPa. This should not add much to the experimental run time, nor should it affect the compressive yield stress results — provided air ingress is avoided, as the dried portions of the cake may not properly rewet. It appears both impractical and unnecessary to drop the pressure below about 10kPa or 10%; care should also be taken not to ‘undershoot’ the low pressure by completely venting the pneumatic cylinder. Investigation by centrifugation is also possible, in principle, although it would require more care experimentally and more effort analytically. The relevant concepts are outlined in Appendix S20.

542


10. OUTCOMES The foregoing chapters have dealt with material of rather wide-ranging nature within the ambit of drinking water treatment sludge production and dewaterability. Conclusions were indicated along the way, and so this final chapter closes with directions to the more prominent of these and a discussion of their industrial application. Unresolved issues are also flagged. Another important outcome is the critical compilation of a range of published information on topics ranging from jar testing, to industrial dewatering device performance, to fractal dimension, among others.

10▪1 Catalogue of outcomes and conclusions Outcomes and conclusions arising from the present work have been categorised as either ‘theoretical’ or ‘experimental’, and are listed accordingly in the catalogue presented below. O u t s t a n d i n g i t e m s in the following lists are identified by the symbol ❋. A more concise overview is provided in the Summary (p. i), and a brief discussion of industrial implications is presented in §10▪2.

10▪1▪1 Theoretical • A unified treatment of dewatering resistances due to flow, various interparticle forces, and particle integrity (§2).

• Confirmation of the correct form(s) of DARCY’s law and relation of KD to R (§2). • Identification of drawbacks of various empirical dewaterability parameters (§2). • Demonstration of the equivalence of several definitions of ‘compressibility’ (§2). • Objective assessment of the usefulness of dt/dV 2 versus d(t/V )/dV in pressure filtration (§2).

543

D. I. VERRELLI

❋ Exploration of the significance of various assumptions in the LANDMAN–WHITE dewatering theory (§2 and passim): o Assumption of strong interparticle bonding (cf. ‘creep’, p. 551; cf. ‘synæresis’).  Experimental support for exponential decay of the height was found to be

weaker than previously thought (§9, §S3). o Assumption of one-dimensional behaviour (cf. ‘particle–wall interaction’, p. 547,

and ‘isotropicity’, p. 547). o Assumption of irreversibility (cf. ‘Elastic rebound’, p. 551).

• Correction of the misconception that D (φ) alone can summarise dewaterability (§2, §5). o Demonstration of the sensitivity of the shape of D (φ) to interpolations specified

for py(φ) and R(φ) (§S10).

• A comprehensive analysis of forces prevailing in centrifugation, and assessment of the significance of forces that do not act radially (primarily adapted and amended from BÜRGER & CONCHA [201]) (§2).

• Presentation of a scheme for obtaining py(φ) by analysing sections of centrifugation cake (cf. the discrete analysis of GREEN [425]) (§2).

❋ Critical review of the justification for the end-point extrapolation method (§7, cf. p. 549). Experimental data indicated that it consistently overestimates R(φ).

• Identification of alternative methods of estimating the parameters in the equation t ≈ E1 ‒ E2 ln(E3 ‒ V ) (§2, §7). • Consideration of the usefulness of several empirical ’creep’ equations (§2, §R2, cf. §S3).

❋ Rigorous analysis of the TERZAGHI theory of one-dimensional soil consolidation: o Identification of errors deriving the ‘hydraulic diffusion’ equation in the original

publication and subsequent texts up to the present day (§R2). o Derivation of the relationship cv c = D (§R2).

• Evaluation of the orifice mixing recommendations of DILLON [315] for polymer conditioning (§7, §S14).

• For sludges that exhibit a macroscopic floc structure (e.g. polymer-conditioned sludges, see below) dewatering may more correctly be characterised by two ‘concentration’ parameters, namely two out of φ, φ, and φfloc (§7).

544

Chapter 10 : Outcomes


• A method to investigate the importance of solvent density change upon freezing and thawing on the efficacy of conditioning was suggested (§8).

• Theories relating to delayed settling were reviewed, and it was concluded that proposed mechanisms of densification resulting from microscopic structural rearrangement — so that py(φ) and R(φ) gradually decrease — are most relevant for WTP sludges (§9, cf. below). o Reference was made to related models in other fields, including fibre bundle

models, spring–block earthquake models, sandpile models, and pedestrian modelling (§9, §R2).

• Prediction of theoretical extent of hydrolysis for four different metals as a function of pH using a partial charge model (§R1, §S21).

• Calculation of metal complexation by various common anions predicted using a partial charge model (§R1, §S21).

• Extension of GREGORY’s [428] schematic diagramme of polymer flocculation dynamics (§R1).

❋ Exploration of Df and aggregate structure: o Illustration of the difference between ‘compactness’ and fractal dimension (§R1). o Clarification of the distinction between Df obtained by correlation of magg and dagg

and the HAUSDORFF dimension (§R1). o Clarification of the distinction between mass, volume and number fractal

dimension (§R1). o Derivation of formulæ to describe (fractal) aggregates built from different

primary particles, viz. a bidisperse mixture (§R1). o Derivation of formulæ to describe fractal aggregates built from fractal clusters,

with values of Df for each structure (§R1).  Suggestion of the relation of this theory to experimentally observed φg

(§R1). o Emphasis of the complexity of real aggregate structure — including multilevel

morphology, shear restructuring, and the multiplicity of limiting aggregation modes — and the consequent dangers of misinterpreting measurements of the apparent fractal dimension (§R1).

10▪1 : Catalogue of outcomes and conclusions

545

D. I. VERRELLI

 Review of the influence of diverse conditions on aggregate compactness

(§R1).  Identification of aggregation modes traditionally ignored in the literature

(§R1).  Discussion of similarities and differences between turbulent CLCA and

DLCA (§R1).

10▪1▪2 Experimental • An experimental protocol was established that gave good reproducibility of sludge (and supernatant) properties (§3). o A number of enhancements to the filtration rig operation were implemented (§3). o Results were compatible with measurements on plant sludges (§4, §5).

• With regard to the use of magnesium as a coagulant: o It is more conveniently employed as magnesium sulfate solution, rather than a

variety of magnesium carbonate (§3). o It may not be as efficient as alum or ferric, and a substantial proportion of the

magnesium appeared to remain in solution in the supernatant (§5).

• Several findings relating to true colour and light absorbance: o Conclusion that true colour is best predicted from absorbance at ~460nm, where

the absorbance of platinum–cobalt standard has a peak (§S8). o Correlation of true colour with absorbance at 460nm (§3). o Preliminary finding that ‘saturation’ may be an alternative surrogate parameter

for perceived ‘colouredness’ (§3, §S8). o Observation of a peak in water sample absorbance at 262±4nm (§S7).

• The importance of membrane material specification and rinsing procedures for syringe filters used to prepare samples for light absorbance or DOC measurements was confirmed, and a suitable protocol was described (§S9).

• Comparison of multiple-test (equilibrium) estimates of φg with those obtained from B-SAMS (§3, §S10).

546



• Consideration of particle–wall interaction suggests that effects may be significant, but are likely to be negligible in the present work for filtration and settling (§3, §9). o Hydrophobised walls did not affect settling behaviour, but helpfully minimised

meniscus effects (§9). o Wall effects are most significant in the settling of polymer-conditioned sludges,

due to the large lengthscale of the floc structure (§9).

• Consideration of theoretical stresses in a filter cake suggests that the assumption of isotropicity may not be justified (§2, §3, §9). o Preliminary experiments indicated no radial variation in solidosity (§3).

❋ A ‘subaqueous’ slump test, especially suitable for low-τy materials, was proposed and successfully demonstrated to prove the concept (§3, §S11).

❋ Proper treatment of the solid phase density (§4): o Demonstration of sensitivity of dewaterability characterisation to ρS (§4). o Determination of ρS for a range of laboratory and plant sludges (§4). o Suggestion of a simple model to correlate ρS with coagulant dose (§4).

❋ Identification of the poorly crystalline phases pseudoböhmite and 2-line ferrihydrite as important constituents of alum and ferric sludges, respectively (§4). o Crystallites were a few nanometres in size (§4). o Amorphous phases were also produced (§4). o Goethite was identified in one sample (§4). o Crystallinity was favoured by higher pH, freeze–thaw conditioning and ageing

(§4).

❋ Identification of the effects of coagulant type and dose, and coagulation pH, and suggestion of underlying mechanisms (§5): o The dewaterabilities of tested aluminium, iron(III), and magnesium sludges were

comparable (§5). o Compressibility and permeability are generally best at the lowest coagulant

doses investigated (§5).  Intermediate coagulant doses may yield the lowest permeability (§5).  At the highest doses, precipitated coagulant dominates sludge behaviour

(§5). 10▪1 : Catalogue of outcomes and conclusions

547

D. I. VERRELLI

o Compressibility and permeability of high-dose alum sludges are worst at high

pH, i.e. pH T 7 (§5).  Low-dose alum sludge dewaterability is not sensitive to pH (§5).  Ferric coagulants are less sensitive to pH (§5). o Plants often operate in the low-dose, moderate-pH range (§5, §R1). o Superior dewaterability was associated with conditions where the coagulation

and aggregation dynamics would be slower — low coagulant dose, and low or moderate alkali dose — which tend to produce more compact aggregate structures (§5, §R1). o pH sensitivity appears to be enhanced by a higher proportion of precipitated

coagulant phases, relative to the natural raw water constituents, and is associated with the solubility envelope (§R1).

• Computation of predicted solids throughputs for a range of representative alum and ferric sludges, and comparison with fundamental dewatering parameters (§S13). o Illustration of the significant influence of apparently small differences in R on

model-predicted filtration performance (§S13).

• Investigation of the influence of NOM on sludge dewaterability (§6). o No consistent trend attributable to the spiking can be found (§6). o For the lower dose sludge a slight improvement in compressibility was

suggested when the amount of NOM was significantly increased (§6). o Generally higher NOM levels were associated with lower permeabilities (§6). o These observations could be explained if the higher NOM levels favoured the

formation of smaller and denser aggregates (§6).

• Investigation of the effects of shear on sludge dewaterability (§7): o Higher coagulation shear rates resulted in slightly higher φg, but also slightly

higher R at low solidosity (§7).  This is consistent with the formation of smaller (but compact) aggregates

(§7). o Shearing of settled sludges yielded a marginal decrease in permeability and

compressibility (§7).

548



• Polymer flocculation immediately after coagulation tended to enhance the dynamics, with compressibility unaffected (§7).

❋ Investigation of the effects of polymer conditioning on sludge dewaterability (§7): o A sludge shearing and conditioning rig was developed to achieve suitable

mixing with the ability to compute G (§7).  A rough estimate of the settled sludge viscosity was found, viz. ~6mPa.s,

based on pressure drop observed for flow through a sequence of tubes and fittings (§7). o Conditioning provided no clear dewaterability enhancement compared to

sludges exposed to the same shear regime;

φg may have increased (and

consequently the low-φ permeability improved) at the lower pH.

It is

hypothesised that significant enhancement can only be achieved around the solidosity at which conditioning occurs (§7).

❋ It was necessary to apply the end-point extrapolation method to estimate R(φ), through D (φ∞), for two of the polymer-condition sludges in filtration. For comparison it was also applied to the other sludges in that section of work (§7). o Impediments to the use of the routine procedure derived from the macroscopic

floc structure (§7). o As a validation the observed filtration h(t) profile was compared against those

predicted using estimates of R(φ). Where mismatch was observed, the highsolidosity R(φ) was scaled by a constant compensatory factor (§7). o The estimates of R(φ) based on the extrapolation method were consistently too

high by a factor of ~2.5 (§7).  A rigorous bootstrap analysis (§S15) demonstrated that experimental and

fitting errors were relatively small compared to the variation associated with V (t) sub-set selection (§7).  R2 is not a reliable indicator that a given fit provides a reliable

extrapolation; overall trends should be checked (§7).  The reason for the consistent mismatch has not been established, but may

be affected by (irreversible) structural changes (§7).


549

D. I. VERRELLI

o The estimates of R(φ) based on the usual stepped-pressure ‘permeability’ method

were too low by a factor of ~1.8 for the high-pH sludges, but for the lower pH were validated without needing correction (§7).  The reason for the discrepant estimates has not been established.

• Ageing of drinking water sludges may improve dewaterability, but the effects are highly variable (§8).

❋ Freeze–thaw conditioning produced a massive improvement in dewaterability (§8). o A particle-exclusion process during freezing was confirmed visually (§8). o Properties of conditioned and unconditioned sludges, especially py, appeared to

be converging as high solidosities (or pressures) were approached (§8). o Freeze–thawing did not have a measurable effect on ρS (§4).

❋ A pilot plant sludge with a high PAC content exhibited substantial improvements in py and R (§8). o These results can be generalised to addition of ‘ballast’ to achieve superior

dewatering (§8). o The effect of the small amount of algæ present was overwhelmed by the PAC

(§8).

• Macroscopic biological growth was observed in a few settling samples at very long times (§9). o Results did not seem to be significantly affected (§9). o Microscopic biological growth could occur more generally and at earlier times,

and if so could influence dewatering, but experiments where light exposure was controlled did not support this (§9).

• Polymer-conditioned samples were observed to exhibit delayed settling (§9). o Settling could apparently be induced by exposure to vibration (§9).

❋ Long-time behaviour in settling and filtration was investigated (§2, §9). o Long-time settling and filtration data did not clearly conform to LANDMAN–

WHITE predictions (§9).  Other functional forms — logarithmic and power-law – for the asymptote

were assessed (§9, §S3).

550



o It was difficult to obtain a reliable estimate (extrapolation) of the end-point,

especially in settling (§9). o Several sludges exhibited ‘false’ end-points, followed by further settling (§9).  Better agreement may have been obtained by LANDMAN–WHITE model

analysis of truncated data up to these ‘false’ equilibria. o Many sludges exhibited creep in settling (§2, §R2, §9, §S10).  Thermally-activated models can (at least partially) account for this,

although results are very sensitive to the model parameters, several of which are not well characterised (§9, §S17).  The ‘bulk viscosity’ model of POTANIN & colleagues [844, 845] predicts that

the viscous-network relaxation time is not likely to exceed the duration of long-time experimental settling tests undertaken in the present work (§9, §S17). o py(φ) and R(φ) curves obtained by (re)predicting h(t) up to long times based on

multiple settling tests resulted in discrepancies that could be due to creep (§S10).

❋ Elastic rebound was observed following unloading (§9): o Features in centrifugation h(t) profiles indicated elastic rebound (§9). o Recovery of elastic deformation was confirmed by running a modified filtration

test (§9). o The bulk modulus (assuming isotropic stress) was estimated from the filtration

test, with magnitudes much lower than typical solids or liquids, but somewhat higher than gases under ambient conditions (§9).  Standard linear elasticity theory was applied to show that rigorous

estimation of the bulk modulus would require knowledge of the true lateral stress or POISSON’s ratio (§9).  A conceptual method to obtain estimates of the bulk modulus from

centrifugation tests was described (§S20).


551

D. I. VERRELLI

10▪2 Industrial implications Although many WTP’s have traditionally operated in the region of relatively low coagulant dose and moderate pH, increasing regulatory requirements and consumer demands have created a tendency to employ higher coagulation doses (‘enhanced coagulation’, §R1▪2▪2) or more ‘extreme’ pH values (e.g. high pH in combination with ferric to aid removal of manganese, as at Macarthur WFP, §3▪2▪6▪2; low pH, to aid removal of NOM, e.g. §R1▪2▪5▪5). A simple balance will show that higher doses ought to lead to a greater m a s s of sludge being generated. On top of this, the results of the present work indicate that such changes in treatment conditions can result in sludge that is less dewaterable. And so there is a chance that future sludge v o l u m e s may be underestimated in design calculations. It has been stressed from the outset (§1) that the driving force behind all of this — the existence of the treatment plant, the production of more sludge — is the provision of higher quality water for potable use.

Considerations of sludge volume production cannot be

expected to lead authorities to prefer a treatment protocol delivering a low or mediocre quality of water with respect to public health — or even æsthetics. Yet such information is of use in suggesting the bounds of economic feasibility for a treatment technology. This avoids the setting of unrealistic conditions (i.e. unnecessarily high standards), and provides a stronger basis for technology selection (e.g. whether to implement membrane filtration). Aside from design matters, sludge dewaterability is of operational concern. The present work did not find a strong influence of NOM, shearing, or polymer flocculation or conditioning upon sludge dewaterability. This result is somewhat surprising. Part of this can be explained by a decreasing dependence upon large-scale floc structure as the sludge is compacted in a thickening, centrifugation or filtration operation, after clarifier settling. Another aspect is that supernatant quality requirements can result in quite different coagulation conditions in response to variation in raw water NOM levels. These results indicate that operators may be best served focussing attention at the upstream end of the plant in terms of creating a settleable floc. With regard to the sludge processing operations, the knowledge gained in the present work can be used to specify appropriate dewatering equipment and in optimising that equipment.

552



The present work provides insight into likely optimum operating conditions. Dewaterability parameters have been presented for a diverse array of sludges, which can be used as inputs to model the operation of specific dewatering device operations for a given sludge type. Clear methodologies have also been described for the measurement of the necessary parameters for WTP sludges different to those characterised here.

10▪3 Further work 10▪3▪1 Experimental The present work has characterised a r e p r e s e n t a t i v e range of water treatment sludges; it has not — and could not — properly consider every permutation, however. The work on magnesium sludges, for example, demonstrates that poor dewaterability need not be a deterrent for using magnesium as a coagulant: if other benefits may accrue from switching to magnesium coagulation, be they health, environmental, or financial, then a more thorough sludge characterisation programme would have to be carried out.

Additional

characterisations could also be carried out on sludges from ‘novel’ water treatment operations, such as the ballast-loading systems referred to in §8▪3. Aside from the ‘controllable’ parameters, other process variables may warrant further investigation, including variation of colour and turbidity; a detailed investigation could even look more closely at the role of different NOM fractions (implicitly treated here in SUVA254nm). A project exploring the influence of algæ upon WTP sludge dewaterability has recently been commenced by F. QIAN. Additional combinations of dose and pH could be explored for alum sludges, but particularly for ferric sludges. These might be to refine or validate data within the ‘gamut’ already considered (as in §5▪5), or to explore more ‘extreme’ conditions. Given the resources were available, it could be useful to generate further laboratory-type WTP sludges under more controlled conditions at low and very low coagulant doses — the key resource here is probably access to a smallish ‘pilot plant’. A further study could also investigate the use of other coagulants, in particular a high-valent species such as Zr4+, which would be expected to have significantly different chemistry [see e.g. 675]. Likewise there is a plethora of alternative flocculants of different size and charge 10▪3 : Further work

553

D. I. VERRELLI

that could be trialled: a further study would advantageously select only a limited number of polymers representative of various classes. A final parameter that could be varied in future work is the chemical mixing sequence.

The solidosity range routinely covered here was limited chiefly to that obtained in laboratory filtration, and in gravity batch settling of sludges that have already sedimented out and been decanted, i.e. are not far below their gel point.

Evidently plant operations involve

dewatering outside of this window, with industrial filtration taking place at pressures up to ~1700kPa, and clarification involving the sedimentation of dilute, just-formed flocs. While e x t r a p o l a t i o n of the dewaterability parameters generated here is always computationally possible, there are limits to its accuracy. By the same token, i n t e r p o l a t i o n is also of limited accuracy. Centrifugation is the obvious candidate to address the issue of interpolation — trusting that dewaterability parameter estimates from the various techniques will be concordant. Centrifugation analysis would be greatly expedited by the development of a robust automated software tool to extract the underlying R(φ) information: progress has recently been made in this regard by S. P. USHER. Another option, not adopted in the present work, is gravity permeation, as performed by AZIZ [105] inter alia, where the equivalent pressure is typically ~1kPa. A disadvantage of this operation is that the analysis typically assumes a uniform bed has been generated: this could potentially be refined (see §10▪3▪2). In this regard it would also be helpful to reconcile the differences between multiple-test equilibrium batch settling estimates of py(φ) and φg and those obtained from B-SAMS.

New studies could also look at directly measuring fractal dimension or otherwise assessing aggregate structure in order to confirm suspected correlations with dewaterability. This might also support investigation of ‘multifactor’ dependence of py and R upon either φ or

φagg in addition to φ.

Further research on freeze–thaw conditioning could be advantageous in view of the massive dewaterability improvements that result.

Community WTP operators would demand

reassurance that the process is robust [cf. 185], and one aspect of this would be confirmation

554



of the insensitivity (or otherwise) of the enhancement to sludge type. As alluded to in the literature review (§8▪2▪1▪2), there is a lot of scope to optimise this process in terms of temperatures, geometries and the like too. An especially important parameter, whose effect on the conditioning would need to be quantified, is φ0.

Future work could consider

characterising the zots in more detail — such as the precise size distribution, average sphericity, and actual settling rates of individual particles — to obtain more comprehensive data and more complete estimates of R(φ). Of academic interest are questions about applied filtration pressures at which prior freeze– thaw operations may cease to affect the output solidosity.

Investigations of the

(un)importance of solvent volume change upon freezing/thawing would probably be most practically conducted on model particle systems.

Several other matters, peripheral to the main theme of drinking water treatment sludge production and dewaterability, have been touched on only briefly in the present work, and could benefit from further experimental study. Examples include the subaqueous slump test, peaks in the ultraviolet absorbance profile, and CIE colour measurements. Of significant academic interest is the topic of elastic rebound upon unloading. This aspect is of minor importance in industrial WTP’s, but may significantly affect laboratory characterisation results. Further data on the proportion of deformation that is elastic, the recovery rate, and estimates of bulk modulus would be useful, especially data covering a range of sludge types, solidosities and pressures.

10▪3▪2 Theoretical development A number of theoretical foundations for the accepted dewatering analysis could benefit from additional investigation or validation.

Often the mathematical analysis will require

empirical support.

Existing justification of (batch) centrifugation analysis with one-dimensional modelling has relied on anecdotal evidence and preliminary, order-of-magnitude mathematical treatment.

10▪3 : Further work

555

D. I. VERRELLI

Confirmation (or correction) of these preliminary results establishing recommended centrifugation rates to avoid non-radial force effects is recommended.

Analyses in Chapter 9 suggested that a complete dewatering theory may need to consider induction times, long-time ‘creep’ behaviour, and elastic recovery. Wall effects have also been discussed, but no observations of relevant manifestations were made in the present work; nevertheless, they could be important in other configurations or systems. It would be helpful to verify estimates of н and ν for WTP sludges in order to assess the assumption that filtration involves the action of isotropic normal stresses. Other tests for the importance of three-dimensional effects have been suggested, such as the comparison of consolidation from nominally one-dimensional processes (e.g. filtration) and osmotic consolidation, or sequential application of uniaxial stresses along different (perpendicular) axes.

The ‘alternative’ method of estimating R(φ) by fitting (and so implicitly extrapolating) longtime V (t) filtration data — according to an exponential decay formula — ought to produce estimates compatible with the usual analysis procedure. Yet in §7▪4 it was seen that this was not the case for the sludges characterised, which included both unflocculated and flocculated materials; instead a systematic bias was found. The reason for the mismatch is unclear, and insights allowing refinement of the theory might be obtained through a dedicated investigation.

Gravity permeation was mentioned in §10▪3▪1 as a potentially useful option for capturing intermediate-solidosity data.

An enhancement to this technique may be possible by

incorporating an idea inspired by the multiple-test gravity batch settling methodology (§2▪4▪5▪3(f), §3▪5▪1▪2). Whereas conventionally a given sample would be subjected to just one gravity permeation run, there may be merit in conducting a number of permeation runs with different (stable) bed heights and a fixed head of liquid. The motivation for this is to potentially permit extrapolation of the collected data to a truly uniform bed condition.

Although shear yield stress was not covered within the scope of the present work, there is an undeniable connection between shear yield stress and compressive yield stress.

556


The


conventional (subaerial) ‘slump test’ is an expedient procedure for estimating shear yield stresses, but is unable to characterise ‘low’ solidosity (i.e. low strength) materials.

An

innovative modification was illustrated in §3▪6▪2 and §S11 consisting of subaqueous slump testing.

In-principle experimental support for the feasibility of this technique was

demonstrated, and so development and validation of corresponding theory could be advantageous. Further confirmation of the importance, or unimportance, of normal stresses in elevating the shear yield stress (at a given solidosity) would also be beneficial.

In the discussion of freeze–thaw conditioning (§8▪2), it was mentioned that particulates sometimes migrated into ‘rhythmic’ bands. It has been suggested that this feature may hold an alternative means of characterising dewaterability, by relating the local solidosity of the frozen (and dissected) sample to permeation of water through the ‘bed’ accumulating ahead of the (advancing, planar) freeze front, and hence R, for a given (slow) freezing rate [1115].

10▪4 Closing remarks Drinking water treatment sludge disposal is an issue of increasing concern, and reliable data on sludge dewaterability is correspondingly valuable. Empirical and ad hoc methods of assessing dewaterability in the past have failed to systematically deliver data of sufficiently high quality. The present work has applied rigorous theoretical models to derive data across a diverse range of sludges, over a wide range of solidosities (or pressures). In the process of performing the research significant gaps in the understanding of more basic aspects — such as the identity of the solid coagulant precipitate phase, the suitability of magnesium as a coagulant, the meaning of fractal dimension, and the correct (mathematically consistent) definition of the coefficient of consolidation — became apparent, and these were also addressed to an appropriate level of detail. Nevertheless, the present work does not claim to answer every question. The findings that have been presented will benefit from independent confirmation (or otherwise) in future research, and further work to help fill some of the remaining knowledge gaps would unquestionably be beneficial.

10▪4 : Closing remarks

557

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is simplified to: Also known as “variable-volume” [797], “membrane” [414], “flexible-membrane” and “fill-and-squeeze” [976] filter presses. Cloths may be cleaned regularly in situ by high-pressure spray [879], e.g. every 5 pressings [797].

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1033. FRANK M. TILLER, STEWART HAYNES, JR. and WEI-MING LU; “The role of porosity in filtration: VII. Effect of sidewall friction in compression–permeability cells”; AIChE Journal; American Institute of Chemical Engineers, New York; January 1972; 18 (1): pp. 13–20. 1034. FRANK M. TILLER and N. B. HSYUNG; “Unifying the theory of thickening, filtration, and centrifugation”; Water Science and Technology; International Association on Water Quality, London; 1993; 28 (1): pp. 1–9. 1035. FRANK M. TILLER and ZARA KHATIB; “The theory of sediment volumes of compressible, particulate structures”; Journal of Colloid and Interface Science; Academic Press, San Diego; July 1984; 100 (1): pp. 55–67. 1036. FRANK M. TILLER and JAE HYUN KWON; “Role of porosity in filtration: XIII. Behavior of highly compactible cakes”; AIChE Journal; American Institute of Chemical Engineers, New York; October 1998; 44 (10): pp. 2159– 2167. 1037. FRANK M. TILLER, WENPING P. LI and JAE BOK LEE; “Determination of the critical pressure drop for filtration of super-compactible cakes” in: Sludge Management Entering the 3rd Millennium — Industrial, Combined, Water and Wastewater Residues [Conference Proceedings]; International Water Association; Taipei, Taiwan; 25–28 March 2001; pp. 258–269. [http://www.iwapublishing.com/template.cfm?name =isbn1843394049 for "selected proceedings" only] 1038. FRANK M. TILLER and WEI-MING LU; “The role of porosity in filtration VIII: Cake nonuniformity in compression– permeability cells”; AIChE Journal; American Institute of Chemical Engineers; May 1972; 18 (3): pp. 569– 572. 1039. FRANK M. TILLER and MOMPEI SHIRATO; “The role of porosity in filtration: VI. New definition of filtration resistance”; AIChE Journal; American Institute of Chemical Engineers; January 1964; 10 (1): pp. 61–67. 1040. FRANK M. TILLER and C. S. YEH; “The role of porosity in filtration. Part XI: Filtration followed by expression”; AIChE Journal; American Institute of Chemical Engineers; August 1987; 33 (8): pp. 1241–1256. 1041. RICHARD J. D. TILLEY; Colour and the Optical Properties of Materials; Cardiff University (Prifysgol Caerdydd) / J. Wiley & Sons, Cardiff; 27 April 2000. [Accessed from http://www.cf.ac.uk/engin/staff/rjdt /colour/supplemt/c5/s6.html, 2005-10-24.] 1042. MARTIN R. TILLOTSON; Yorkshire Water; Bradford, England; Personal communication; 2003. 1043. JAMES N. TILTON; “§6 : Fluid and particle dynamics” in: Robert H. Perry, Don W. Green and James O'Hara Maloney (Eds.); Perry's Chemical Engineers' Handbook, Seventh Edition; McGraw–Hill, New York; 1997. 1044. RICHARD C. TOLMAN; “Equilibria in dispersed systems and the thermodynamic theory of theory of colloids”; Journal of the American Chemical Society; American Chemical Society; April 1913; 35 (4): pp. 317–333. 1045. G. TONCHEVA, D. HADJIKINOV and I. PANCHEV; “Investigation of syneresis of agar jellies with sorbitol”; Food Chemistry; Elsevier Science; 1994; 49 (1): pp. 29–31. 1046. J. M. J. DEN TOONDER, M. A. HULSEN, G. D. C. KUIKEN and F. T. M. NIEUWSTADT; “Drag reduction by polymer additives in a turbulent pipe flow: numerical and laboratory experiments”; Journal of Fluid Mechanics; Cambridge University Press, New York; 25 April 1997; 337: pp. 193–231. 1047. FRANCISCO E. TORRES, WILLIAM B. RUSSEL and WILLIAM R. SCHOWALTER; “Floc structure and growth kinetics for rapid shear coagulation of polystyrene colloids”; Journal of Colloid and Interface Science; Academic Press; 15 March 1991; 142 (2): pp. 554–574. 1048. FRANCISCO E. TORRES, WILLIAM B. RUSSEL and WILLIAM R. SCHOWALTER; “Simulations of coagulation in viscous flows”; Journal of Colloid and Interface Science; Academic Press; August 1991; 145 (1): pp. 51–73. 1049. ELMER M. TORY; “Stochastic sedimentation and hydrodynamic diffusion”; Chemical Engineering Journal; Elsevier Science; 01 December 2000; 80 (1–3): pp. 81–89. 1050. ELMER M. TORY and PAUL T. SHANNON; “Reappraisal of the concept of settling in compression. Settling behavior and concentration profiles for initially concentrated calcium carbonate slurries”; Industrial & Engineering Chemistry Fundamentals; American Chemical Society, Washington, D.C.; May 1965; 4 (2): pp. 194–204. 1051. KENNETH M. TOWE and WILLIAM F. BRADLEY; “Mineralogical constitution of colloidal "hydrous ferric oxides"”; Journal of Colloid and Interface Science; July 1967; 24 (3): pp. 384–392. 1052. VERONIQUE TRAPPE, V. PRASAD, LUCA CIPELLETTI, P. N. SEGRÈ and DAVID A. WEITZ; “Jamming phase diagram for attractive particles”; Nature; Nature; 14 June 2001; 411 (6839): pp. 772–775. Chapter 11 : Bibliography

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617

APPENDICES

619

REVIEW

The following sections contain a critical review of the current state of understanding in a number of fundamental areas relevant to WTP sludge formation and behaviour. Common misconceptions are identified and flaws are corrected where possible. For more contentious matters, that remain unresolved in the literature, the alternative proposals are assessed and the more persuasive emphasised. Appendix R1 contains a comprehensive treatment of the processes that determine the nature of the aggregates (and hence sludge) that is produced. Appendix R2 further discusses a selection of more laterally related topics regarding the behaviour of particulate materials with similarities to WTP sludges.

621

DETAILED CONTENTS OF REVIEW

R1.

CONDITIONS AFFECTING THE NATURE OF THE SLUDGE MATERIAL FORMED ............................................................. 627

R1▪1 Important constituents of raw water — natural organic matter (NOM) ........................................................................................... 627 R1▪1▪1 Classification of NOM...............................................................................................628 Dissolution ......................................................................................................................628 Source...............................................................................................................................628 Hydrophobicity–hydrophilicity and charge...............................................................629 Humic substances...........................................................................................................630

R1▪1▪2 Properties of NOM ....................................................................................................631 R1▪1▪3 Effects of NOM ..........................................................................................................633 R1▪1▪4 Measurement of NOM..............................................................................................634 R1▪1▪4▪1 Organic carbon: TOC and DOC......................................................................635 R1▪1▪4▪2 SUVA254nm ............................................................................................................635 R1▪1▪5 Variation in NOM levels and composition ............................................................636 R1▪1▪6 NOM removal ............................................................................................................637 R1▪1▪6▪1 NOM adsorption................................................................................................638 R1▪2 Coagulation ................................................................................... 640 R1▪2▪1 The terminology of aggregation ..............................................................................641 R1▪2▪2 Coagulation regimes .................................................................................................642 R1▪2▪2▪1 Charge neutralisation........................................................................................642 R1▪2▪2▪1(a) Particle charge and potential ......................................................................644 R1▪2▪2▪2 Sweep coagulation.............................................................................................645 R1▪2▪2▪3 Enhanced coagulation.......................................................................................646 R1▪2▪3 Coagulant species solubility ....................................................................................647 R1▪2▪4 Coagulant species hydrolysis, polymerisation, and precipitation .....................649 R1▪2▪4▪1 Hydrolysis ..........................................................................................................649 R1▪2▪4▪1(a) Anion complexation.....................................................................................653 R1▪2▪4▪2 Polymerisation ...................................................................................................656 R1▪2▪4▪3 Precipitation .......................................................................................................658 R1▪2▪4▪4 OSTWALD’s rule of stages..................................................................................661 R1▪2▪4▪5 OSTWALD ripening.............................................................................................661 R1▪2▪5 Aluminium .................................................................................................................662 R1▪2▪5▪1 Hydrolysis ..........................................................................................................662 R1▪2▪5▪2 Polynuclear aluminium species.......................................................................664 R1▪2▪5▪2(a) Tridecameric aluminium: Al13 ...................................................................667 R1▪2▪5▪3 Solid aluminium phases ...................................................................................670 R1▪2▪5▪3(a) Solubility and stability.................................................................................672 R1▪2▪5▪3(b) Formation and transformation ...................................................................672 R1▪2▪5▪4 Reaction pathways ............................................................................................678 Review

623

D. I. VERRELLI

R1▪2▪5▪5 Industrial practice..............................................................................................681 R1▪2▪6 Iron ..............................................................................................................................682 R1▪2▪6▪1 Hydrolysis ..........................................................................................................682 R1▪2▪6▪2 Polynuclear iron species ...................................................................................683 R1▪2▪6▪3 Solid iron phases................................................................................................685 R1▪2▪6▪3(a) Formation of important phases ..................................................................688 R1▪2▪6▪3(b) Solubility and stability.................................................................................689 R1▪2▪6▪3(c) Formation and transformation ...................................................................690 R1▪2▪6▪3(d) Transformation of ferrihydrite ...................................................................693 R1▪2▪6▪4 Industrial practice..............................................................................................696 R1▪2▪7 Magnesium .................................................................................................................697 R1▪2▪7▪1 Application .........................................................................................................697 R1▪2▪7▪2 Reagents ..............................................................................................................699 R1▪2▪7▪3 Hydrolysis, polymerisation, and solubility ...................................................701 R1▪2▪7▪4 Solid phases and transformation.....................................................................702 R1▪2▪7▪5 Industrial practice..............................................................................................702 R1▪2▪7▪6 Health aspects ....................................................................................................704 R1▪2▪8 Alkalis .........................................................................................................................704 R1▪3 Flocculation ................................................................................... 704 R1▪3▪1 Sequence of events ....................................................................................................705 R1▪3▪2 Flocculation regimes .................................................................................................707 R1▪3▪2▪1 Charge-driven mechanisms .............................................................................708 R1▪3▪2▪2 The hydrophobic effect .....................................................................................708 R1▪3▪2▪3 Flocculation conditions.....................................................................................709 R1▪3▪3 Flocculants ..................................................................................................................710 R1▪3▪3▪1 Polymer classification and dose ......................................................................711 R1▪3▪3▪2 Polymer stability and activity ..........................................................................713 R1▪3▪3▪3 Industrial practice..............................................................................................715 R1▪4 Mixing ........................................................................................... 715 R1▪4▪1 Characterisation.........................................................................................................716 R1▪4▪1▪1 Characteristic velocity gradient.......................................................................717 R1▪4▪2 Turbulence..................................................................................................................718 R1▪4▪3 Velocity and shear distribution ...............................................................................720 R1▪4▪4 Scale-up.......................................................................................................................722 R1▪4▪4▪1 General principles..............................................................................................722 R1▪4▪4▪2 Turbulent coagulation and flocculation .........................................................724 R1▪4▪4▪3 Model mechanisms of aggregation and disaggregation ..............................726 R1▪4▪4▪3(a) Agglomeration..............................................................................................727 DUCOSTE’s model...........................................................................................................727 Alternatives ....................................................................................................................728 R1▪4▪4▪3(b) Break-up ........................................................................................................730 DUCOSTE’s model...........................................................................................................730 Alternatives ....................................................................................................................730 R1▪4▪5 Industry.......................................................................................................................733

624

Review


R1▪5 Aggregate structure and fractal dimension ..................................... 735 R1▪5▪1 Fractal objects .............................................................................................................736 R1▪5▪1▪1 Fractal aggregates ..............................................................................................737 R1▪5▪2 Definitions of fractal dimension ..............................................................................738 R1▪5▪3 Theoretical properties of fractal objects..................................................................741 R1▪5▪4 Measurement of fractal dimension .........................................................................748 R1▪5▪4▪1 General ................................................................................................................748 R1▪5▪4▪2 Scattering ............................................................................................................750 R1▪5▪4▪3 Settling.................................................................................................................753 R1▪5▪4▪4 Imaging ...............................................................................................................755 R1▪5▪5 Effect of aggregation mode ......................................................................................756 R1▪5▪6 Details of aggregation mode mechanics.................................................................761 R1▪5▪6▪1 Perikinetic and ballistic aggregation...............................................................761 R1▪5▪6▪1(a) Trajectories ....................................................................................................762 R1▪5▪6▪1(b) Underlying cause of reaction-limited aggregation..................................763 Short-range structural repulsion forces......................................................................763 Importance of dynamic aspects of aggregation kinetics..........................................764 R1▪5▪6▪1(c) Intermediate cases and transitions ............................................................764 R1▪5▪6▪2 Reversibility and restructuring........................................................................765 R1▪5▪6▪3 Particle–cluster aggregation.............................................................................766 R1▪5▪6▪4 Orthokinetic aggregation..................................................................................767 R1▪5▪6▪4(a) PÉCLET number and characteristic times ..................................................769 R1▪5▪6▪4(b) Restructuring ................................................................................................771 R1▪5▪6▪5 Polarisability.......................................................................................................771 R1▪5▪6▪6 Flocculation ........................................................................................................772 R1▪5▪6▪7 Differential settling............................................................................................773 R1▪5▪7 Specific results............................................................................................................773 R1▪5▪7▪1 Aluminium .........................................................................................................774 R1▪5▪7▪2 Iron.......................................................................................................................777 R1▪5▪7▪3 Other....................................................................................................................779 R1▪5▪7▪4 Levels of aggregate structure...........................................................................780 R1▪5▪7▪5 Shear ....................................................................................................................784

R2.

BEHAVIOUR OF SLUDGE-LIKE MATTER ............................... 791

R2▪1 Endogenous synæresis ................................................................... 791 R2▪1▪1 General ........................................................................................................................791 R2▪1▪2 Particulate networks .................................................................................................792 R2▪1▪2▪1 Theory .................................................................................................................792 R2▪1▪2▪2 Observation — milk gels ..................................................................................794 R2▪1▪2▪3 Observation — clayey soils ..............................................................................795 R2▪1▪2▪3(a) Subaerial soils ...............................................................................................796 R2▪1▪2▪3(b) Subaqueous soils ..........................................................................................796 R2▪1▪2▪4 Observation — polystyrene .............................................................................797 R2▪1▪2▪5 Observation — silica .........................................................................................797 R2▪1▪3 Flexible macromolecular networks .........................................................................797 R2▪1▪3▪1 Theory .................................................................................................................797 Review

625

D. I. VERRELLI

R2▪1▪3▪2 Observation ........................................................................................................798 R2▪1▪4 Microgels ....................................................................................................................799 R2▪1▪4▪1 Theory .................................................................................................................799 R2▪2 Geomechanics and creep ................................................................ 799 R2▪2▪1 Phases of consolidation.............................................................................................799 R2▪2▪2 Primary consolidation...............................................................................................800 R2▪2▪2▪1 TERZAGHI diffusion equation ...........................................................................800 R2▪2▪2▪1(a) Basic equation ...............................................................................................800 R2▪2▪2▪1(b) Relation to DARCY’s law and LANDMAN–WHITE theory ........................801 R2▪2▪2▪2 Empirical correlations .......................................................................................804 R2▪2▪3 Creep, or secondary consolidation..........................................................................804 R2▪2▪3▪1 Phases of creep...................................................................................................805 R2▪2▪3▪2 Primary creep .....................................................................................................805 R2▪2▪3▪2(a) Primary creep in settling .............................................................................809 R2▪2▪3▪2(b) Primary creep in filtration...........................................................................809 R2▪2▪3▪3 Secondary and tertiary creep, and failure ......................................................810 R2▪2▪3▪4 Micromechanics .................................................................................................812 R2▪3 Macrorheological models ............................................................... 814 R2▪3▪1 Basic elements ............................................................................................................814 R2▪3▪2 Application to consolidation....................................................................................815 R2▪3▪3 Fibre bundle models..................................................................................................819 R2▪3▪4 Parallel friction-element model ...............................................................................822 R2▪3▪5 Spring–block earthquake models............................................................................822

A listing of tables and figures can be found at the front of this thesis.

626

Review

R1.

CONDITIONS AFFECTING THE NATURE OF THE SLUDGE MATERIAL FORMED

Water treatment sludges are exceedingly complex materials. They are created ‘in situ’ in raw waters that contain a vast range of natural matter, and aggregate in a way that depends upon factors such as the prevailing shear field, the particle size, particle concentration, and particle interaction. The last factor is in turn affected by both the speciation of the liquid phase and the composition of the solid phase. Even once an aggregate has formed it may subsequently restructure!

R1▪1

Important constituents of raw water — natural organic matter (NOM)

Raw water can contain a vast range of both organic and inorganic chemicals derived from natural and anthropogenic sources, and these can be present in either ‘particulate’ or ‘dissolved’ form (cf. §S9). Often the particulate matter is — on a mass basis — predominantly composed of ‘inert’ materials such as clays and other minerals. (Exceptional cases such as raw water with a high algal loading are not relevant to the present work.) Various other species such as metals and microbes may, however, be attached to these particles. The overall surface charge on particles as found in raw water is generally negative [113, 505, 511, 533, 569, 855], although this is implicitly a function of the solution composition. The mass of suspended solids was negligible in the raw water primarily used in the present work (see §3▪2▪2, §3▪4▪5). With these ‘simplifications’ the dissolved fraction becomes of more interest. The discussion can be further condensed by considering only naturally-derived organic species, which are assumed to predominate [854, 979] *. Collectively this is commonly known as ‘natural organic matter’ (NOM).

*

Comparison of the salt mass-concentration e s t i m a t e d by equation 3-4 from the typical conductivity of 10mS/m (§3▪4▪6) does n o t obviously yield a much lower figure than the total mass of dissolved species (median 0.065g/kg — §3▪2▪2) in the present work, although the estimate is sensitive to the electrolyte valences. Reference to the sodium concentration (0.013g/L) in Table 3-2 suggests that equation 3-4 overestimates the salt concentration, although a concentration of 0.033g/L as NaCl is still not negligibly small compared to the TDS. R1▪1 : Important constituents of raw water — natural organic matter (NOM)

627

D. I. VERRELLI

R1▪1▪1

Classification of NOM [Water] contains a spectrum of organic structures ranging in size from small molecules ‒10 (approximately 10 m) to whales (approximately 10+1m). — BENNER et alii (1993) [138]

Natural organic matter (NOM) is an exceedingly complex mixture of chemical species which defies precise characterisation [e.g. 300]. Classes of molecule typically found in NOM include amino acids and polypeptides, fatty acids and lipids, sugars and polysaccharides, phenols, sterols, and (other) humic substances [171, cf. 512]. While ‘aromatic’ moieties are important components of many NOM species [e.g. 597], these do not behave in the same manner as ‘pure’ aromatic compounds [see 657]. Besides the wide range of substances included within the term ‘NOM’, even greater uncertainty remains over the details of their reactions with other species both in the natural environment and in water treatment [657]. Insight is gained by classifying the NOM components into various divisions and subdivisions.

Dissolution The n o m i n a l l y dissolved fraction of NOM, which may include some colloidal material, is termed dissolved organic matter (DOM) [553]. Particulate NOM includes bacteria, phytoplankton, and zooplankton [171]. In the present work DOM is expected to dominate particulate NOM.

Source NOM is derived both from sources external to the aquatic system ( a l l o c h t h o n o u s ) and sources within it ( a u t o c h t h o n o u s ) [512]. Autochthonous NOM is due to the excretions or decay products of bacteria, algæ, other phytoplankton, and macrophytes [596, 647]. Hence this source is dependent on the level of photosynthetic activity occurring. Similarly to the bacteria used to digest WWTP sludges, microscopic flora such as algæ can influence the macroscopic dewatering properties of a water treatment plant sludge. The main contribution is through polysaccharide and proteinaceous exudates — variously termed extracellular polymer (ECP), exocellular polymer (EP), exopolymer, extracellular polymeric substance (EPS), or extracellular organic matter (EOM) [811]. Due to their biological nature, these substances can induce time-dependent effects ranging from ‘bioflocculation’ [811], which may aid dewatering, to ‘blinding’ (i.e. blockage) of filter media. Allochthonous NOM also originates from photosynthetic activity, except that the decay products are derived from terrestrial biomass [596, 647]. This material may enter the water system as surface or subsurface runoff (following major rainfall events) or as soil leachate, and is typically the primary cause of highly coloured water [596], which is consistent with its higher aromaticity [512]. Due to the link with photosynthetic activity, NOM often strongly absorbs light in the photosynthetic waveband of approximately 400 to 500nm, giving the substances a yellow 628

Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


appearance [572]. The yellow-coloured substance (‘gilvin’ [572]) is approximately 50% dissolved organic carbon (DOC) [cf. 1024], is very soluble, and readily extracted from leaves [399]. Colour has also been correlated with soil composition (percentage peat in the catchment) [1105].

Hydrophobicity–hydrophilicity and charge The hydrophilicity or hydrophobicity of components of NOM has also been used as a means of classifying fractions. The average hydrophobicity measured for different samples of unfractionated NOM can vary over more than one order of magnitude [400]. More recent work refers to three fractions, although they are defined (or, at least, named) differently by different workers, as in Table R1-1. These schemes tend to be strongly associated with the fractionation technique employed — especially in terms of their tendency to adsorb on certain resins [e.g. 445, 1116]. Further discussion of NOM classification is presented by LEENHEER & CROUÉ [647]. Table R1-1: Various NOM classification schemes based on hydrophilicity–hydrophobicity and charge. The hierarchy presented is intended to indicate approximate synonyms and hyponyms.

SINGER [941]

ELDRIDGE et alii [341]

Hydrophobic Hydrophobic

HARBOUR [447]

Very hydrophobic

WHITE et alii BOLTO et alia HARBOUR et alii [445] [1116] [172], CHOW et alia [252], and MORRAN et alia [760] Hydrophobic acids h f

Slightly hydrophobic Hydrophobic neutrals

Very hydrophobic acids

Very hydrophobic weak acids h

Slightly hydrophobic acids

Moderately hydrophobic acids f Hydrophobic neutrals h

Transphilic

Hydrophilic

Neutral hydrophilic

Hydrophilic

Charged hydrophilic Notes

h

includes humic acids;

f

Hydrophilic

Neutral hydrophilic

Hydrophilic neutrals

Charged hydrophilic

Hydrophilic acids

includes fulvic acids.

The neutral fraction includes polysaccharides, which tend to have large molecular masses and be colourless. Conventional coagulation removes such large, uncharged, hydrophobic species most readily, as they adsorb strongly to the metal (oxy)hydroxides formed [171].

R1▪1 : Important constituents of raw water — natural organic matter (NOM)

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D. I. VERRELLI

Higher ratios of hydrophobic fraction to hydrophilic fraction are associated with [941]: • greater TOC and DOC reductions upon coagulation [1116]; • higher proportions of aromatic (and phenolic hydroxyl) carbon structures; • greater overall yield of disinfection by-products (DBP’s); and • a predominance of haloacetic acids (HAA’s) over trihalomethanes (THM’s).

Humic substances NOM consists of humic and non-humic substances [596]. Most of the organic materials present in water introduced by microbial activity are classified as h u m u s [456] [cf. 1012], typically referred to as ‘ h u m i c s u b s t a n c e s ’ [854] or simply ‘ h u m i c s ’. Humic substances are the major fraction of organic matter in both natural waters [456, 1105] and soils [334]. (According to EATHERALL, fulvic and humic acids make up 50 to 75% of DOC in stream waters [1105].) Humic substances are mixtures whose chemical composition exhibits great variety [171] and is “poorly understood” [334], even though humic acid was first extracted scientifically (from peat) in 1786 [see 1016]. Aquatic humic substances (AHS) are “heterogeneous, yellow to black, organic materials that include most of the naturally occurring dissolved organic matter in water” [334] [see also 300] [cf. 647]. Humic substances have been characterised [854] as amorphous, acidic, hydrophilic, chemically complex, and often aromatic anionic polyelectrolytes, ranging in molecular [mass] from several hundred to tens of thousands of grams per mole. Humic materials are classified as humic, fulvic, or hy[m]atomelanic acids.

An alternative description is of “high molecular mass polyhydroxycarboxylates comprised of polyaromatic and aliphatic subunits” with variable levels of ionisation, and tending to have an anionic character [903]. Yet another: “dark coloured, acidic and predominantly aromatic compounds” with a “wide compositional range” [171]. Nitrogen is often incorporated [1016]. The references to anionic character apply at neutral pH [cf. 802], with typical pKa values of 3 to 5 [171, cf. 1016]. Humic substances were traditionally classified into one of three fractions, depending upon their “solubility” [see 334]: • F u l v i c a c i d s are soluble in water at any pH. • H u m i c a c i d s are not soluble in water at pH < 2. • H u m i n is not soluble in water at any pH. (Older schemes included hymatomelanic acids [854] as an alcohol-soluble class ‘intermediate’ to humic and fulvic acids [see 1016]. Humic b a s e s have also been described [1016].) Humic and fulvic acids dissociate to form humates and fulvates. The chemical structures of the two soluble fractions is believed to be “similar” [171]. On average the ratio of fulvic to humic acids in natural water sources is about 4 [171], but it should be understood that this varies (see §R1▪1▪4▪2, SUVA254nm).

630



The precise nature of humin is not known, but STEVENSON suggests that it comprises, “at least in part, humic and fulvic acids so intimately bound to clay minerals (by linkages with polyvalent cations) that they cannot be solubilized” [1066]. The more recent convention, referring to AwwaRF practice, identifies four constituents [360]: • FAF Fulvic acid fraction • HAF Humic acid fraction • HPI-A Hydrophilic acid fraction • HPI-NA Hydrophilic non-acid fraction The ‘fractions’ referred to cannot be considered pure solutions of the specific class of humic substance [300, 1066]. Rather, the fractions that are practically produced are ‘rich’ in one of the three classes of humic substance, with some impurities (e.g. biochemical compounds, polysaccharides) [300, 1066].

R1▪1▪2

Properties of NOM

The size range defined for NOM varies between researchers; assignment of molecular masses is complicated by the tendency of NOM species to aggregate (see below). It has been suggested that molecular NOM species exist up to O(105) g/mol [647, 903], but generally not above 106 [1024]. A practical view is to consider NOM as part of a c o n t i n u u m (or sequence) from simple molecules to polymers through to amorphous carbohydrate colloids [1016]. Humic acids tend to be larger than fulvic acids. An indicative range for fulvic acids is 500 to 2000g/mol; reported values for humic acids range from O(103) to 105g/mol [326]. SCHLAUTMAN and co-workers [553, 554] found the number-average molecular mass of humic acids ranged from 1395 to 2210g/mol *, with mass-average values from 3982 to 6202g/mol (polydispersities from 1.7 to 4.2). For two fulvic acid fractions number-average molecular masses of 1228 and 1698g/mol, with mass-average values of 1920 and 2402g/mol (polydispersities of 1.4 and 1.6) were obtained [553, 554]. (There is some overlap in the number-average molecular masses, but this is principally due to comparison of fractions from different sources.) Humic acids generally have a greater polydispersity than fulvic acids [565]. CHIN, AIKEN & O’LOUGHLIN reported a close relationship between dissolved NOM aromaticity and the mass-average molecular mass [554]. Reported aromaticities for humic acids range from 33 to 58%, tending to be greater than those for fulvic acids, with values around 25 to 28% [554]. In comparison to humic acids, fulvic acids generally [171, 554]: • have lower carbon contents; • are smaller [456, 553, 554, 566], and less polydisperse [565];

*

These molecular masses were found by high-performance size-exclusion chromatography (HPSEC) based on calibration with polystyrene sulfonate (PSS) [554] (justifications in KILDUFF et alii [565] and HONGVE et alia [488]). R1▪1 : Important constituents of raw water — natural organic matter (NOM)

631

D. I. VERRELLI

• are more hydrophilic and hence more soluble in water; • have a lower light absorbance [456] (perhaps not for ultraviolet light [139]), and are less intensely coloured [334] *; • fluoresce more [456]; • are more acidic (have weaker conjugate anion bases), and do not bind metal ions as strongly; and • adsorb onto mineral surfaces to a lesser extent [766], which is associated with their lower aromaticity [554, 597]. Early studies indicated that humic acids were dispersed at a pH value of about 5.1, and fulvic acids at about 3.0 [1086]. SINGER [941] associates the hydrophobic/hydrophilic ratio specifically with trihalomethane (THM) and haloacetic acid (HAA) formation upon chlorination, and the aromatic/aliphatic ratio more generally (but still self-consistently) with increased DBP formation potential. KARANFIL, ERDOGAN & SCHLAUTMAN [555] emphasise the importance of aromatic structures as the primary sites of attack by chlorine and other oxidants in the formation of DBP species. MURPHY et alii [766] found that the more aromatic humic substances adsorbed to a greater extent on hæmatite and kaolinite. VANCE, STEVENSON & SIKORA [1066] attribute the ability of humic substances to form stable complexes with polyvalent cations (e.g. Al3+) to their high content of oxygen-containing functional groups. These oxygen-containing functional groups include [1066]: ‒COOH; phenolic (including “acidic”) ‒OH; enolic † ‒OH; alcoholic ‒OH; and ‒C=O [see also 647]. It has been reported that humic acids have a fractal structure (see §R1▪5▪1), with a fractal dimension of 2.35, and exist in solution in the form of discrete, negatively-charged aggregates with sizes from 100 to 300nm [803, 935]. Some results indicate that humic substances take on a globular form, while others suggest a flexible model [409] — a popular theory is that the smallest NOM particles are spheroidal, while the larger ones are random coils [1024]. VISSER found that aquatic humic acids at pH 7 had an especially voluminous structure, but also concluded that data supported a flexible, linear–polymeric structure [1086]. One explanation is that increasing hydration (as from lower ionic strength) leads to a change from a spherical to an elongated configuration [802, 1086]. GONET & WEGNER [409] found that soil humic acids had an aspect ratio of about 13 in pH neutral solution and about 20 at a pH of 10.5. This is explained by dissociation under alkaline conditions giving rise to charges along the molecules, which naturally repel each other and extend the molecule (subject to solution ionic strength) [802], also leading to an increase in the ‘active’ area [409]. The viscosimetric-average molecular mass increased from around 1370g/mol at pH 7 to 5600 to 8800g/mol at pH 10.5 [409]. THORSEN [1024] suggests that the size and structure of NOM particulates varies greatly depending upon the constituents of the NOM, their concentration, the pH, and the ionic

*

According to GIPPEL, RIEGER & OLIVE [399] the natural, yellow–brown dissolved organic acids characteristic of Australian stream waters are dominantly fulvic acids.

†

Although generally (with few exceptions) “the keto–enol tautomeric equilibrium lies heavily on the side of the ketone” and enols conceptually only exist as intermediates, enols “are nevertheless extremely important and are involved in much of the chemistry of carbonyl compounds” [723].

632



strength. HAUTALA, PEURAVUORI & PIHLAJA [456] reported that NOM absorbs differently following dilution, suggesting that a different conformation is adopted; furthermore, the measured size distribution was affected by prior shaking of the sample. Table R1-2 indicates the range of NOM configurations and conformations typically observed. THORSEN [1024] associates raw water colour with the presence of intermediate to large size particles. Several researchers have found that the restructuring of NOM particles (aggregates) can take a few days to complete [1016, 1024]. Table R1-2: Typical observed NOM configurations and conformations under a variety of conditions [1024].

Structure

Size

Dominant composition

Spheroidal particles

<2 up to 20nm

Slightly (prolate) ellipsoidal particles Fibres

<2 up to 20nm

Linear chains

–

Particulate aggregates

Up to 30nm

Irregular fibrous networks, low-density webs

Up to 2 to 3μm

Dominated by fulvic acids and simple organics (i.e. species of lower molecular mass) Dominated by humic High pH acids Dominated by Low pH polysaccharides – Neutral pH Low concentrations Low ionic strength – Low pH Multivalent cations present Formed from all species Neutral pH of NOM

–

Typical conditions favouring structure High pH

ÖSTERBERG & SHIRSHOVA [803] found that the redox (reduction–oxidation) potential of soil humic acids varied linearly * from +0.53V at pH zero to +0.19V at pH 8. This implies that (soil) humic acids will reduce iron from Fe3+ to Fe2+, increasingly favoured at higher pH values, as this half-reaction has a pH-independent redox potential of +0.77V [662, 803]. However the presence of significant levels of dissolved oxygen in most parts of a water treatment plant would probably tend to counteract this reaction, leaving Fe3+ as the dominant species in solution.

R1▪1▪3

Effects of NOM

The presence of NOM gives colour to the water [e.g. 300], which must be removed for æsthetic reasons. NOM can also contribute to taste and odour problems [340, 596, 647]. *

This behaviour is caused by the involvement of protons (H+) in the half-reaction [803]. R1▪1 : Important constituents of raw water — natural organic matter (NOM)

633

D. I. VERRELLI

Coagulation tends to be controlled by NOM removal requirements, especially when operating in the charge-neutralisation regime, as NOM has a much higher surface area and negative charge than turbidity-causing matter [533, 569]. (Fortunately turbidity tends to be satisfactorily removed even when the process is optimised for NOM removal [569], e.g. with a lower pH of circa 5 to 6 [326].) Presence of certain aquatic humic substances can make water difficult to treat, such as requiring a higher chemical dose [cf. 1012] or affecting robustness (hence ultimate size) and settleability of the flocs [1124]. Waters of low turbidity containing large amounts of small humic substances are generally difficult to treat by conventional coagulation [171] — raw water sources can fall into this condition following the first heavy rainfall of winter [524, 1124]. Presence of NOM also increases the potential to form mutagenic trihalomethanes (THM’s) upon chlorination [300, 337, 647, 1124] as well as other undesirable disinfection by-products such as haloacetic acids (HAA’s). Disinfection by-products also arise when chlorination is not practised, e.g. ozonation generates low-molecular-mass aldehydes such as methanal and ethanal [34]. Other concerns with NOM in drinking water include [340, 553, 596]: • increased chemical usage (mainly coagulants) and increased sludge production; • increased disinfectant doses [34, 300] (conceptually ‘shielding’ of pathogens); • higher consumption of disinfectant residuals [34, 276] and potential to serve as a biological substrate * [1116], promoting biological growth or regrowth in the distribution system; • increased use of granular activated carbon (GAC) for removal of taste and odour — and increased adsorption loading of activated carbon beds [300]; • membrane fouling (usually not a major problem [340]); • corrosion enhancement; • complexation of heavy metals and organic micro-pollutants [cf. 300, 647], and “corresponding increased human exposure”; and • degradation of ion-exchange capability [334]. Algal toxins (cyanotoxins) may be classed as natural organic matter [34], but are not usually present. While not directly a problem, NOM can affect the solid phase formed upon precipitation of coagulant, and any subsequent transformation (see §R1▪2▪5▪3(b) and §R1▪2▪6▪3(d)).

R1▪1▪4

Measurement of NOM

Humic substances are very difficult to quantify, as alluded to in the foregoing discussion. The a m o u n t of humic substance present in a sample of water may be indicated by measure of (true) colour, spectrophotometric absorbance — for ultraviolet (especially 254nm) or visible light [553] — or fluorescence, total organic carbon (TOC), or dissolved organic carbon (DOC) as surrogates [456, 596, 941, 1124], as well as high-performance size exclusion

*

634

Indeed the oxidative breakdown ensuing from disinfection with either chlorine and ozone yields species that are more biodegradable [21, 34]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


chromatography (HPSEC). TOC includes both humic and non-humic portions of NOM [596]. The c o m p o s i t i o n of the NOM population itself may be indicated by the “specific ultraviolet absorbance” (SUVA), or by the ratio of (true) colour to TOC [340]. Another common approach is to make inferences about the molecular mass distribution or the preponderance of various fractions based on ratios of measurements at (two) different wavelengths in either absorbance or fluorescence spectra [292, 456, 512]. Features in the derivatives of (absorbance) spectra could also be used in this way [512]. Direct measurements are possible, but are often not practical. Molecular mass distributions tend to be measured by HPSEC [252, 276, 292, 340, 456, 488, 512, 647]. Other measurements to determine molecular mass and charge distributions have included ultrafiltration, osmometry [647], and gel [935] and capillary zone [903] electrophoresis. Other methods, such as NMR and pyrolysis, are also used to infer aspects of NOM character [see 252, 647]. Various techniques exist to fractionate NOM (ion exchange resins are popular), which in principle permits separate analysis of the various fractions, including measurement of the mass of the dried isolates [456, 647]. Two problems are that the fractionation techniques arbitrarily classify the isolated populations although in practice the separations are not sharp, and the procedure can also alter the properties of the NOM species [456, cf. 1016].

R1▪1▪4▪1

Organic carbon:

TOC and DOC

While not d i r e c t l y detrimental to water quality, TOC (or DOC) is of interest to water treatment plant operators as an indicator of possible water quality issues. As noted, TOC corresponds more or less to the amount of NOM present in the water, and so the consequences of a high TOC value are implicit in §R1▪1▪3. Typical TOC values in U.S. drinking water sources are from 1 to 4mg(C)/L [553]. Nevertheless, TOC levels in drinking water may range from less than 0.1 to more than 25mg(C)/L [334].

R1▪1▪4▪2

SUVA254nm

SUVA254nm is defined as the ratio of linear absorbance at 254nm [m‒1] (see §S7▪1) to DOC [mg/L] [553, 941]. As such, it gives no information about the total amount of organic material present. SUVA254nm has been found to correlate very well with NOM composition, although it is less practical as a field measurement due to the requirement to analyse for DOC [512]. (Occasionally SUVA is measured and reported at wavelengths other than 254nm, e.g. 272nm or 280nm [512, 657]. TOC may also be used in place of DOC, giving TSUVA [553]; as noted, often TOC ≈ DOC.) Elevated SUVA254nm values are associated with [276, 335, 553, 555, 941, 1116]: • a greater proportion of DOC being made up by aquatic h u m i c s u b s t a n c e s ; • a higher ratio of h y d r o p h o b i c to hydrophilic constituents; • a higher proportion of a r o m a t i c to aliphatic structures; R1▪1 : Important constituents of raw water — natural organic matter (NOM)

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D. I. VERRELLI

• a greater average m o l e c u l a r m a s s ; • an increased D B P f o r m a t i o n potential [cf. 647]; and • greater t r e a t a b i l i t y by coagulation/flocculation (greater dependence of operation on NOM, greater percentage removal of DOC). Yet, surprisingly (see p. 631), WILSON [1124] observed an increase in SUVA254nm due to an increase in the proportion of the NOM present as fulvic acids. As an indication of the SUVA254nm values associated with purified fractions, TSUVA254nm values of 3.6±0.2L/mg.m for fulvic acids (aromaticity 26.5±2%), and 4.9±0.1L/mg.m for natural * humic acids (aromaticity ~42% †) have been obtained [553]. In natural waters, SUVA254nm values above 4L/mg.m are considered ‘high’, while values below 3L/mg.m are considered ‘low’ [555, cf. 657]. U.S. drinking water regulations (40CFR §141.135) allow that s o u r c e water SUVA254nm values of ≤ 2.0L/mg.m are sufficiently difficult to treat — at least by coagulation/flocculation — that the usual TOC removal requirements no longer apply [56]. As treatment typically reduces the SUVA254nm value (see below and §R1▪1▪6), likewise t r e a t e d water SUVA254nm values of ≤ 2.0L/mg.m are recognised as a ‘best practicable’ result [56]. Although high SUVA254nm values are associated with the larger humic fraction rather than the smaller fulvic fraction, a different picture emerges when a single humic acid fraction is further fractionated according to molecular mass. KILDUFF et alii [565] found SUVA254nm values d e c r e a s e d by a factor of at least two as molecular mass of ultrafiltered ‘subfractions’ of a natural humic acid fraction i n c r e a s e d (though with little apparent change below about 4000g/mol). However some workers have found either no trend or the opposite trend [565]. Coagulation (e.g. with aluminium sulfate) tends to reduce the SUVA254nm value, as coagulation preferentially removes the UV-absorbing constituents of NOM (i.e. the hydrophobic fraction) relative to the DOC as a whole [555, 941]. To look at this from another perspective, waters with high SUVA254nm values tend to be easier to treat, with up to 80% DOC reduction by coagulation/flocculation, compared to reductions of less than 30% in the case of low SUVA254nm values [555].

R1▪1▪5

Variation in NOM levels and composition

Colour in water shows a response to rainfall and hence runoff and stream flowrates: during summer, when flows are low, colour tends to decrease; colour tends to increase during the high-flow, autumn–winter season [1105]. Likewise, colour tends to decrease during a drought and in the period immediately thereafter, but exhibits an above-average increase some time after the drought breaks as the water saturates the soil again. The enhanced colour at this time is due to the build-up of colour-causing compounds in the catchment that

*

A TSUVA254nm value of 6.6±0.1L/mg.m was reported for a ‘commercial’ humic acid [553], however such materials “may not be appropriate as analogues of true soil or aqueous humic substances” [565].

†

Other humic acids have aromaticities ranging from 33% to 58% [554].

636



were not washed out during the drought (and in the period immediately thereafter, when the water has not yet re-wet the soil) [1105]. Colour is enhanced by decomposition of organic matter that is exposed as the water level falls, and subsequent flushing upon reservoir refill [1105]. Colour in the reservoir is reduced due to photo-oxidation near the water surface during spring and summer [292, 1105]. Humic substance content in soil is closely related to the total organic matter content [1066]. Examples of the organic matter contents in specific soils are presented in Table R1-3. Table R1-3: Typical organic matter contents in common soil types [1066].

Soil

Typical location / description

Psamments Hapludolls et cetera Aquatic suborders

Coarse-textured soils Prairie grassland soils Poorly drained soils (e.g. hydric soils in wetlands) Peat

Histosols

Total organic matter content [%] ≤ 1.0 ≥ 6.5 < 20 > 30

The ratio of humic acids to fulvic acids is [1066]: • high in histic and mollic epipedons; • low in Alfisols, Spodosols and Ultisols (i.e. forest soils); • lower near the surface, and higher deeper in the soil profile. WILSON [1124] found that the proportion of r a w water NOM made up of the fulvic acid fraction (FAF) increased from a ‘normal’ value of 37% to 61% following the ‘first flush’ of winter rains in Yorkshire (where soils have a high peat content). Furthermore, the FAF makes up 13% of the NOM in the t r e a t e d water ‘normally’, but this increases to 31% following this ‘first flush’ [1124]. JARVIS, JEFFERSON & PARSONS [524] made similar observations at the same site, with SUVA254nm decreasing sharply from 5.9 to 4.4L/mg.m between autumn and winter, coinciding with an increase in FAF proportion from 39% to 58% of total NOM. In contrast, LEENHEER & CROUÉ [647] reported increased proportions of hydrophobic fractions following winter runoff events. There are reports of an increasing trend in raw surface water colour over recent decades in Northern Europe (Sweden, Norway, Great Britain) [340, 1124].

R1▪1▪6

NOM removal

There are four main processes used for removal of NOM from raw water, which are [272]: • coagulation (and flocculation); • adsorption on activated carbon; • membrane filtration; and • adsorption onto ion exchange resin [172].

R1▪1 : Important constituents of raw water — natural organic matter (NOM)

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D. I. VERRELLI

Coagulation is the most widely used of these [272], as it is generally effective and of relatively low cost. NOM removal by coagulation is highly dependent on the size- and charge-distributions of the NOM species [903]. Waters containing high proportions of low-molecular-mass humic substances, viz. (103g/mol [252, 760], have been reported to be difficult to treat by coagulation, especially if the raw water has low turbidity [172] or alkalinity [360]. HPI-NA has a reputation as being the most “recalcitrant” fraction to remove — at least by conventional treatment (i.e. coagulation) [360]. Colour may be removed in enhanced coagulation by a combination of precipitation and adsorption [854]. A discussion of NOM adsorption follows in §R1▪1▪6▪1. Prechlorination to partially oxidise colour-causing compounds in the raw water also has the side-effect of acting as a coagulant aid, resulting in a decrease in the coagulant dose required [854]. However there is a risk of producing trihalomethanes [337, 1124]. Investigations into the adsorption of specific NOM constituents on GAC variously suggest greater adsorption of humic acid compared to fulvic acid [554] and of smaller humic (acid) species rather than larger ones [565, 566]. Attempts to normalise the adsorption by a c c e s s i b l e surface area for each component indicate that larger molecules actually have the higher affinities when steric exclusion effects are eliminated [565, 566]. Ion exchange treatment can remove from 60% to over 90% of the NOM in raw water, depending on the proportional presence of different fractions [172]; uncharged fractions are most difficult to remove by ion exchange [172]. Aside from hydrophobicity and charge, polarity can also affect the efficiency with which species are removed [172]. Some researchers have found removal efficiency tended to improve as the molecular mass (or ‘size’) of the compounds decreased [360].

R1▪1▪6▪1

NOM adsorption

NOM is known to adsorb onto particles such as might be generated in water treatment (hæmatite, goethite, ferrihydrite), as well as many others [see 300], and their exposed functional groups (especially carboxyl groups) affect the potential [280]. A sufficient amount of NOM can be adsorbed for the coated particles to become negatively charged [171] and therefore stabilised through electrostatic repulsive forces [280] at environmental concentrations of NOM [1031]. ( B a r e particles are typically positively charged at typical pH values, as shown by their i.e.p. — see §R1▪2▪2▪1(a).) In some cases the degree of stabilisation can be greater than would be predicted for a purely charge-based mechanism, so other effects may also be relevant (e.g. steric repulsion *) [1031]. TIPPING (1981) found that 2-line ferrihydrite had a greater adsorption capacity for aquatic NOM (150 to 255mg/g) compared to either goethite (10mg/g) or hæmatite (20 to 40mg/g) at pH 7 [280]. When calcium or magnesium ions were present in low concentrations,

*

638

Steric effects may be important at high ionic strength or for NOM species with higher molecular masses, lower charge densities, or more hydrophobic character [1031]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


adsorption capacities were increased, as these cations were co-adsorbed [280] (partly balancing the charge). Adsorption also generally increases as the pH is decreased, due to elements of the NOM with acidic character [280]. Fulvic acids were seen to bind to goethite through inner-sphere co-ordination * at low pH, but through outer-sphere co-ordination † at high pH [280]. Increase in NOM adsorption onto iron oxides with decreasing pH generally is due to the acidic character of the NOM [280]. (Also, in general, as pH decreases, the anionic form(s) of the conjugate acid of the adsorbate is converted to positively charged forms so that electrostatic repulsion with the adsorbent is increased, while the number of surface FeOH2+ groups increases so that the potential for binding is promoted [280].) Adsorption of anions is usually a two-step process, with a rapid initial stage (minutes to hours) limited mainly by diffusion to the adsorbent surface, followed by a slower second stage which may involve diffusion of the adsorbate into an particulate aggregate or crystal micropores and structural rearrangements [280]. Anionic adsorption onto iron oxides appears to be promoted with rising temperature [280]. Experimental results have shown that humic substances adsorb more strongly onto mineral surfaces as aromaticity increases and as polarity — approximated as elemental O:C ratio — decreases (i.e. hydrophobicity increases [280]), suggesting a ligand-exchange mechanism [766]. Increased adsorption is also seen as the size of the moieties increases [280]. Humic substances have also been shown to adsorb to a greater extent as ionic strength increases [566, 766]. Higher ionic strengths imply greater charge shielding, such that carboxylic acid functional groups (negatively charged at natural water pH values) on the NOM chains experience less charge repulsion from each other, and the molecule enters a more compact configuration [566]. The effect of chain compaction at increased ionic strength is similar to a decrease of molecular mass [566]. Ionic strength has a greater influence on the adsorbability of the higher molecular mass species [566]. Further, fulvic acids are reported to have a high surface affinity, which suggests a ligand exchange mechanism, and so their extent of adsorption is not significantly affected by ionic strength [566]. High ionic strengths may also be expected to enable closer packing of adsorbate when the surface affinity is not high [566]. However SUMMERS & ROBERTS showed that the adsorption

*

This is also termed “specific adsorption” (in certain cases also “ligand exchange” or “chemisorption”), and involves the replacement of surface hydroxyl groups by the adsorbing species, such that the character of the bond is significantly covalent [280]. Adsorption proceeds according to # bFeL + OH‒ bFeOH + L‒ ‒ b(FeOH)2 + L # bFe2L+ + 2OH‒ where b signifies a surface group and L represents an adsorbing ligand [280]. Given this mechanism, an overall positive surface charge is n o t required on the adsorbent in order to adsorb anionic species, only FeOH2+ and FeOH groups [280].

†

This is also termed “non-specific adsorption” and “ion pair formation”, and the adsorbing species retains its primary hydration shell (at least one molecule of water is interposed between the adsorbent and the adsorbate), which typically forms a hydrogen bond to the surface — so the adsorbent can be readily displaced (or ‘exchanged’) by another ion [280]. Given this mechanism, the process is strongly governed by electrostatics, and thus influenced also by the ionic strength of the system [280]. This mode is usually dominant in the case of organic ligands [280]. R1▪1 : Important constituents of raw water — natural organic matter (NOM)

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density on positively charged adsorbents actually d e c r e a s e s with increasing ionic strength [566]. Enhancement of adsorption in the presence of electrolytes may also occur by a reduction in solubility of the humic substances through common ion, ion pairing, or complexation mechanisms [566]. Electrolytes can also change the charge distribution at the adsorbent surface and reduce the affinity of the adsorbate for the aqueous phase (i.e. solvent) [566]. In the case of multivalent cations, humic substances may complex to form insoluble aggregates (i.e. precipitate), decreasing adsorption, while also adsorbing to the solid surface via cation bridges, increasing adsorption [566]. It has been shown that undesirable hydrophobic organic compounds, in this case polycyclic aromatic hydrocarbons (PAH’s) [see 34], adsorb much more strongly to mineral surfaces coated with humic substances than to bare surfaces [766]. It was proposed that this effect was enhanced by conditions that would favour more open conformations of the humic substance, making more hydrophobic domains available, such as low ionic strength or an even distribution of surface hydroxyl sites (e.g. hæmatite) [766].

R1▪2

Coagulation

A discussion here is presented of important aspects of coagulation and is followed by a discussion of flocculation. A good deal of basic knowledge of colloid and surface science is assumed, and a comprehensive review is beyond the scope of the present work. Standard references include the books by SHAW [924], HUNTER [511], ISRAELACHVILI [517] and RUSSEL, SAVILLE & SCHOWALTER [878] inter alia, besides the original works cited therein. JOLIVET [538] provides an extended discussion with specific application to colloidal metal ‘oxides’, and clearly identifies some l i m i t a t i o n s of the theoretical approaches. Various IUPAC publications [e.g. 349, 687] are also helpful. Coagulants (and flocculants) that are used typically fall into three categories: • inorganic coagulants; • prepolymerised or prehydrolysed inorganic coagulants; and • organic coagulants. Inorganic coagulants are used in the greatest quantities, and are the focus of the present work. For most WTP’s, coagulant costs comprise up to 30% of the overall plant operating costs [272]. Organic coagulants are discussed briefly in §R1▪3▪3▪1. The commonly used inorganic coagulants [854] are: • aluminium sulfate; • ferric sulfate; and • ferric chloride. Ferrous sulfate and chlorinated ferrous sulfate are also used [797, 854, 1139]. ‘Pre-polymerised’ [see 79, 98, 136, 161, 231, 300, 339, 430, 668, 797, 827, 1001, 1085, 1113, 1140, 1141] and ‘hybrid’ or ‘mixed’ [cf. 98, 340] versions have more recently become popular too, but are not specifically covered in the present work. 640



Aluminium sulfate is “by far” the most commonly used coagulant in water treatment [892, also 1098] [cf. 79, 389], including in Australian operations [e.g. 685]. Ferric coagulant use is relatively uncommon in Australia: still, ferric chloride is the more popular coagulant in New South Wales [685], including usage at four major plants in the Sydney area [1095], and several smaller WTP’s use ferric chloride [e.g. 294] or ferric sulfate [835]. It is also uncommon in New Zealand (one plant, sited at a mine, uses ferric chloride) [797] and the U.S.A. (though this may change [see 79]). However, in the U.K. ferric coagulants — generally ferric sulfate, based on local cost considerations [475, 1042] — are almost as common as alum, accounting for on the order of 40% of usage [827]. Use of ferric coagulant is favoured for upland or reservoir waters of high colour but low turbidity [1042]. Specific advantages are indicated, such as superior Cryptosporidium parvum oocyst [e.g. 685] and NOM [79] removal, although these are not necessarily applicable to every site. Ferric coagulants tend to be less sensitive to pH than alum [e.g. 1124], due to their wider solubility envelope (see Figure R1-1). This permits operation at higher pH, which can be beneficial for (say) manganese removal. Less commonly used inorganic coagulants include [28]: • magnesium carbonate; and • sodium aluminate. A few treatment plants have been designed to be able to routinely switch between different coagulants (e.g. aluminium sulfate and ferric chloride) as desired throughout the year [434].

R1▪2▪1

The terminology of aggregation

The present work draws a pragmatic distinction between two sorts of a g g r e g a t i o n , namely c o a g u l a t i o n and f l o c c u l a t i o n . Generally the distinction made is adapted from that of LA MER & HEALY (1963) [see 155] (inter alia [511, 619, 924]): Coagulation is brought about primarily by a reduction of the repulsive potential of the electrical double layer [...]. Flocculation is usually brought about by the action of high molecular weight materials [...] acting as linear polymers which bridge and unite the solid particles of the dispersion into a random structure which is three dimensional, loose, and porous.

Coagulation occurs by a neutralisation of most of the particle charge through the addition of charged species (ions, small polyelectrolytes [171, 426]), and the particles interact directly. Flocculation occurs when (long-chain) polymers adsorb by some mechanism and create a link between particles. Other forms of flocculation (e.g. in a secondary minimum of the interaction potential) exist [see 80, 510, 511], but are less relevant to water treatment. In certain cases ambiguity might exist as to whether ‘coagulation’ or ‘flocculation’ has occurred, but this is not critical. It is, however, vital to emphasise that references to flocculation in the present work do n o t refer to gentle mixing, as is common in water industry parlance [e.g. 283, 523] [cf. 505]. A further convenient distinction can be made between coagulation or flocculation of raw water colloids at the head of the WTP, and polymer c o n d i t i o n i n g of the settled or dewatered sludge further downstream, as explained in §R1▪3 (p. 704). R1▪2 : Coagulation

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D. I. VERRELLI

R1▪2▪2

Coagulation regimes

There are three regimes in which coagulation could be operated for the purposes of water treatment. ‘Charge neutralisation’ works by neutralisation of the overall surface charge of 1. suspended particulates such that they no longer repel each other, and even aggregate. Coagulant demand is sensitive to raw water quality, and so this is impracticable on a large scale. ‘Sweep coagulation’ has been the most commonly used treatment regime in 2. WTP’s. In this regime a large excess of coagulant is added, such that coagulant precipitate forms in such volume that particulate matter becomes ‘swept up’ in it. ‘Enhanced coagulation’ is the most recent mode of operation. It is similar to 3. sweep coagulation, except that still more coagulant is added, to remove still more contaminant, primarily natural organic matter (NOM), from the raw water, and minimise DBP formation potential. The delineation follows from the amount of coagulant added, and so the boundaries between regimes are ‘fuzzy’ [see 90, 533].

R1▪2▪2▪1

Charge neutralisation

Charge neutralisation, or adsorption–destabilisation [90], makes use of the fact that most particles found in natural waters carry a nett negative residual surface charge [113, 505, 511, 533, 569, 855]. The surface charges may arise through one of three mechanisms [505]: • defects in crystalline lattices — common in clays; • equilibria with dissolution products — common in metal oxides and hydroxides, for which H+ and OH‒ are potential-determining ions (indicated in pH); • adsorption of specific ions, especially hydrogen-bonding of large organic species. It is important to emphasise that the overall charges encountered in the raw water may be very different to the surface charges measured for the pure, monolithic, defect-free solid phase in purified water (cf. the isoelectric points given in §R1▪2▪2▪1(a)). In practice there are also three mechanisms by which the suspension may be destabilised in this regime, namely [533, 854]: • compression of the double layer; • counter-ion adsorption; and • heterocoagulation — coagulation of particles with non-uniform surface charges. These mechanisms are probably more or less reversible [cf. 742]. Charge neutralisation is not used widely in industry [569] for the following reasons [1140]: 1. Difficulty in maintaining robust equipment to measure coagulant demand continuously, and control systems to respond to changes in demand. Sensitivity to non-uniformity of mixing, where local overdosing may occur. 2. 3. Risk of restabilisation through charge reversal upon overdosing — larger particles are more susceptible [533]. Slower aggregation kinetics. 4.

642



The first three concerns all stem from the narrowness of the dosage range at which satisfactory charge neutralisation occurs [326]. Coagulation by charge neutralisation is counteracted by humic acids, which can adsorb onto suspended particulates, giving them enhanced stability against cations, such as the trivalent metal ions commonly used as coagulants [430, 1072]. Sorption of humate onto hæmatite [1031, 1072] and interaction of a range of organic species, including humic substances, with goethite [280] induced coagulation at low concentrations, but caused restabilisation at higher doses. A related phenomenon occurs when coagulants are added to a raw water rich in hydrophobic organic compounds without adequate mixing: the coagulant may hydrolyse and precipitate to form a colloid without significant interaction with the NOM; with the passage of more time the NOM may then adsorb onto the freshly formed positive metal (oxy)hydroxide surfaces, resulting in electrostatic or steric stabilisation [272]. Ultimately the adsorption of soluble aluminium hydroxide onto raw water particulates may nucleate the formation of a thin surface hydroxide precipitate [326]. The degree of colloid destabilisation due to double-layer compression is strongly correlated with the valence of the counter-ion, according to the SCHULZE–HARDY ‘rule’ [817, 924], and is also associated with other factors including ion adsorption, ion hydration (or hydrated ion radius [802, 1072]), and surface hydration [505]. According to the SCHULZE–HARDY rule * the relative influence of an ion depends upon its valence in the approximate ratio 1‒6 monovalent : 2‒6 divalent : 3‒6 trivalent, or 1 : 0.0156 : 0.00137, for symmetric electrolytes and bare colloids with high surface potential [303, 379, 380, 497, 806, 1072, 1074]. This formulation of the SCHULZE–HARDY rule is consistent with DLVO theory for the two special cases of high surface potential unaffected by electrolyte valence and low surface potential inversely proportional to valence [497, 517] [cf. 806]. In contrast, at constant low surface potential the ratios 1‒2 : 2‒2 : 3‒2 (i.e. 1 : 0.25 : 0.167) are predicted [517, 806, 924, 1074], albeit seldom attained in practice [497]; intermediate results are predicted in the transition [e.g. 924, 1074]. Numerous divergences from the SCHULZE–HARDY rule have been observed experimentally. For example, VERALL, WARWICK & FAIRHURST [1072] reported ratios of: • 1 : 0.010 : 0.0006 for “bare” hæmatite colloids; • 1 : 0.04 : 0.0005 complexed with humic acid; and • 1 : 0.045 : 0.0002 with further humic addition. The valence and nature of the co-ions also affect the behaviour somewhat [806], and analogous ratios have been published for asymmetric electrolytes [see 497]. [See also 449, 854, 856.] Data on the hydrated ionic radii of Al3+, Fe3+ and Mg2+ [208, 564, 699, 700] do not show any conclusive difference. ONG & BISQUE [802] state that the effect of radius is relevant only for monovalent and divalent ions, which are more likely to occur as simple cation species and have lower charge densities.

*

Actually, neither SCHULZE nor HARDY formulated a rule in this precise form, although they pioneered experimental investigations of these phenomena [see 449, 806]. R1▪2 : Coagulation

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D. I. VERRELLI

R1▪2▪2▪1(a)

Particle charge and potential

It is helpful to consolidate the information on particle charge and potential into this subsection for comparison. Further discussion of the solid aluminium and iron phases follows in §R1▪2▪5▪3 and §R1▪2▪6▪3. The p o i n t o f z e r o c h a r g e (p.z.c.) is the condition at which the s u r f a c e charge density is zero [687, 725]. The i s o e l e c t r i c p o i n t (i.e.p.) is the condition at which the n e t t electric charge of an elementary entity is zero [725]. For oxides and similar phases the condition is normally specified in terms of pH [see 687]. At the i.e.p. the ζ-potential (or electrokinetic potential) is zero [280, 449, 687]. The ζ-potential is practically equal * to the potential at the outer HELMHOLTZ plane — corresponding to the diffuse layer [279] — which “plays a crucial role in colloid stability” [687] and dependent phenomena. Often the i.e.p. is approximately equal to the p.z.c. [370, cf. 924], which is expected when the n e t t specific-adsorption of anions and cations is negligible [280, 687]. Both the i.e.p. and p.z.c. have been found to be affected by an increase in temperature [687], which for iron oxides typically results in a decrease [280]. This might be partly explained by variation in the dissociation constant for water (cf. §R1▪2▪3). Particulate † aluminium oxides (including gibbsite and pseudoböhmite) attain their p.z.c’s at a pH of around 9 [see 312, 370, 537], while for iron oxides this occurs in the range 6 to 10, with goethite around 9.2, ferrihydrite around 7.8, and hæmatite around 9 [280, cf. 325, 538]. However these values are for the ‘pure’ oxides only, and adsorbed species, including CO2, can dramatically alter (typically decrease) the p.z.c. value: e.g. for ferrihydrite it reduces to around 5.3 upon adsorption of silicates [280]. The p.z.c. of brucite, Mg(OH)2, is significantly higher, around 12 [537]. Isoelectric points of around 9 for goethite and hæmatite have been specified (fractionally less than their p.z.c’s) [280], and likewise for gibbsite [370]. The precipitate formed by neutralising aluminium sulfate was reported to have a lower i.e.p. (~8) than that formed from aluminium chloride (~9) [326]. As for the p.z.c., the i.e.p. is extremely sensitive to adsorbed species [538], such that e.g. chloride can depress the i.e.p. of hæmatite to about 5.5 to 6 [280]. (BI et alia [148] quoted an i.e.p. of 6.5 to 7.0 for aluminium “hydroxide”, but noted it is “not easy to determine”.) The adsorption of humic substances (of order 2mg/L) from natural waters has been found to decrease the ζ-potential of iron oxides including hæmatite, ferrihydrite and goethite, such that they may be negative instead of positive for pH values down to about 4 [280]. Similar results have been reported for aluminium (oxy)hydroxide precipitated in a raw water coagulation process [319]. (The i.e.p’s of humic acids and fulvic acids are ~1.8 and <3, respectively [827].)

*

Discrepancy would be greatest at large magnitudes of potential or high electrolyte concentrations [924].

†

The p.z.c. and i.e.p. of aluminium and ferric (oxy)hydroxides depend upon the c o - o r d i n a t i o n of surface hydroxyl groups, which often varies between different crystallographic planes [537], and furthermore is affected by defects [370, 538]. These in turn depend upon particle size and morphology [538]. Defect-free, low-index crystallographic planes tend to have a lower p.z.c., e.g. 5 to 6, but make up a small proportion of the surface for submicron particles [370, 538] [cf. 1118].

644



In summary, then, the surface properties of a particle depend upon its history, including synthesis conditions [538].

R1▪2▪2▪2

Sweep coagulation

Sweep coagulation operates chiefly on the principle of particle enmeshment. Particles in water become enmeshed in growing amorphous hydroxide precipitates that are formed [377, 430, 569]. This mechanism of enmeshment and interparticle bridging is closer to a flocculation procedure [cf. 533, 854]. The process is essentially irreversible [cf. 961]. The raw water colloids are generally negatively charged, and coagulation causes the formation of a positively-charged layer on the particle surface [113]. This may be derived directly from charged metal ions (e.g. Al3+, Fe3+), or oligomers or polycations of these metals. In sweep coagulation a significant ‘excess’ of coagulant is added, and this precipitates as an amorphous mass, which is mobile, cohesive, and of low charge [113]. BACHE and co-workers propose that the raw water colloids are “held together through localised bridging promoted by electrostatic forces” [113]. According to PAPAVASILOPOULOS & BACHE [816], the combination of aluminium sulfate coagulant with humic acids by charge attraction is generally faster than the precipitation of aluminium precipitate. Hydrolysis of aluminium to more-or-less pure Al(OH)3 only dominates initially if the number of coagulant ‘particles’ exceeds the number of contaminant particles: either throughout the volume, at high coagulant doses (or high pH), or locally, due to inadequate mixing [816]. In such cases colour colloids will adsorb onto the preformed aluminium hydroxide floc [816]. Although hydrolysis of the mononuclear species may occur in less than 1s [816], polynuclear cations are generally far more persistent [113]. Coagulation is more efficient when the coagulant contacts the colloidal particles “before the hydrolysis reaction with the alkalinity is completed” [754] [see also 251]. Consideration of competing kinetics is important for the large number of (small) particles contributing to colouration, but not for the smaller number of particles contributing to turbidity, where hydroxide precipitation dominates [816]. At low coagulant doses DOC is removed, but TOC stays about the same, indicating that dissolved organic material has been converted to “nonsettleable particulate form” [1116]. The mechanism for this removal was proposed by EDWARDS & AMIRTHARAJAH in 1985 to vary according to the coagulation pH [171, 331, 1116]: • Low pH (e.g. <5½) — complex formation and precipitation of aluminium–humates and –fulvates. • Higher pH (e.g. >5½) — adsorption of dissolved NOM onto aluminium hydroxide flocs. This pH dependence was not observed by VILGÉ-RITTER et alia, who found complexation up to pH 7.5 [1082]. According to WHITE et alii [1116], in general TOC and turbidity are not removed in significant amounts until an ‘intermediate’ (threshold) coagulant dose is reached.

R1▪2 : Coagulation

645

D. I. VERRELLI

The amount of ‘free’ coagulant (e.g. aluminium sulfate) is decreased by formation of flocs composed of precipitated coagulant species and by adsorption of the coagulant on surfaces [459]. In the sweep coagulation regime, sludge volume depends linearly upon the dosage of coagulant. GREGORY & DUPONT [430] observed that a plot of these two variables could be extrapolated back to zero dosage. However it was unclear why the intercept sludge volume was greater than expected from the known amount of sediment in the raw water. The precipitation of hydroxide species in sweep coagulation means that the “effective” particle concentration is increased [430]. This improves the aggregation kinetics (by increased particle collision frequency), making sweep coagulation a more rapid process than charge neutralisation, and gives better clarification [430]. Compared to charge neutralisation, sweep coagulation is more tolerant of variation in processing conditions (especially increased coagulant dose) [113].

R1▪2▪2▪3

Enhanced coagulation

Enhanced coagulation was pioneered for greater removal of NOM and TOC in order to avoid formation of by-products such as THM’s [942] upon chlorination (or other disinfection) [335, 557, 596, 1116]. KORNEGAY, TORRES & KORNEGAY (2001) [596] claimed that “in many [U.S.] water treatment plants the removal of NOM serving as disinfection byproduct precursors will be the major constraint in treatment plant design.” Additionally, QASIM, MOTLEY & ZHU [854] describe enhanced coagulation as becoming practical for removal of colour (usually due to NOM in natural waters), arsenic, and other heavy metals. While in principle enhanced coagulation could refer to any modification that achieves greater NOM removals than the ‘conventional’ sweep coagulation [1116], in practice this is achieved simply by adding a significantly larger dose of coagulant — which produces correspondingly more sludge in a linear relationship. LIND [668], writing in 1997, indicated a two- to three-fold increase in coagulant dose under this regime, and KAWAMURA [557] indicated the same level of increase in sludge production compared to conventional treatment. The mechanism of enhanced coagulation is essentially no different to that of sweep coagulation. With the increased coagulant doses comes a reduced sensitivity of the treatment process to pH [161], as the range of ‘optimum’ pH broadens with increasing coagulant concentration [339]. This is implicit in the solubility curves for aluminium and ferric species (Figure R1-1, p. 648). Treatment may be improved by operating at a lower pH than for conventional sweep coagulation [668]. This encourages precipitation of higher molecular mass humic substances as complexed humates, although turbidity and particle removal would be optimised at slightly higher pH values [668]. A disadvantage of low-pH operation is that the water becomes more corrosive, and metal solubilities increase, prompting additional treatment steps [557].

646



Aside from the mechanisms at work in the charge neutralisation and sweep coagulation regimes, in the enhanced coagulation regime the following mechanisms are increasingly important: Precipitation of contaminants out of solution. This involves a substitution 1. reaction that produces a substance with a lower solubility. Adsorption of contaminants onto hydrous metal flocs. 2. “Coprecipitation” or “surface complex formation” is the adsorption of otherwise soluble contaminant onto hydrous metal oxide at a surface hydroxyl group (a “reactive” or “exchangeable” site) [854]. Co-precipitation is defined [135] as having four types: Inclusion — especially for large crystals; involves mechanical entrapment of 1. solution in particle. Adsorption — especially for small particles; involves adsorption of contaminant. 2. Occlusion — adsorption onto small precipitate, covered by subsequent 3. precipitate particle growth. Solid-solution formation — describes the formation of a (microscopically) 4. heterogeneous mixture of particles in a precipitate.

R1▪2▪3

Coagulant species solubility

Equilibrium solubilities pertaining to alum and ferric are presented in Figure R1-1. Discrepancies between results for a given metal reflect experimental uncertainty for the most part, along with the effects of ionic strength and total metal concentration in the data of BUTLER & COGLEY [219]. The features of most interest are the location of minimum solubility — around pH 6 for Al, and pH 8 for Fe(III) — and the width of the solubility envelope at a given total metal concentration — broader for Fe(III). In a WTP the relations portrayed in Figure R1-1 will not be obeyed precisely. The real behaviour will deviate because of shifting of the equilibria caused by the complex electrolyte mixture and because of kinetic effects [see also 614]. Temperature can also affect the equilibria (and kinetics). As temperature is decreased, the equilibrium constants governing the solubilities in Figure R1-1 change — in particular the equilibrium dissociation constant of water [326], Kw, decreases from 10‒14.00 at 25°C to 10‒14.73 at 5°C [387, 662, 978]. This tends to shift the solubility curves to higher pH [326, 335, 787]; for example, while the minimum overall solubility of Al species occurs at about pH 6.0 at 25°C, at 4°C this shifts to about pH 6.8 [335]. Correspondingly the optimum coagulation pH tends to increase (linearly) [113]. A simple means of compensation is to target a constant pOH (or [OH‒]), rather than pH (or [H+]), which renders the effect of temperature relatively minor [113, 326, 978] [cf. 675]. Small deviations in Kw due to the presence of additional electrolytes [e.g. 1017] are assumed negligible.


647

D. I. VERRELLI

1.E+5 1.E+4 1.E+3

Solubility [mg/L]

1.E+2 1.E+1 Al

1.E+0 1.E-1 1.E-2

Fe

1.E-3 1.E-4 1.E-5 1.E-6 0

2

4

6

Black in: Faust & Hunter (1967), p. 278 Duan & Gregory (2003) — I ~ 0M Amirtharajah & Mills (1982) Butler & Cogley (1998), p. 268 — 0.5M Al, I = 1.0M Black in: Faust & Hunter (1967), p. 279 Duan & Gregory (2003) — I ~ 0M Johnson & Amirtharajah (1983) Butler & Cogley (1998), p. 274 — 0.5M Fe

8

10

12

14

pH [–]

Figure R1-1: Solubility curves for Al and Fe(III) from various references [90, 155, 219, 326, 533] at various ionic strengths. Temperature is assumed to be 25°C in all cases.

Equilibrium solubility data for magnesium is presented in Figure R1-2. The total amount of magnesium added by THOMPSON, SINGLEY & BLACK [1022] was presumably higher (the experimental curve of BAES & MESMER [118] agrees when calculated for 1M total Mg), partly explaining the increased dissolution, or rather, the shift to higher pH. The solubility envelope is seen to be very different to that for the trivalent metal species: negligible solid phase is predicted, except for at high pH.

648



1.E+02 1.E+00

Concentation [mg(Mg)/L]

1.E-02 1.E-04 1.E-06 1.E-08 1.E-10

T,S&B Theory T,S&B Experiment B&M Mg All dissolved B&M Dissolved 2+ B&M Mg B&M Mg2+ B&M MgOH+ MgOH+ B&M B&M Mg4(OH)44+ Mg4(OH)44+ B&M

1.E-12 1.E-14 1.E-16 1.E-18 1.E-20 6

7

8

9

10

11

12

13

14

pH [–] Figure R1-2: Solubility of magnesium in equilibrium with Mg(OH)2, and indicative speciation. Data from THOMPSON, SINGLEY & BLACK [1022] (“T,S&B”) and BAES & MESMER [118] (“B&M”, calculated for 10–3M total Mg). All data for 25°C. The T,S&B experimental curve is a ‘best fit’ to data obtained after circa 1h ‘equilibration’ that exhibited significant scatter.

R1▪2▪4

Coagulant species hydrolysis, polymerisation, and precipitation

Prior to discussion of features of the hydrolysis, polymerisation and precipitation processes specific to aluminium, iron(III) or magnesium, it is instructive to outline key features from more general models.

R1▪2▪4▪1

Hydrolysis

LIVAGE, HENRY, JOLIVET and colleagues [e.g. 466, 538, 675, 676, 677] have elucidated a comprehensive model for the hydrolysis and polymerisation (§R1▪2▪4▪2) of metal ions. Each metal species behaves differently depending upon its electronegativity and ‘hardness’ (reciprocal of electron cloud polarisability), underlying which are the ion size and charge,


649

D. I. VERRELLI

according to the “partial charge” model [466, 538, 675, 677]. This model implicitly works by comparing estimates of electronic chemical potential * for given chemical species [466, 538, 677]. Limitations of the partial charge model a s u s e d are: • it does not account for molecular structure [538, 677] — o this affects the computation of electronegativities, as it is equivalent to the “drastic” approximation that the electrostatic perturbations are much smaller than the covalent perturbations [466] †, o the presence of multiple bonds can lead to stable chelates which are unreactive, insensitive to pH, and remain in solution as monomers [538] (cf. action of NOM, e.g. §R1▪2▪6▪3(d)), o also it ignores steric effects which might be important for large ligands [see e.g. 99, 208]; • ‘hardness’ is estimated from a structure-free correlation obtained by linear regression [466, 538] ‡; • effects of temperature, pressure, ionic strength, metal concentration and ‘foreign’ ligand concentration [538] are not accounted for [466] — o the predictions are formally for the cation in its standard state (unit activity) [538]; • the oxidation state of the metal must be known (or guessed) a priori [466, 538]; • π overlapping [538] and resonance effects are not included [677]; and • the influence of other physico-chemical and kinetic aspects (e.g. mixing, cf. locallyelevated concentrations [499, 500, 573, 1100]) cannot be treated [see 677]. Following WERNER and PFEIFFER the above researchers took hydrolysis as equivalent to d e p r o t o n a t i o n , which occurs according to the scheme [466, 675, 676, 677]: [M(H2O)N]z+ + h H2O # [MONH2N‒h](z‒h)+ + h H3O+ , where M represents the metal species, z is the charge on the unhydrolysed cation (equivalent to the oxidation number), and h is the extent of ‘hydrolysis’. N indicates the co-ordination number; although the equation indicates this to be constant, in fact it can vary as a function of h — and thus as a function of pH [466, 674, 675]. Different values of h indicate different aqueous species, as in Table R1-4.

*

These are not exact, as strictly electronegativity can only be equated to the reactivity of f r e e a t o m s [538].

†

Otherwise a set of linear equations would have to be solved simultaneously [466].

‡

Otherwise dipole moments and interatomic distances for various (neutral diatomic) molecules would be required [466].

650



Table R1-4: Classes of hydrolysed species arising in sequence [466, 677].

Extent of hydrolysis h=0 0
Species a [M(H2O)N]z+ [M(OH)h(H2O)N-h](z‒h)+ [M(OH)N](N‒z)‒ [MOh‒N(OH)2N‒h](h‒z)‒ c [MON](2N‒z)‒

b

‘aquo-ion’ hydroxo-aquo complex hydroxo complex oxo-hydroxo complex c ‘oxo-ion’

b

Note: a By the latest IUPAC recommendations [275] the complexes would be named (in order) aqua, aquahydroxido, hydroxido, hydroxido-oxido, and oxido. The non-standard usage is retained to be consistent with the terms ‘oxolation’ and ‘oxyhydroxide’ used elsewhere. b Formation of an oxo-aquo ion by prototropic transfer is favoured for small, high-valent (z ≥ 4) metals: e.g. for Ti(IV) and V(IV) the stable form for h = 2 is [MO(H2O)5]2+ rather than [M(OH)2(H2O)4]2+ [677] and for V(V) h = 4 yields [VO2(H2O)4]+ rather than [V(OH)4(H2O)2]+ [538, cf. 675]. c If co-ordination expansion can occur, then ‘oxo-hydroxo-aquo’ species such as [MoO2(OH)2(H2O)2]0 and [WO(OH)4(H2O)]0 can form in preference to [MO2(OH)2]0 [466].

It should be noted that generally N is larger than z [e.g. 677]. For example: Mg2+ hydrolyses with N = 6 (at least for small h); Al3+ and Fe3+ hydrolyse with N = 6 (small h) or N = 4 (large h); Zr4+ hydrolyses with N = 8 (small h) or N = 6 (large h) [466, 538, 675, 677] *. In fact the coordination unsaturation, max {N} ‒ z, is related to the ease of nucleophilic addition [see 677]. The partial charge model permits prediction of the theoretical extent of hydrolysis, h, of a given species (characterised by its electronegativity, co-ordination number and charge) at a given pH [466]. This is presented in Figure R1-3 for four different metals. It must be noted that at any given value of pH a variety of species will exist, and the prediction presented is an indication only of the most prevalent ion or complex. To illustrate the interpretation of Figure R1-3, at pH = 10.5 Mg(II) is predicted to predominantly form either [Mg(OH)2(H2O)2]0 or [Mg(OH)2(H2O)4]0, depending upon N.

*

Feasible (crystal) co-ordination numbers are given as 4, 6 and 8 for Mg2+ [662]; N = 4 likely occurs at high pH (by analogy to Al3+ and Fe3+), and N = 8 likely does not occur in aqueous solutions. For Al3+ values of 4, 5 and 6 [662] and 3 [99, 671] are given for N, but N = 5 is less common than N = 4 or N = 6, occurring in certain organometallic complexes [see 99, 671] and rarely in inorganic solids [e.g. 610], and N = 3 is only known in a few organometallic complexes [see 99, 671]. For Fe3+ values of 4, 6 and 8 are given for N [662], but 8-fold co-ordination does not appear to occur with the ligands considered here [see 466, 675, 677]. For Zr4+ values of 4, 6, 8 and 9 [662], and 5 [676] and 7 [538, 677] and 10 [759] are given for N. The existence of multiple more-or-less stable co-ordination states increases reactivity through the option of co-ordination expansion in solution of ‘unsaturated’ metal cations to accommodate — even if only temporarily — additional ligands [677]. R1▪2 : Coagulation

651

h , theoretical extent of hydrolysis (deprotonation)

D. I. VERRELLI

7

Al(III), N=6 Al(III), N=4 Fe(III), N=6 Fe(III), N=4 Mg(II), N=6 Mg(II), N=4 Zr(IV), N=8 Zr(IV), N=6 Zr(IV), N=4

6 5 4 3 2 1 0 0.0

3.5

7.0

10.5

14.0

pH [–]

Figure R1-3: Prediction of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals as a function of pH according to the partial charge model [466, 675] referenced to [H9O4]+, H2O, and [H7O4]− at pH 0, 7 and 14 respectively (see §S21) [538]. The domain of some curves has been constrained to omit some improbable species.

The extent of hydrolysis of all four metals shown in Figure R1-3 can be roughly summarised as 0 ( h ( N, indicating that hydroxo-aquo species are predicted to predominate at most pH values, along with ‘aquo-ions’ at low pH and hydroxo complexes at high pH. This behaviour is not followed by small, high-valent metal cations — e.g. Cr6+, Mn7+ (both N = 4) — whose polarising power is too strong for aquo complexes to form [466, 675]. In fact, Mn7+ forms only ‘oxo ions’ (permanganate), and behaves purely as an acid [466, 538, 676]. Also the following discussions will not be relevant to large, low-valent cations (e.g. Na+, K+, Cs+, Ba2+) with low electronegativity and LEWIS acidity (cf. pKa [662]) [see 675] — i.e. low polarising power — if these form only aquo complexes and cannot be deprotonated [466, 677]. (The partial charge model in fact predicts hydrolysis up to h ≈ 4 for Ba2+ at high pH, much like Mg2+, and up to h ≈ 3 for the other three metals.) Indeed NaOH et cetera are strong bases which completely dissociate [466, 538, 676]. An obvious question arising from Figure R1-3 is which co-ordination number will prevail at a given pH. An indication based on experimental observations has already been given, and further specifics will be provided in later sections. A quantitative theoretical analysis based on the partial charge model can also be carried out to predict this. The parameter of interest is the partial charge on the metal component of the complex: this governs the ‘ideal’ number of nucleophilic groups, which facilitate charge transfer toward the metal and so lower its partial charge [cf. 677]. (Equivalently, a decrease in co-ordination is predicted when the partial charge of H2O ligands becomes negative [538].)

652



Taking this concept further, it is proposed that, f o r a g i v e n h , formation of the complex with the lowest (positive) partial charge on the metal will be favoured. Relevant values are plotted in Figure R1-4 for species of interest. At pH = 14 aluminium may form a complex with h ≈ 4.24 ~ 4 (N = 4) or with h ≈ 4.99 ~ 5 (N = 6), as shown in Figure R1-3. In either case the theoretical partial charge on Al is +0.468. However, the tetrahedral complex is preferred. Referring back to Figure R1-3 again, the simplest conclusion is that, for a given pH, the coordination with the smallest h is favoured. Where the curves at a given h are close, more than one co-ordination may be found.

Partial charge on M [elementary charge units]

1.2

Al(III), N=6 Al(III), N=4 Fe(III), N=6 Fe(III), N=4 Mg(II), N=6 Mg(II), N=4 Zr(IV), N=8 Zr(IV), N=6 Zr(IV), N=4

1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0

1

2

3

4

5

6

7


Figure R1-4: Prediction of partial charge on the metal, M, in various series of aqueous complexes as a function of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals according to the partial charge model [466, 675].

R1▪2▪4▪1(a)

Anion complexation

Real systems contain impurities in large or small concentrations. While the foregoing provides a useful indication of hydrolysis trends for various metals, it is important to recognise the importance of anions other than those derived from water. These ‘foreign’ anions can also complex with the metal, in some cases [466, 677]. This can affect oligomer formation and nucleation, and in the precipitate it can control the solid phase formed, and the size and shape of particles [e.g. 466, 573, 677] — even if the complexation only occurs ‘temporarily’ at a specific stage of the hydrolysis–condensation process, and even if only weak ‘outer-sphere’ complexation is involved [538]. Theories to explain these influences are incomplete [538, 677]. Aggregation can also be affected through changes in the double layer [677].


653

D. I. VERRELLI

Some anions do not successfully ‘compete’ with water, either because they tend to dissociate from the complex (e.g. ClO4‒, NO3‒), liberated as the anion, or they undergo ‘hydrolysis’ (e.g. iodide [cf. 648] or chloride at low pH), liberated as the salt [466]. This is illustrated in Figure R1-5 for the most general case. Ionic dissociation ( to ) occurs when the anion Xn‒ is m o r e e l e c t r o n e g a t i v e than the complexed species (), which is more likely at high pH (i.e. large h) [466, 538]. ‘Hydrolysis’ ( to  ...or  to  [677]) occurs when the fully protonated anion — i.e. salt — HnX is l e s s e l e c t r o n e g a t i v e than the complexed species ( ...or ), which is more likely at low pH (i.e. small h) [466, 538]. In theory ionic dissociation ( to ) of the q-protonated anion HqX(n‒q)‒, with 0 < q < n, is also p o s s i b l e when that species is m o r e e l e c t r o n e g a t i v e than the complexed species () [466, 538]. Note that under the partial charge model intramolecular prototropic transfer does not affect electronegativity (same for ,  and ). complexation

[M(OH)h(H2O)N‒h](z‒h)+ + mXn‒ # [M(OH)h(H2O)N‒h‒mα(X)m](z‒h‒mn)+ + mαH2O  ionic dissociation  (de)protonation q (de)protonation i.p.t. q i.p.t. complexation (z‒h‒mq)+

(n‒q)‒

[M(OH)h+mq(H2O)N‒h‒mq] + mHqX # [M(OH)h+mq(H2O)N‒h‒mα‒mq(HqX)m](z‒h‒mn)+ + mαH2O  ionic dissociation  (de)protonation q (de)protonation i.p.t. q i.p.t. complexation

[M(OH)h+mn(H2O)N‒h‒mn] 

(z‒h‒mn)+

+ mHnX

# [M(OH)h+mn(H2O)N‒h‒mα‒mn(HnX)m](z‒h‒mn)+ + mαH2O ‘hydrolysis’ 

Figure R1-5: Schematic of anion complexation, ‘hydrolysis’ and ionic dissociation [466, 677]. “i.p.t.” denotes intramolecular prototropic transfer. Ligand X has denticity α and valence –n; h is the extent of hydrolysis (deprotonation) of the ‘precursor’ (); q is the anion protonation [466]. For clarity the formulæ are arranged for 0 ≤ h ≤ N, but rearrangement to allow for larger values of h is trivial.

A result of these considerations is that multivalent anions (e.g. SO42‒, PO43‒) are better ligands, as their variously protonated forms are likely to yield stable complexes across a range of pH values [see 466]. Complexes incorporating anions which can bind multidentally (or in a bridging mode) are favoured, including monovalent anions [466, 538]. When the complexed precursor has an electronegativity between those of Hn‒1X‒ and HnX, then the most stable complexes are obtained: the anions act as “network formers”, and remain tightly bonded with the metal even following precipitation [466] (e.g. sulfate in basic salts such as Fe3(SO4)2(OH)5·2H2O and Fe4(SO4)(OH)10 [cf. 677], in schwertmannite (§R1▪2▪6▪3), or in jarosite, KFe3(SO4)2(OH)6 [520]) *. When the complexed precursor has an electronegativity between those of Xn‒ and Hn‒1X‒, then complexation with the metal is expected, but ultimately liberation can occur “during growth leading to an oxide network free of anions” [466].

*

654

What is described here is different from the precipitation of ‘pure’ crystallites of (say) hæmatite, which form larger particles with ‘foreign’ anions chiefly located between ‘grain’ boundaries [see 929]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


Al(III), N =6, α =2, m =1 PO4

q=0 q=1 q=2 q=3 q=4

Ionic dissociation

21

SO42– C2O42–

14 Critical pH [–]

2.10

3–

HPO42–

Cl–

7

2.50

F–

Complexation

0

2.30

HCl 2.70

H2CO4–

H2PO4–

HSO4–

NO3–

-7 2.90

H2C2O4 H3PO4

-14 -21

H2SO4

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

2.6

HF

2.8

HNO3

3.0

Mean electronegativity of aqueous solution

28

3.10

3.2

Electronegativity of q -protonated anion [–] Figure R1-6: Plot of critical pH against the mean electronegativity of the q-protonated anion, HqX(n−q)− for various values of q and illustrated by a selection of real ions. As indicated, the basis is complexation of octahedral Al3+ by a single ‘foreign’ bidentate ion. The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7 and 14 respectively (see §S21).

All of this information can be summarised in a diagramme such as Figure R1-6. This is obtained by equating the mean electronegativity of the stable complex to that of the system — from which the pH can be calculated by choosing appropriate reference species [see 466, 538]. (Again the simple model ignores the fact that at any condition a d i s t r i b u t i o n of several species will exist in reality, even at equilibrium.) The interpretation can be illustrated by considering complexation by sulfate. If the system pH is very high (above ~12.5 *) then sulfate will simply act as a counter ion. For pH less than ‒14.4 a sulfate complex would be expected to hydrolyse; of course, such conditions are physically unattainable in real aqueous systems. Although complexation in solution is feasible between these limits, for all pH values above –3.0 ionic dissociation of HSO4‒ can also occur (after proton transfer), so a sulfate-free precipitate may form. *

As shown in Appendix S21 the correct limit is closer to pH 10.5, as aluminium is more likely to be found in tetrahedral complexes at high pH [675, 786]. . R1▪2 : Coagulation

655

D. I. VERRELLI

Several other combinations of interest are presented in Appendix S21. LIVAGE, HENRY & SANCHEZ [677] entreated: More reliable experimental data and accurate characterization of all the chemical species involved [...] have to be obtained before a real science of inorganic polymerization can be established.

— this appears to be a practically impossible task for real systems. JOLIVET [538] also warned that plots such as Figure R1-6 must be “handled with extreme caution”: they provide no indication of the extent of reaction, and their “qualitative” information should only be used in the absence of reliable experimental (e.g. thermodynamic) data. Detailed analysis of the role of anions in the present water treatment systems would be very involved, not to mention uncertain. Hence discussion is generally restricted to mention of the role of likely counterions added along with the coagulating metal species, viz. chloride and sulfate. Complexation by chloride generally is only expected around neutral conditions, whereas both inner-sphere and outer-sphere complexation by sulfate is possible across a wide range of pH values [466, 677]. (Chloride is unlikely to bind bidentally, unless stabilised in certain solids [535], but computations for monodentate complexation are similar: see Appendix S21.) Naturally occurring organic species pose a special problem, as their composition varies widely, and is generally not well known at any given point. Organic species can certainly act as anions; however, they typically do not form stable complexes in aqueous solutions [671, 677] [cf. 99]. More pertinent to associations in water treatment systems are probably complexation or chelation of the metals by the NOM species (rather than vice versa), especially at low metal concentrations, and physico-chemical processes such as surface adsorption at higher coagulant doses — these are not modelled by the foregoing theory, and are treated phenomenologically in the present work. Incorporation of ‘foreign’ cations [e.g. 538, 614] is a separate complication.

R1▪2▪4▪2

Polymerisation

The key feature of metal ion polymerisation is a condensation reaction, yielding an H2O molecule, which can proceed by one of two mechanisms [466, 675]. The OH group attached to one cation can react with an H2O ligand on a second complex ‒M‒OH + H2O‒M‒ → ‒M···OH···M‒ + H2O , in which M represents the metal, and non-participating ligands are not shown; this is called o l a t i o n [466, 536, 538, 539, 675, 1017] [cf. 573]. It is a nucleophilic substitution reaction, with H2O as the leaving group [538, 677]. Alternatively, the OH group on one cation can react with the OH group on a second cation ‒M‒OH + HO‒M‒ → ‒M‒O‒M‒ + H2O , which is called o x o l a t i o n [466, 536, 538, 539, 675] [cf. 573, 1017]. This is often a nucleophilic substitution reaction with H2O as the leaving group (as written), but OH‒ can also act as leaving group, and nucleophilic addition is possible if the metal co-ordination is unsaturated [538, 677].

656



Olation is usually governed by the lability of the H2O‒M bond, which increases when the cation’s size increases or its oxidation number decreases [466, 538, 675, 677]. Where the lability of co-ordinated water molecules is high [539] — which is common [538] — olation processes are generally faster than oxolation processes [675], and this has been attributed to the absence of proton transfer in olation [466] (although it may not be entirely accurate [538]). Thus olation is often a d i f f u s i o n - l i m i t e d process, especially for low-valent (0 ≤ z ‒ h ( 2) complexes of large cations without crystal field stabilisation (e.g. octahedral Fe3+) [677] and in the absence of steric hinderance from complexing ligands [538]. As a diffusion-limited process, all aspects which control the rate of encounters (e.g. mixing intensity, concentration) can affect the outcome [677]. Oxolation is “never” a diffusion-limited process [677]. However it can be catalysed by acids or bases, and so occurs over a wide(r) range of pH [466, 538, 677]. The minimum oxolation rate does not necessarily occur at precisely pH 7, but rather when the reactants are uncharged [538, 677]. The main constraint on polymerisation is the presence of coordinated hydroxo groups [466, 676]. The divalent, trivalent and tetravalent metals in Figure R1-3 will tend to undergo olation [466, 677]. However oxolation can also occur in parallel, so the ultimate solid precipitate may be a hydroxide or it may be an oxyhydroxide or hydrous oxide [466, 677]. Oxides * are favoured when oxolation proceeds faster than olation (e.g. Zr4+), and oxyhydroxides (e.g. Fe3+) in the converse case [538] [cf. 325]. Oxolation may also prevail eventually if h is large [538]. (If the pH were too low, such that only aquo complexes were present — with maximum cation co-ordination — then condensation could not proceed [538, 677].) Oxo-hydroxo species, such as from Ta5+ or Cr6+, would be predicted to undergo only oxolation, rather than olation — and, ultimately, to precipitate as oxides or oxyhydroxides rather than hydroxides, unless reduction occurs [466, 675, 677]. (If the pH were too high, such that only oxo complexes were present, e.g. Cr6+, Mn7+, then neither olation nor even oxolation could proceed — except by way of co-ordination expansion if the precursor is unsaturated, e.g. V5+, Mo6+ [538, 677].) Olation commonly results in sharing of two OH groups between a given pair of cations [675]. (Therefore a better generic representation of ‘ol’ linkage is ‒M···(OH)n···M‒.) Thus oxolation commonly occurs at a double ‘ol’ linkage, viz. [675] ‒M···(OH)2···M‒ → ‒M‒O‒M‒ + H2O , or [535, 1017] [cf. 539, 677] ‒(OH)M···(OH)2···M(OH)‒ → ‒M···(O)2···M‒ + 2H2O . The bridging OH groups also “tend to get their highest co-ordination”, which promotes the formation of more compact structures, such as cyclic polycations, over linear † structures [675] [cf. 677]. Thus, while a dimer of edge-sharing MO6 octahedra possesses two μ2-OH bridges, a stable cyclic trimer with a central μ3-OH group (and three μ2-OH bridges) —

*

Hydroxides of tetravalent metals are often unstable and spontaneously dehydrate (by oxolation) to form hydrated oxides [538].

†

Although oligomers comprising a chain of single MO6 octahedra formed via μ2-OH bridges “are never observed” [675], dioctahedral chains are observed [504, 520, 536, 539]. Formation of such chains is consistent with rapid olation and slow oxolation. R1▪2 : Coagulation

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formula M3(OH)4(H2O)95+ — is favoured in order to minimise electrostatic repulsion between cations [466, 538, 675]. Even μ4-OH groups are possible, as with Cu(II), albeit rare and unstable [466, 519, 538, cf. 677]. ‘Oxo’ linkages may also be shared between more than two cations, as in the μ3-O bridges which have been hypothesised to link the double-octahedra-chains to form sheets of goethite [536, 538, 539] [see also 312, 677], or even μ4-O bridges in the skewed [Al4O(OH)10(H2O)5]0 tetramers proposed as precursors to (pseudo)böhmite [538, 675] (and in pseudoböhmite itself [312]) and elsewhere [538, 677]. Condensation must cease if all of the hydroxo ligands have been reacted and no more “expendable” groups remain [538]. Charged oligomers usually do not grow to contain more than about 20 metal species; they are limited by the decreasing nucleophilic power of the hydroxide group (measured as partial charge) [675, 677], and corresponding decrease in cation electrophilicity [538]. On this basis LIVAGE [675] stated that “polycations cannot be considered as secondary building units [...] for the formation of solid phases”; yet he also stated that “inert species such as Al13 could withstand neutralisation and can actually be found in the amorphous gel”. Polymerisation and condensation or precipitation is thus favoured around the point of zero charge of the system, where repulsion between precursors is small [676] (although the oxolation rate passes through a minimum here [538, 677]). Solid phases can only be precipitated from neutral precursors — either due to hydrolysis (and olation or oxolation) to a neutral ‘aquo-oxo-hydroxo’ complex, or through the addition of counterions to charged complexes to form a neutral salt — to avoid electrostatic repulsion [538, 675, 677]. While the formation of compact oligomers has been emphasised, geometric constraints can lead to more open structures, especially when the reaction rate is slow [677] *.

R1▪2▪4▪3

Precipitation

BUYANOV & KRIVORUCHKO † developed a detailed theory regarding the mechanism of precipitation and crystallisation of slightly soluble metal oxides and hydroxides, especially for trivalent species [221]. A key feature of this work is its ability to describe the processes for a number of metal species, including Al, Fe, and Cr [cf. 221].

*

Fractal aggregate theory would rather predict open structures to be favoured by rapid (diffusion-limited) reaction (see §R1▪5▪5). Condensation is, in any case, contingent upon hydrolysis. LIVAGE, HENRY & SANCHEZ [677] gave the following “good rule of thumb” for transition metal alkoxides: Hydrolysis rate Slow Fast Fast Slow Condensation rate Slow Slow Fast Fast Result Colloids/sols Polymeric gels Colloidal gel or Controlled gelatinous precipitate precipitation Analogously, for the ferric nitrate system, at low alkali additions (i.e. hydrolysis ratios) polymer formation is slow and crystalline precipitate predominantly forms from low-molecular-mass species, while at greater hydrolysis ratios there is rapid formation of large polycations (and corresponding decrease in pH) which don’t readily convert to crystalline phases [573]. KNIGHT & SYLVA [573] suggest that addition of a mononuclear entity such as Fe(OH)2+ to a crystal face would be favoured over addition of an oligomer, because the monomer’s ligands would more readily rearrange to the required geometry.

†

Р. А. БУЯНОВ & О. П. КРИВОРУЧКО.

658



To elucidate their theory BUYANOV & KRIVORUCHKO also coined a number of terms describing the phases formed [221]. These are presented in sequence below [221]: P o l y n u c l e a r h y d r o c o m p l e x e s ( P H C ’ s ) . PHC’s are the polycations 1. formed by progressive hydrolysis from m o n o m e r to d i m e r to oligomer and eventually to PP (see point 2). PHC composition depends on cation concentration and anion species, pH, et cetera. Equilibrium in the formation of PHC’s is generally approached relatively slowly, so that the method of alkali addition is not important. ‘ D e a d l o c k ’ P H C ’ s . ‘Deadlock’ PHC’s are the PHC’s from which the a. PP’s are formed, and each has a distinct structure *. For aluminium two ‘deadlock’ PHC’s were identified: Al13O4(OH)24(H2O)127+ (1.6nm) and Al7O4(OH)24(H2O)127+ (1.2nm) †. For iron a double polymer molecule forms. 2. P r i m a r y p a r t i c l e s ( P P ’ s ) . PP’s form directly from the ‘deadlock’ PHC’s, and i n h e r i t their structure. Hence the precipitate contains as many types of amorphous hydroxides as there were ‘deadlock’ PHC’s present. They are of fairly constant size, viz. >1 to 6nm (e.g. 4nm for Fe), regardless of pH (4 to 13), temperature (10 to 100°C), or reagent concentration. F r e s h P P ’ s . These have a “polymeric structure with coordinative type a. bonds”, and molecular mass of order 105g/mol. The fresh PP’s are i s o t r o p i c and interact through VAN DER WAALS attraction and hydrogen bonding, and thus tend to form aggregates — variously disordered or densely packed. These are termed a g g r e g a t e s o f P P ’ s ( A P P ’ s ) . After precipitation the polymeric structures become unstable and undergo spontaneous evolution, or ‘ageing’, consisting of dehydration, oxolation, and structural rearrangement inside the volume of each PP, and finally formation of a monocrystal. N u c l e i . Nuclei are “embryonic” crystals formed from the PP’s. Unlike b. the fresh PP’s they are a n i s o t r o p i c , and “capable of providing specific directed interactions” with CC’s (see point c). Although they predominantly have the crystal structure of the CC’s, residues of highly labile polymeric structure are still present. Crystallisation centres (CC’s). CC’s are formed when PP c. crystallisation is “practically” complete. Due to their low solubilities, the CC’s are “almost inert towards each other unless they contact tightly for a long time”. S e c o n d a r y c r y s t a l s ( S C ’ s ) . SC’s form from aligned growth of nuclei with 3. CC’s, which in turn accrete to growing SC’s. Fresh PP’s serve solely as a source of nuclei. This crystallisation of amorphous precipitates is described as an *

Compare to the stable oligomeric structures identified by MEAKIN & DJORDJEVIĆ [732] and the favoured and unfavoured (for kinetic, steric and thermodynamic reasons) oligomeric structures identified by MEAKIN & MIYAZIMA [736] in modelling aggregation in systems with two types of monomer.

†

Recent research suggests that an octameric Al8 species — with a formula something like Al8(OH)20(H2O)x4+ [146], Al8O(OH)148+ or [Al8(OH)14(H2O)18](SO4)5·16H2O [cf. 231] — may be more relevant than Al7 species [892]. Indeed it has been suggested that a certain form of Al8 polycation (which has a structure like that of g i b b s i t e ) may have unusual reactive properties [see 231]. However the principle remains the same. It has also been suggested that a hexameric Al6 species — perhaps [Al6(H3O2)12]0, in which H3O2‒ acts as a bidentate chelating ligand — forms “a critical nucleus for bayerite or gibbsite” [466]. R1▪2 : Coagulation

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4.

“ o r i e n t e d a c c r e t i o n ” process *. Given the mechanism described, a corollary is that the PP’s preserve their individuality even in the SC, which thus forms a block mosaic. P r o d u c t . The final crystalline product forms from SC’s. The phase formed depends on the ‘inherited’ structure determined by the ‘deadlock’ PHC’s. Each ‘deadlock’ PHC ultimately gives rise to a distinct crystalline phase [cf. 892]. E.g. bayerite forms from Al13 [cf. 1100], while pseudoböhmite forms from Al7. This is termed the r u l e o f “ h e r e d i t a b i l i t y ” .

Hereditability is similar to the concept of a “memory effect” used by SAKHAROV et alia [890]. It is the concept of hereditability that most strongly differentiates this model from ‘conventional’ descriptions [e.g. 325, 767]. MURPHY, POSNER & QUIRK [767] showed experimentally that “ferric-hydroxy polycations” (molecular mass ~ 104g/mol) formed in the presence of one anion (nitrate) could maintain their properties if separated after ~1 day and exposed to another anion (chloride). Significant proportions of fresher “polycations”, 2h old, underwent a transformation upon anion replacement [767]. Although this could lead ultimately to a different solid phase, it does not contradict the theory of BUYANOV & KRIVORUCHKO, as even thermodynamically stable solid phases may transform if the environmental conditions are altered. Support is found in very recent work by SARPOLA et alia [892] on alum hydrolysis: [...] resemblance between the observed aqueous polyions and the elementary units of typical natural aluminium compounds proved to be astonishingly high.

[see also 146]. JOLIVET [538] drew a distinction between very hydrated and chemically inert polycations (e.g. [Al13O4(OH)24(H2O)12]7+), which form in the early stages of hydrolysis and condensation and can maintain their structure during charge cancellation, and transient polycations, whose structure changes upon slow alkalinisation when the solid (hydroxide) is able to form. In the context of the foregoing model, this corresponds to the difference between regular PHC’s and ‘deadlock’ PHC’s. Inert polycations aggregate to form poorly structured † solids — rather than acting as a monomer “reservoir” through a dissolution–recrystallisation process [538]. In contrast, the labile polycations are “not usually the nuclei from which the solid forms”, and may bear “no structural relationship” to the solid phase [538]. The presence of organic acids or NOM in general could seriously disrupt this sequence, resulting in entirely different atomic arrangements [707].

*

A dissolution–re-precipitation mechanism was ruled out after contrasting the low solubilities with the relatively rapid crystallisation observed, and realising that dissolution would destroy PHC structure, precluding structure hereditability [221]. (A dissolution–re-precipitation mechanism was suggested by LIVAGE [675] for the formation of bayerite.)

†

Polycations may sometimes form structural templates for nuclei which condense directly to stable, structured phases — especially upon thermolysis, and perhaps also upon dissolution–recrystallisation [538].

660



R1▪2▪4▪4

OSTWALD’s rule of stages

For a number of metals, including aluminium and iron(III), there are several solid phases that could form upon neutralisation, depending upon both thermodynamics and kinetics. In competition between the formation of a crystalline or a poorly ordered (or amorphous) phase, STRANSKI & TOTOMANOV [981] showed that OSTWALD’s ‘rule of stages’ u s u a l l y applies [538], and thus the less ordered, more soluble phase precipitates first [280, 982] [cf. 841]. The underlying reason for this is the inverse relationship between solid–solution interfacial tension and solubility [538], and correspondingly the greater molecular-scale surface roughness (promoting nucleation) of less-ordered, less-stable phases [982]. Further extensions to the theory have been made in more recent times [see 982]. The level of s u p e r s a t u r a t i o n , which ‘drives’ the precipitation, is often a critical factor, with low supersaturation tending to promote equilibrium processes [280, 982] [see also 146, 818, 895]. CORNELL & SCHWERTMANN [280] describe three categories of crystal nucleation and growth, with application especially to ferric systems [cf. 982]: At l o w s u p e r s a t u r a t i o n * nucleation/growth proceeds by dislocations 1. (BURTON–CABRERA–FRANK (BCF) mechanism [cf. 982]). A smooth surface is obtained with a high energy barrier to nucleation, leading to a low growth rate. At h i g h s u p e r s a t u r a t i o n there is “abundant” nucleation on the molecularly 2. rough surface that develops, and so diffusion is the rate-controlling step. At i n t e r m e d i a t e s u p e r s a t u r a t i o n a relatively smooth interface is still 3. obtained. The mechanism of formation and growth is two-dimensional nucleation and spreading. Although nucleation here is significantly more likely than was the case at low supersaturation, nucleation remains the rate-limiting step. The overall crystal growth rate is intermediate. It is notable that as precipitation proceeds, the level of (super)saturation must decrease [982].

R1▪2▪4▪5

OSTWALD ripening

A final aspect of precipitation that is of general interest is the development of particle size. Aside from simple particle growth by deposition in the initial precipitation, the most famous manifestation of this is OSTWALD ripening. This states that solubility is enhanced where the curvature (convexity) of the solid is higher. As a consequence of this, larger particles are predicted to grow at the expense of smaller particles (which may be consumed). This localised solubility enhancement is usually only appreciable for crystals smaller than about 1μm [773]. OSTWALD ripening can be modelled by the GIBBS–THOMSON (or GIBBS–KELVIN, or OSTWALD– FREUNDLICH) equation, which is analogous to the KELVIN (or THOMSON–FREUNDLICH) equation for evaporation from liquid to vapour [538, 773, 977] [cf. 188, 550, 571, 849, 1044]. The driving force for OSTWALD ripening is the reduction of surface energy in order to minimise the free energy [see 344, 688] of the s y s t e m [678, 773, 805]. This implies that the total surface area must be minimised, assuming the specific surface energy to be constant [678, 688, 773] — though, in fact, it depends upon the chemical composition of the solid–

*

The supersaturation can be described in terms of the chemical potential difference, Δμ / kB T [280]. R1▪2 : Coagulation

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solution interface * [536, 537, 538, 1067]. (Moreover, the specific surface energy thus can also differ between crystallographic faces [see 537, 538], so that spherical particles are not necessarily favoured!) Indeed, OSTWALD ripening relies on another assumption, namely that the specific surface energy is positive [1044] (or, more precisely, significantly more than zero) [538, 805, 977]. This usually holds, but zero and even negative specific surface energies can be reached at high ionic strength and far from the p.z.c. of the solid [538, cf. 1044]. (This leads to a transition between regimes in which thermodynamics favours theoretically unlimited particle growth †, no growth, and particle dissolution [538, 977, 1067].) Indications of non-positive surface energy have been observed for colloidal “Fe(OH)3” [1044] [see also 325], “Al(OH)3” [977], böhmite, brucite and other (oxy)hydroxides [537, 1067] under certain circumstances. This led to the suggestion that some “oxide–gel” systems may be considered as “immobilized”, thermodynamically-stabilised dispersions [977]. With the moderate ionic strengths, pH values [cf. 538, 805, 977] and temperatures [cf. 1067] of the present work, the above assumption could seem reasonable. Yet the present work includes natural specifically-adsorbing species which may produce a thermodynamically stable dispersion [cf. 538, 805, 977].

R1▪2▪5

Aluminium

Aluminium is generally dosed in the form of aluminium sulfate solution. Aluminium sulfate is commonly known as ‘ a l u m ’ . The molecule is sometimes written with its bound water explicitly shown, Al2(SO4)3·xH2O, with x = 14 [90, 161, 827, 854], 14.3 [90, 854], 16 [90], or 18 [28] for the powder, and circa 49.6 [854] for the typical commercial stock solution used industrially, which is 4.2 to 4.4%m Al [93, 161, 668, 1085].

R1▪2▪5▪1

Hydrolysis

The aluminium ion undergoes a complex set of (reversible) hydrolysis reactions, in which coordinated water molecules are successively replaced by hydroxyl ligands, viz. [90, 675, 786] Al(H2O)63+ + H2O # Al(H2O)5OH2+ + H3O+. The sequence can be summarised as [90, 466, 675, 786]: Al(H2O)63+ # Al(OH)(H2O)52+ # Al(OH)2(H2O)4+ # Al(OH)3(H2O)30 , Al(OH)3(H2O)0 # Al(OH)4‒ . Although Al(III) has sometimes been assumed to form only octahedral complexes [e.g. 90, 118], it transforms to a tetrahedral complex at pH ~ 6 [675] [cf. 538]. The tetrahedral aluminate ion would not be expected to behave in the same way as octahedrally coordinated species [786]. The existence of Al(H2O)(OH)52‒ or Al(OH)63‒ is not supported ‡.

*

Thus major factors are potential-determining ions (or the pH) [977], specifically-adsorbing ions, [982] and ionic strength [538].

†

In practice particle size may be k i n e t i c a l l y stable (e.g. for reduced solubility [1067]), or particle growth may be limited simply through consumption of precursors [538, 977].

‡

However BURGESS [208] presumes the existence of not only Al(OH)63‒, but even Al(OH)74‒ (and [AlO2]‒ [see also 982]) under alkaline conditions.

662



For simplicity, the co-ordinated water molecules are almost always omitted, and the hydroxonium ion (H3O+) is often represented by the hydron ion (H+) — cf. §S21. In such reactions, it may be recalled that the ligand field of the hydroxide ion is very slightly weaker than that of water, implying that it will have a slightly destabilising effect in reactions such as depicted above (moving from left to right) [118]. Following from the change in speciation of dissolved Al as pH increases, it is anticipated that at high pH supersaturation of the aluminate ion, Al(OH)4‒, will be greater and hydrolysis will be faster [895]. Al(OH)2+ forms at pH values greater than 3, although it “becomes important only in dilute [< 0.001 molal] solutions” [118]. Al3+ is found at pH ( 3 [675]. NORDSTROM & MAY [786] surveyed the literature prior to 1996 and came up with recommended equilibrium constants for the progressive hydrolysis of the aluminium ion, based on a total of 60 published values at 298.15K in the limit of zero ionic strength, I. Their recommendations are as follows, with error estimates in parentheses [662, 786]. ΔH°298 = 55kJ/mol p∗β1 = 5.00 (±0.04) Al3+ + H2O # Al(OH)2+ + H+ ΔH°298 = 123kJ/mol p∗β2 = 10.1 Al3+ + 2H2O # Al(OH)2+ + 2H+ Al3+ + 3H2O # Al(OH)30 + 3H+ ΔH°298 = 176kJ/mol p∗β3 = 16.8 3+ ‒ + ΔH°298 = 181kJ/mol p∗β4 = 22.99 (±0.62) Al + 4H2O # Al(OH)4 + 4H The operator “p” represents the negative decimal logarithm. The ∗βn represent the c u m u l a t i v e equilibrium-formation constants, in the notation of SILLÉN & MARTELL [see 482], and may be related to the equilibrium constants, Ki, by p∗βn = ∑ p∗Ki [786]. The prefixed asterisk denotes addition of a protonated ligand with elimination of the proton [482]. Although equilibrium constants are strictly defined in terms of activities, thereby incorporating variation in activity coefficients [see e.g. 181], molar [e.g. 482] or molal [e.g. 994] concentrations are typically used for convenience. ∗ β4 is typically obtained from solubility studies, although reported values of the solubility product constant for gibbsite vary over three orders of magnitude [786]. The p∗βi tend to decrease as temperature increases: in the range 0 to 50°C the decrease is approximately 11% per 25°C (p∗β4) to 15% per 25°C (p∗β1 and p∗β2) [see 786]. According to EDZWALD & TOBIASON [335], the ‘average’ charge of hydrolysed aluminium species increases as water temperature is decreased, reducing the stoichiometric coagulant demand (for charge neutralisation) — although problems with residual aluminium and particles in the treated water may arise. The pH of maximum precipitation of aluminium is generally increased by stronglycomplexing ligands (e.g. F‒) and decreased by polyvalent anions (e.g. SO42‒) with respect to more weakly complexing, univalent anions (e.g. Cl‒, NO3‒, ClO4‒) [146]. NORDSTROM & MAY [786] also recommended values for the corresponding sulfato complexes: ΔH°298 = 9.6kJ/mol pβ1 = ‒3.5 (±0.5) Al3+ + SO42‒ # AlSO4+ 3+ 2‒ ‒ ΔH°298 = 13kJ/mol pβ2 = ‒5.0 (±0.5) Al + 2SO4 # Al(SO4)2 Concentrations of aluminium encountered in water treatment are expected to be ( 10‒3M, with Al3+ making up no more than about 10‒6M [90], so very little Al(SO4)2‒ would be formed. The sulfate ion can also be stably incorporated into a precipitate [155]. R1▪2 : Coagulation

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It is reasonable to assume equilibrium for most mononuclear aluminium species reactions [978], “especially ionic reactions or simple electrostatic reactions such as ion pairing”, as their reaction rates are “extremely” high [786] [300]. In fact, the rate of aluminium hydrolysis is “nearly as fast as that for the hydrolysis of water” [786]. The system chemistry is controlled by these reactions at low Al concentrations (e.g. [Al] < 10‒4M) and hydrolysis ratios ([OH‒]added/[Al] < 0.5) [978]. However, some reactions, such as inner-sphere complexation, are too slow to be modelled as equilibrium reactions on practical timescales [786, 893, 978]. Modelling is also complicated by the presence of ‘impurity’ ions and particulates [e.g. 367].

R1▪2▪5▪2

Polynuclear aluminium species At each stage in the hydrolysis–precipitation process one would like to know the composition and structure of the aluminium-bearing components. [...] this would appear to be an impossible task. The [...] task [...], however, is not as hopeless as it would seem to be. — STOL, VAN HELDEN & DE BRUYN (1976) [978]

BERTSCH & PARKER (1996) [146] grouped the polymeric aluminium species with “convincing experimental support” for their existence into three categories: Al2(OH)2(H2O)84+ [cf. 466, 538, 675], Al2(OH)5(H2O)x+, Al3(OH)8(H2O)x+, 1. Al3(OH)4(H2O)y5+ (y = 9 (cyclic) [538, 675], 10 [466] or 12 [538]), and Al8(OH)20(H2O)x4+. (The stable cyclic trimer, Al3(OH)4(H2O)95+, proposed in §R1▪2▪4▪2 would yield a number of derivatives, as in §R1▪2▪5▪2(a).) Those of the “core + links” or “gibbsite fragment” model, namely species from 2. Al6(OH)12(H2O)126+ [see also 148, 466, 1100] through to Al54(OH)144(H2O)3618+. These species are considered to be made up of small polynuclear units (single or double hexameric rings) that are linked together to form large polynuclear structures “having the basic structural features of the trihydroxide mineral phases, such as gibbsite” [see also 148, 300]. These polynuclear units are believed to coalesce upon ageing via deprotonation of edge-group water molecules, forming double hydroxide bridges. BERTSCH & PARKER [146] present several criticisms of this model. AlO4Al12(OH)24(H2O)127+ and the larger condensation products thereof (usually 3. combined through other species such as the dimer or trimer). The Al13 species comprises a tetrahedrally co-ordinated aluminium (AlO4) surrounded, in a “cagelike” KEGGIN structure *, by 12 octahedrally co-ordinated aluminium atoms [146, 231, 466, 1100]. It is suggested that these slowly † transform into the more

*

Theoretically this can manifest as one of five BAKER–FIGGIS isomers, although only the ε and δ forms have been synthesised in isolation and structurally characterised [231].

†

For the nucleation of polynuclear aluminium species, the time to reach s t e a d y s t a t e at 25°C may be on the order of weeks to years [146].

664



thermodynamically stable gibbsite (or bayerite), leading them to be described as “metastable” [146]. Significant formation of Al2(OH)2(H2O)84+ upon alkalinisation has been disputed [197, 466, 538, 675]. Other suggestions have been briefly reviewed by BOTTERO et alia [181]. Subsequent research identified and established a structure for the Al30 polycation with formula Al2O8Al28(OH)56(H2O)2618+ [231, cf. 893]. This is essentially a dimer of Al13 (with four bridging AlO6 octahedra) [893, 894], and has a length of approximately 2nm [231]. Still more recent work identified e.g. Al26O15(OH)48Cl44‒ in solution at [Al] = 0.100 and 0.010M, likewise proposed to comprise two Al13 units [894]. While these may be the best-known polycation species, other as-yet uncharacterised and unidentified species certainly exist [231]. Part of the reason for this is widespread reliance upon nuclear magnetic resonance (NMR), which can only isolate complexes containing tetrahedral sites [231] [cf. 148], and solid-state methods such as XRD [893] [see also 197, 677]. BAES & MESMER [118] indicated support in 1976 for the existence of Al2(OH)33+. However they stated that species such as the dimer and trimer were unimportant at 25°C [118]. Despite the ability of aluminium sulfate to form polymeric products in water, dissolution of aluminium sulfate precipitates in acid has been reported to produce only monomeric species [430] (see also PARKER & BERTSCH [818]). According to BAES & MESMER [118], mononuclear species are “the only significant hydrolysis products” in saturated solutions at pH values greater than 3.5. The co-ordination number of the aqueous complex can lead to the formation of different oligomers and ultimately (cf. §R1▪2▪4▪3) the formation of different solid phases [466]. The neutral [Al(OH)3(H2O)x]0 precursor can form with x = 1 or x = 3 [466]. The tetrahedral complex is associated with the aluminate ion found at high pH *, and is expected to rapidly form octahedral oligomers by addition reaction, viz. trimers, tetramers, and hexamers [466]. The hexamer is identified as “a critical nucleus for bayerite or gibbsite”, while the smaller oligomers “could act as critical nuclei for oxy-hydroxide phases” † [466]. The octahedral complex, written as [Al(H3O2)3]0, was proposed to firstly condense to cyclic hexamers, [Al6(H3O2)12]0, with bridging by twelve H3O2‒ groups, which could aggregate and lose water (to form stronger μ2-OH bridges [see also 671]), tending to lead to gibbsite or bayerite [466]. (At higher temperature these hexamers may be destabilised in favour of cyclic [Al3(OH)9(H2O)4]0 trimers, which could form a skewed [Al4O(OH)10(H2O)5]0 tetramer, and thence böhmite [466].) Recent research [892, 893, 894] using electrospray ionisation mass spectrometry confirms that a vast variety of polymeric aluminium species exist i n s o l u t i o n , and these are present in varying proportions depending especially upon the total aluminium concentration and the

*

At very high pH the polyanion [Al4(OH)16]4‒ is reported to form [538].

†

In theory diaspore and böhmite [cf. 466], but in practice perhaps pseudoböhmite. R1▪2 : Coagulation

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D. I. VERRELLI

solution pH. Reported species cover a spectrum from 1 to 32 Al atoms per species, with charges from 4‒ to 3+ [893, 894]. With regard to the pH, prior to the addition of alkali, only univalent aluminium species were observed to be present (for the chloride system *), and no species larger than Al9 (chloride; [Al] = 0.1M) [894] or Al13 (sulfate; [Al] = 0.01M) were identified [892]. Subsequent to partial neutralisation, larger polycations were detected [892] — identified as Al10, Al11, Al13, Al14, Al15 and Al26 species in the chloride system [894]. Increases in concentration yielded more of the larger Al species [894]. Aside from Al13, important larger polycations were identified as Al14 species for the chloride system [894] and Al8 for the sulfate system [892]. The structures of these species were inferred to variously contain olation (Al‒(OH)2‒Al) linkages and unhydrolysed oxolation (Al‒O‒Al) linkages † [892]. Generally olation bridging is more common in Al polycations [e.g. 536, 539]. Increasing the sample ageing time from 4h to 14 days resulted in increases in the total occurrence of hydrolysed aluminium complexes [893], with slight changes in the distribution of species, including a tendency for the trimer to become preponderant rather than the dimer [894]. It has been found that multivalent complexes tend to occur in a narrow pH range immediately below (under acid conditions) the pH at which precipitation occurs [894]. Recent appreciation of the broad and complicated speciation of aluminium prompted BI et alia [148] to propose a “continuous” model that ‘unifies’ the core–links and KEGGIN models. They suggest that the former can explain instantaneous, reversible transformations, while the latter requires ageing or “self-assembly” and yields a “metastable” species [148]. The latter is favoured at high sulfate concentrations, elevated temperatures, and slow neutralisation rates [148]. MATIJEVIĆ has illustrated the importance of highly charged polymeric species, stating that such species at concentrations as low as 10‒8M, making up perhaps 0.1% of an already dilute system, can achieve coagulation and would in that regard thus be equivalent to a potassium ion concentration of around 0.6M [155, 359]. It is not practically possible to obtain even equilibrium constants for all of the relevant polynuclear hydrolysis products (see below) [197, 538, 892]. The combination of slow kinetics, incomplete knowledge of the equilibrium constants, and uncertainties regarding the solid phase to be formed [see also 499] greatly limit the usefulness of equilibrium modelling of oligomeric aluminium chemistry [892]. The speciation also depends upon temperature [1100] and mixing protocol [148].

*

The sulfate system yields consistent results: only univalent cations were detected, and the multivalent anions are likely artefacts of the analysis procedure [892]. Al(H2O)63+ must have been present, but could not be detected as its mass/charge ratio was below the instrument detection limit [892].

†

It is unclear whether associated sulfate entities act as additional bridging ligands, as cluster anions, or as undissociated alum [892].

666



R1▪2▪5▪2(a)

Tridecameric aluminium:

Al13

The “best known” of the polymeric products is so-called “Al13”, with the formula AlO4Al12(OH)24(H2O)127+ * [146, 231, 326, 466, 538, 675]. Alternatively Al13(OH)345+ [90], et cetera †. Recent research [893, 894] into the species in solution for [AlCl3] from 0.001 to 0.100M observed Al13 species of charge variously 2‒ up to 3+, with assorted combinations of O, OH, Cl and H2O ligands bound to the species. The same research group [892] recently reported early results of a similar investigation for [Al2(SO4)3] = 0.005M at pH 3.76 ‡, which detected Al13 as only anionic complexes (including two to four sulfates) of charge 2‒. In both cases the detection of anionic forms may be an artefact of the analysis procedure, which promotes pairing of otherwise ‘free’ counter anions upon evaporation [892]. Polycations such as Al13 arise from the formation of hydroxo bridges between metal ions [183]. Trimeric cations are conventionally considered precursors [892], although other pathways have been suggested [231]. Estimates of the size of the Al13 polycation range from 2.5 § [103] [cf. 148] or 2nm [104] down to approximately 1.6 [221] or 1.4nm [183]. The Al13 polycation has been demonstrated to be the primary polynuclear species in “most” Al solutions to which base has been added (but never without [146]), and is a “very efficient scavenger of anions in physicochemical water treatment processes” [146]. Research has indicated that “significant” quantities of Al13 form in partially-neutralised solutions with total aluminium concentrations as low as 10‒5M, and that strong and weak bases are equally effective in generating Al13 [146, 818]. This range includes the conditions typically encountered in natural waters and in drinking water treatment ** [818]. WANG, WANG & TZOU [1100] supported AKITT’s model of Al13 formation, which relies on ‘nucleation’ by Al(OH)4‒ species. Under acidic conditions Al(OH)4‒ species will not normally survive long enough for significant Al13 formation to occur; however, if significant amounts of colloidal aluminium are present, due to local concentration effects, then these may ‘shield’ Al(OH)4‒ species, promoting Al13 formation [1100]. At the same time, dissolution of colloidal aluminium leads to the formation of monomeric Al (cf. §R1▪2▪5▪3(a)), oligomers and, specifically, Al6 [1100]. Evidently Al6 formation should be favoured over Al13 at lower pH, i.e. at low hydrolysis ratios, where the dissolution of colloidal aluminium is greater [1100]. There appears to be more evidence in favour of formation from the stable cyclic trimer, Al3(OH)4(H2O)95+, however. The μ3-OH group is readily deprotonated by a strongly

*

BAES & MESMER [118] describe this as “equivalent to a 13,32 species” (24 + 2 × 4 = 32). PARKER & BERTSCH [818] gave a more inclusive version of the formula as AlO4Al12(OH)(24 + n)(H2O)(12 ‒ n)(7 ‒ n)+.

†

The charge on the tridecameric polymer species “has been reported to range from 3+ to 7+” [146] [e.g. 181]. The charge tends to be reduced considerably as pH is increased, which would reduce repulsive forces between the polycations and favour aggregation [146]. BI et alia [148] associated a charge of 7+ with the KEGGIN form and 9+ with a tridecameric core–links species, although all lesser charges down to 0 were deemed theoretically possible.

‡

This was the pH without neutralisation; only minor differences were noted after slight neutralisation to pH 3.95 [892].

§

Smaller values (of order 1.8nm) may be relevant at high ionic strength due to double layer compression [103]. Even this seems large compared with more recent size estimates of several Al polycations [see 183, 231, 1100].

**

Concentrations of aluminium expected to be encountered in water treatment are ( 10‒3M [90]. R1▪2 : Coagulation

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D. I. VERRELLI

polarising metal such as Al to form Al3O(OH)3(H2O)94+ [538, 675, 677] *. Under mild conditions (hydrolysis ratio < 2.6) this would hydrolyse to Al3O(OH)6(H2O)6+, and four of these can bond to a single aquo ion to yield Al13O4(OH)24(H2O)127+ [466, 538, 675]. It may be argued that the precipitate is of more direct relevance to drinking water treatment operations than the tridecamer. However, it is pertinent that, for a given ratio of added base to total aluminium, the proportion of mononuclear aluminium is “remarkably consistent [...] despite wide variation in total Al and synthesis conditions” [818]. That is, there is a ‘competition’ between formation of Al13 and formation of solid trihydroxides — either as parallel reactions or as series reactions [818]. Above an [OH‒]added/[Al] molar ratio of unity, the proportion of the total aluminium present as Al13 is predicted to be more than about 32% †, with less than about 53% present as mononuclear species [146]. It is important to recognise that the concentration of aluminium in the double layer of, say, a clay particle could be “several orders of magnitude” greater than in solution, which is presumed to make polynucleation at the mineral–water interface a more favourable process [146]. Theoretical mononuclear aluminium yield varies linearly from 100% of the total aluminium at [OH‒]added/[Al] ≤ 0 down to 0% at [OH‒]added/[Al] ≥ 2.46, and this closely matches experimental results [146]. Theoretical Al13 yield varies linearly from 0% at [OH‒]added/[Al] ≤ 0 up to 100% at [OH‒]added/[Al] ≥ 2.46, although actual yields can be much less than the theoretical values [146, see also 1100]. At [OH ‒]added/[Al] T 2.5 the Al13 aggregates [146, 1100]. (If aluminium concentrations are decreased, to levels of order 10‒5M, much greater proportions of mononuclear to polynuclear species are found [978].) Al13 species formation has been described in terms of interfacial disequilibrium and also in terms of thermodynamic ‘supersaturation’ and equilibrium [146]. BERTSCH & PARKER [146] present observations in favour of the interfacial disequilibrium model, whereby the Al13 polycation forms exclusively from the precursor Al(OH)4‒. Al(OH)4‒ is the favoured mononuclear species at the relatively high pH region at the boundary between an acidic aluminium solution and an alkaline solution (or solid) [818]. It may also be noted that the Al in Al(OH)4‒ is t e t r a h e d r a l l y c o - o r d i n a t e d , just as the Al in the central AlO4 unit of the tridecamer [145]. For the purposes of illustration, and at low concentrations, the equilibrium constant concept (e.g. BAES & MESMER [118]) will suffice: 13Al3+ + 28H2O # Al13O4(OH)247+ + 32H+ ΔH°298 = 1167kJ/mol pK = 98.7

*

However μ3-OH apparently persists in diaspore [671].

†

This is the relevant value at a total aluminium concentration of 10‒4M. As the total aluminium concentration increases, the proportion present as Al13 approaches 40% when [OH‒]added/[Al] = 1 [146], while the proportion presumably decreases (approaching zero) for very low total aluminium concentrations. Tridecamer yields of ~95% are reported at high values of both [Al] and [OH‒]added/[Al] (e.g. 0.1M and 2.5, respectively) [146].

668



The order of addition of aluminium ions and base affects the Al13 yield [146, 818]: • Adding base to an (acidic) aluminium solution (“forward”) tends to produce the most Al13 species. • Adding aluminium to an (initially) basic solution (“reverse”) tends to produce the least Al13 species. In this case the pH is initially high, and thus the solution passes through the pH of minimum gibbsite solubility (i.e. maximum precipitation, ~6.3) as the acidic aluminium solution is added. • Simultaneous (dropwise, unstirred) addition of aluminium and base to water resulted in intermediate proportions of Al13 species. In this regime the pH is stays fairly constant, and close to its final value. In summary [818]: [...] as compared to the forward method, both the reverse and simultaneous methods lead to conditions of greater supersaturation with respect to gibbsite or other solid phases during much (or all) of the reaction period.

For the “reverse” protocol the fractional Al13 yield depends on the rate of base addition, being maximal at intermediate rates of base addition [146]. Unfortunately, the rates of base addition are not well quantified, and it is unclear whether this is the best measure of ‘time to distribute the base throughout the volume’ [146]. At very low rates of base addition — e.g. reaction times on the order of w e e k s [818] — the proportion of aluminium as Al13 is generally low [146]. BERTSCH [145] showed that in this case the yield of Al13 can be enhanced by increasing the mixing efficacy. Quantitative results that illustrate the above findings were presented by PARKER & BERTSCH [818]. PARKER & BERTSCH [818] also demonstrated the formation of Al13 upon addition of solid MgO or CaCO3 powder, as a model of the ‘liming’ of natural surface waters. They found that “the faster-dissolving CaCO3 appeared to actually yield less tridecamer than MgO” under comparable conditions [818]. Aggregation of polycations such as Al13 can occur by sharing of hydroxo bridges [183]. Such aggregation can be controlled by varying the hydrolysis ratio: for [OH‒]added/[Al] = 2, Al13 species are isolated, while dosing alkali such that [OH‒]added/[Al] = 2.5 leads to formation of linear aggregates, and dosing further alkali yields more compact aggregates [183]. Anions such as SO42‒ have been shown to cause aggregation of polynuclear aluminium species due to [146]: • anion inclusion in the resulting solid phase; or • supersaturation and precipitation of solid phases other than Al(OH)3; or • physical aggregation caused by a reduction in electrostatic repulsion between aluminium polynuclear centres. When the anions are added prior to neutralisation, complexation inhibits aluminium hydrolysis–precipitation reactions, while anion addition to (partially) neutralised aluminium solutions causes rapid aggregation and precipitation of polynuclear aluminium species [146].


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The aggregates described above form due to bridging of ‘whole’ Al13 units by anions, and are characterised as outer-sphere associations [146]. In contrast, the Al13 condensation products described are formed by inner-sphere associations in which one of the Al13 units ‘loses’ * an octahedrally co-ordinated aluminium, the ‘gap’ being filled by ‘sharing’ with the other Al13 unit [146]. Tridecameric aluminium has been produced in solutions prepared with AlCl3 [893, 894], Al(NO)3, and Al(ClO4)3 [145]. Tridecameric aluminium formation is hindered by the presence of organic species (at pH 3.5 to 6.5), especially those that are able to form chelates and perhaps bridges (e.g. oxalate (ethanedioate, ‒O‒CO‒CO‒O‒)) [see also 536, 538, 539, 675], as they compete with OH‒ ions for hydrolysis sites, which would otherwise form hydroxo bonds [183, 707]. The presence of organic species thus favours the formation of oligomers such as dimers and trimers [183, 707]. It has also been reported that organic acids can even ‘depolymerise’ Al13 through a solidphase transformation [707, 708].

R1▪2▪5▪3

Solid aluminium phases

There are four p o l y m o r p h s † of Al(OH)3 (s) with similar (but not identical) thermodynamic properties [463]. They are [118, 463]: • α-Al(OH)3 ‡ ( g i b b s i t e §) . This is the most common polymorph [463], and is the most stable phase at room temperature [118, 231, 313, 895, 1100] — it is favoured by a GIBBS energy difference of only about 6 to 11kJ/mol over bayerite [313]. It can be formed from alkaline solution [118]. The minimum solubility of gibbsite is about 10‒6.5M (as Al) at approximately neutral pH [118]. It forms triclinic and monoclinic crystals that may attain quite large sizes (up to 1mm) [504]. However particle sizes between 0.5 and 200μm are more common [749]. Smaller crystals are platy or prismoid [e.g. 1118], while the larger particles “appear as agglomerates of tabular and prismatic crystals” [749]. Gibbsite is built up in a layered structure, denoted ABBA, with bonding between AA and BB layers based on polarisation of the hydroxyl anions by proximal aluminium cations [463]. Each layer consists of a stacking of AlO6 octahedra sharing one edge [313]. • γ-Al(OH)3 ( b a y e r i t e ) . This is the second crystalline form of aluminium that commonly occurs, and can also be formed from alkaline solution [118]. Its formation is

*

I.e. it condenses out, forming a mononuclear aluminium species [146].

†

The polymorphism of Al(OH)3 phases is attributed to “differences in stacking of the Al(OH)6 octahedra” [463], and specifically to differences in the stacking of the olation (Al‒(OH)2‒Al) bridges — described as OH‒ “bilayers” — of each sheet perpendicular to the crystallographic c-axis [978].

‡

The labelling of the Al(OH)3 polymorphs by various researchers is not consistent. HUDSON et alia [504] recommend labelling bayerite as α-Al(OH)3, because it is the most densely packed, and the cubically packed gibbsite as γ-Al(OH)3. However this logic was followed in a minority of publications reviewed [exceptions are 370, 616], and the nomenclature used in the body of the text appears to be traditional. βAl(OH)3 is also occasionally used to refer to bayerite [749, 1100].

§

Historically also called “hydrargillite” [504, 675, 1109, cf. 1150].

670



favoured by faster precipitation rates [940]. Bayerite has a similar layered organisation to gibbsite, except in approximately a hexagonal close-packed arrangement [749]. • β-Al(OH)3 ( n o r d s t r a n d i t e ) . This “can be considered as a bayerite crystal with a distorted crystal structure because of the substitution of aluminium ions by other ions” [367]. • Al(OH)3 ( d o y l e i t e ) . A rare triclinic form, inherently unstable at ambient temperature and pressure [265]. All four have a layered structure, but whereas the octahedral structures in gibbsite stack alternately, denoted ABBA, the other three polymorphs have the ‘upright’ stacking ABAB [265]. At higher temperatures (about 102°C under equilibrium water vapour pressure [504]) two dehydrated forms become important [118]: • α-AlOOH * ( d i a s p o r e ) . [463, 675] This is the thermodynamically stable polymorph — it is favoured by a GIBBS energy difference of only about 4 to 9kJ/mol over böhmite [313, 504]. Diaspore has a paired-layer structure (symbolically: ABAB [313]) in a hexagonal close-packed arrangement [749]. • γ-AlOOH ( b ö h m i t e ) . Below about 300°C this polymorph will generally form (first) in preference to diaspore [504, 538]. Böhmite consists of layers of aluminium, hydroxyls and oxygen ions, denoted ABC, arranged in cubic packing [313, 749]. Böhmite tends to form laths below its p.z.c. (~9.2) and platelets at high pH [537]. It has been suggested that the traces of molecular water detected in well-crystallised böhmite may have been trapped † in the double hydroxyl layer, and “would behave like water condensed in a capillary and would exhibit a depressed freezing point” ‡ [121]. Further dehydration yields α-Al2O3 ( c o r u n d u m ) , the stable polymorph of Al2O3 in the presence of water [504]. This phase is stable only at high temperatures (say >500°C) [313] [cf. 1118]. DIGNE et alii [313] noted that the stability of a given phase at ambient conditions increases with increasing hydration and speculated further that stability of a given polymorph increased with decreasing O/H distances, and thus (perhaps) stronger hydrogen bonds. Other aluminium oxides and oxyhydroxides have been proposed, but without general acceptance [749]; there is also disagreement over some of the detail regarding, for example, packing of hydrogen atoms [313] or presence of adsorbed or interlamellar water and impurities in various structures [749]. Aside from the above crystalline forms, paracrystalline p s e u d o b ö h m i t e and truly a m o r p h o u s aluminium (oxy)hydroxides are of special interest, because they are often formed. The existence of “poorly crystalline bayerite” has also been suggested [1100].

*

Similarly to the footnoted discussion for gibbsite, diaspore has also been called β-AlOOH [1]; however the nomenclature used in the text, α-AlOOH, seems more usual.

†

It could not be easily removed due to the large planar dimensions of böhmite platelets [121].

‡

This is presumably an analogue of the KELVIN equation [see 849], which gives that evaporation from a concave liquid surface (as for water in a capillary) would be depressed. R1▪2 : Coagulation

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D. I. VERRELLI

According to HUDSON et alia [504]: Gelatinous hydroxides may consist of predominantly x-ray–indifferent aluminum hydroxide or pseudoboehmite.

A chemical formula for pseudoböhmite has been suggested, namely Al2O3·xH2O with 1.0 < x < 2.0 [870], which corresponds to a compound between AlOOH (as for böhmite) and a slightly more hydrous species [cf. 499], AlOOH·0.5H2O *. This is consistent with ageing experiments which indicated that x decreased from ≥2.6 to 1.9 over a timespan of order hours [223, 1150]. The species has also been reported as having a formula corresponding to x = 3, namely AlOOH·H2O [1099]. Pseudoböhmite is made up of AlOOH dioctahedral chains, along with some molecular water [121], and is described as having a “small” particle size [504]. This is similar to one model of the ferrihydrite configuration [520, 539] (see §R1▪2▪6▪3(d)), in which oligomers formed by olation are subsequently (partially) dehydrated by oxolation so that they combine to ultimately form the solid phase [see 675]. A detailed discussion of pseudoböhmite’s internal structure and composition is presented in Appendix S22. Pseudoböhmite has also been termed “gelatinous boehmite” [223, 749] and “poorly crystalline boehmite” (PCB) [312, 1099], cf. §4▪2▪1▪2(b).

R1▪2▪5▪3(a)

Solubility and stability

The solubility of gibbsite has been given as Al3+ + 3H2O # Al(OH)3 (gibbsite) + 3H+ ΔH°298 = 105kJ/mol at 298.15K and I → 0 [146, 809].

pK = ‒p∗Ks0 = 7.74

KVECH & EDWARDS [614] cited pK values of 10.72 for “amorphous Al(OH)3” and 9.06 for gibbsite at 20°C — i.e. decreasing solubility. VAN STRATEN, HOLTKAMP & DE BRUYN [982] obtained estimates equivalent to 10.9 for x-ray amorphous precipitate and 10.3 for pseudoböhmite (using p∗β4 = 22.99, p. 663).

R1▪2▪5▪3(b)

Formation and transformation

Amorphous aluminium hydroxide preferentially or even exclusively precipitates from (partially) neutralised aluminium solutions unless the pH is above about 7 to 8 or the reaction occurs at “high” temperature (say >50°C) [749, 870]. Precipitates derived from alum will also contain forms of sulfate [113]. Even after prolonged drying at 100 to 110°C, (amorphous) aluminium hydroxide gels can retain up to 5 moles of H2O per mole of Al2O3 (equivalent) [749]. At higher pH values or temperatures pseudoböhmite, böhmite or bayerite may form [870]. According to DIGNE et alii [313], gibbsite, bayerite, nordstrandite and böhmite may all be formed by aqueous precipitation of aluminium salts under appropriate conditions.

*

672

These are n o t intended as s t r u c t u r a l formulæ. Note that Al2O3·3H2O and AlOOH·1H2O would be equivalent to Al(OH)3. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


Once an apparently amorphous, gelatinous aluminium hydroxide is formed (as by addition of alkali to an aluminium salt solution), this gel will slowly become more crystalline upon ageing, with the rate increasing with hydroxide concentration (i.e. the pH) and temperature [749, 870]. According to BYE et alia [224], crystallisation of precipitates generated by reaction of aluminium salt and alkali around room temperature is very slow unless the pH is near or above the i.e.p., “when hydroxyl ions readily displace contaminating anions”. Even for a sample formed and held at 30°C and pH 7, the proportion of pseudoböhmite in the sample increases from zero to >40% within 2 days [870]. At pH 9 at the same temperature the sample composition stabilises at about 80% pseudoböhmite within 1 day [870]. The ageing temperature is only important at low or neutral values of pH [870]. Pseudoböhmite is said to form during ageing of hydroxide gels as a precursor of (crystalline) trihydroxide [504]. The mechanism of its formation may be dehydration of the amorphous gel through condensation and polymerisation reactions or “the oriented growth of particles in a needle shape” [870]. Evidence supporting alternately the former [223] and the latter, “directional growth”, mechanisms has been presented [e.g. 221, 1150]. Pseudoböhmite was found to adopt two morphologies *, with the ~3nm primary crystallites either forming long needles and fibrils or combining to form aggregates [616, 940, 1150]. Pseudoböhmite particles were reported to aggregate more than the amorphous particles [223]. Despite the aggregation and transformation to a more ordered phase, which might be expected to yield a decrease in surface area, early measurements indicated that pseudoböhmite has a greater surface area than the x-ray–amorphous aluminium phase [223]. It was suggested that this could be due to the creation of new surfaces due to fracture arising from stresses caused by internal restructuring [223]. As such, the surface area increase may be diminished or even reversed in cases where the transformation occurs more slowly [cf. 223]. Furthermore, phase-transformation involving high internal stresses leading to high surface areas ultimately promotes dissolution, so that the phase is unlikely to be stable and persist [223]. MISRA [749] suggests that the stability of pseudoböhmite is also highly dependent upon the pH, with supernatant pH values above 7 leading to the formation of crystalline trihydroxide phases, and again proceeding more rapidly at higher pH and temperature. It has been proposed that pseudoböhmite first changes to bayerite or nordstrandite (say, at pH 10), and may convert to gibbsite in the presence of sodium or potassium ions [749]. In comparison, ROČEK et alia [870] stated that pseudoböhmite transforms to bayerite above pH 9, but to böhmite in a neutral or acidic environment [870]. In any case, ageing invariably increases the crystallinity of the phase [870] †. JOLIVET, CHANÉAC & TRONC [536] drew an analogy to the transformation of ferrihydrite (§R1▪2▪6▪3(d)) at room temperature, in which the more extreme pH conditions imply greater solubility, allowing for a dissolution–crystallisation transformation route, while under more neutral pH conditions (closer to the p.z.c.) an internal reorganisation mechanism would be

*

In one case “elongated rectangular-shaped particles” with ill-defined outlines composed of “numerous small grains” of order 1nm length were reported [584]. In another case aggregates of roughly isodimensional particles of 5 to 25nm diameter were reported [500]. In a third case ~8nm equivalentdiameter acicular particles were described, which aggregated readily [616]. Early research indicated pseudoböhmite was comprised of small platelet or lath particles that associated to form folded sheets [224].

†

Only if the hydrolysis ratio is at least 2.0 to 2.75, according to FRANÇOIS’s [367] brief review. R1▪2 : Coagulation

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D. I. VERRELLI

favoured; the former yields böhmite (γ-AlOOH) while the latter yields gibbsite or bayerite (Al(OH)3). The results of BACHE et alia [112] suggest that the phase that ‘condenses’ or adsorbs onto the surface of raw water turbidity elements may be different to that which forms freely, given that the two appear to have significantly different ζ-potentials. In general the aluminium phases favoured as the pH * is increased (from, say, 5 to 12) follow the sequence: amorphous precipitate, gibbsite, pseudoböhmite, bayerite [895]. JOLIVET [538] described a similar scheme in which ‘gel’ formed initially by neutralisation would transform to böhmite for 6 ( pH ( 7, where solubility is lowest (see Figure R1-1), or to an Al(OH)3 species outside of this range — gibbsite for pH ( 5, and bayerite for pH T 8. The former process operates by in-solid reorganisation, while the latter involves dissolution and re(This parallels the transformations of ferrihydrite described in precipitation [538]. §R1▪2▪6▪3(d).) Increasing the rate of alkali addition tends to result in the formation of more crystalline forms [895, 940]. The type of anion (e.g. chloride, nitrate) does not appear to be important [895]. Lower temperatures tend to favour formation of an amorphous phase (possibly associated with the reduced Al solubility) [895]. HSU & BATES [500] conducted a systematic investigation into the precipitation of both aluminium sulfate and aluminium chloride across a range of hydrolysis ratios (0.2 to 3.3). (Hydrolysis ratio was found to be a better predictor of product formation than pH [499, 500].) In their study dilute alkali was added to concentrated aluminium solutions in order to avoid localised high alkalinity [500], in contrast to the present work. Following hydrolysis of Al3+, polycations form: HSU & BATES [500] postulated the formation of a stable ring-shaped species, Al6(OH)126+ (cf. the ‘deadlock’ PHC’s, §R1▪2▪4▪3) as OH‒ is added to the system. (Later researchers justified this by analogy to the supposed hexameric solid-state structure of Al(OH)3 [e.g. 978, 1100] [see also 466].) Increasing the hydrolysis ratio would increase the fraction of Al found in such ring units (maximal at a hydrolysis ratio of about 1.5 to 1.8 [1100]); a few double and triple rings would form through OH‒ bridging as [OH‒]added/[Al] = 2.0 is approached [500]. At this point negligible mononuclear Al would remain [500]. However formation of larger polycations would be unfavourable, due to their significantly lower charge density †, until hydrolysis ratios larger than 2.0 [500]. In this stage, the pH is relatively steady at about 4.0. Precipitates of more-or-less constant composition were formed, namely Al(OH)2.2X0.8, where X is Cl‒ or ½SO42‒; the formula was not affected by addition of an excess of anions [500]. As the hydrolysis ratio is increased from 2.0 to 3.0 or 3.1 the pH experiences a sharp increase [500]. The rate of change is greatest around pH 7, where the hydrolysis ratio was about 2.65 for the sulfate and 2.85 for the chloride [500]. In this stage larger polycations form [500]. The polymers were predicted to remain positively charged, and hence mutually repellent, up until complete neutralisation — i.e. a hydrolysis ratio of 3.0 [500] (by stoichiometry). *

Or (better) hydrolysis ratio [e.g. 499, see also 573, 1017].

†

The proposed ring-based structures exhibit an increasing basicity with increasing size, as the Al shared between rings are exposed to OH‒ from t h r e e neighbours [148, 500, 978]. This is a general feature of the Al polycations, however, and does not depend exclusively on a ring-based structure [cf. 231, 893].

674



However precipitates could form through the incorporation of the added anions (Cl‒ or SO42‒), yielding “basic aluminium salts”, whose formula varies continuously from Al(OH)2.2X0.8 to Al(OH)2.75X0.25 [500]. These appear to be fairly stable: only one sample exhibited any changes upon extended ageing, namely transformation to a slightly more basic The basic sulfate salt is not very soluble, and precipitates at formula [500]. ‒ [OH ]added/[Al] ≥ 0.3; the basic chloride salt is highly soluble, and does not readily precipitate * [500]. The basic aluminium salts still contain significant amounts of water ligands associated with the polycations, and so their structure is amorphous [500]. Below [OH‒]added/[Al] = 2.75 all of the precipitates formed slowly and were amorphous [500]. At higher hydrolysis ratios the reduced charge repulsion permitted rapid precipitation and formation of crystalline phases [500]. From the sulfate solution bayerite formed in combination with either nordstrandite, or gibbsite, or both at [OH‒]added/[Al] ≥ 3.0; pseudoböhmite also formed, although this eventually (weeks) transformed to a crystalline phase at [OH‒]added/[Al] = 3.3 [500, see also 1100]. The chloride system behaved similarly, with bayerite forming at [OH‒]added/[Al] ≥ 2.93; neither gibbsite nor nordstrandite nor pseudoböhmite were detected — however böhmite and pseudoböhmite formation was observed by other researchers in this system [500]. STOL, VAN HELDEN & DE BRUYN [978] identified two critical ‘corrected’ [OH‒]/[Al] ratios. (The correction yields a lower value than [OH‒]added/[Al] [978].) The kinetics were reported to undergo a transition from reaction-limited (i.e. slow reaction) to diffusion-limited (i.e. fast) behaviour at a corrected ratio of ~2.5, while precipitate was observed to form at a threshold ratio of about 2.75 to 2.8 [978] [cf. 499] [see also 148]. By increasing the ionic strength to 2.8M, precipitate could be formed at corrected ratios as low as ~2.6 [978]. Equivalent results were obtained for both aluminium chloride and aluminium nitrate [978]. RAUSCH & BALE (1964) found that freshly hydrolysed solutions of aluminium nitrate (Al(NO3)3), at about 1M concentration, contain large aggregates apparently in the form of thin (< 1μm) platelets, whose size increased with increasing ligand number and decreased with time [118]. “Solutions aged six months at room temperature or heated to 70°[C] for 1 [hour] seemed to be stable and were found to contain much smaller particles,” with radii of gyration of about 0.4μm [118]. Experiments have shown that the presence of foreign ions or organic species can change the type of aluminium phase precipitated from solution [e.g. 223, 499] [see also 466, 675]. Commonly the presence of higher concentrations of ‘impurities’ in solution (i.e. lower water activities) discourage the formation of crystalline phases, and favour the formation of amorphous phases [e.g. 499, 622], although this is not a general rule [cf. 940]. Small organic acids are particularly effective [940]: The occupation of the co-ordination sites of Al by organic ligands apparently disrupts the hydroxyl bridging mechanism, which is indispensable for the polymerization of Al ions.

The affinity of the organic ligand for Al and the molar ratio are important parameters influencing the efficacy [940]. However there are some complications [940]:

*

At [Al] = 0.05M no precipitate could be separated up to [OH‒]added/[Al] = 2.7, although sol formation was observed at [OH‒]added/[Al] ≥ 2.55, with a particle size perhaps somewhat larger than 1nm [500]. R1▪2 : Coagulation

675

D. I. VERRELLI

The influence of organic ligands on retardation or acceleration of the crystallization process or precipitation products of Al is not always related to their chelating power for Al [...].

For example, tartrate is more effective than citrate in inhibiting crystallization of Al hydroxides [940]. HSU (1967) [499] proposed that high salt concentrations — especially with NaCl (aq) * — favour oxolation (Al‒O‒Al) linkages, as in böhmite and pseudoböhmite, rather than olation (Al‒(OH)2‒Al) linkages or hydroxyaluminium polymers, the precursors of bayerite [584]. (BYE & ROBINSON (1964) [223] had earlier described pseudoböhmite as an olation polymer.) Upon ageing of pure pseudoböhmite some transformation of ‘oxo’ linkages to ‘ol’ linkages apparently occurred, but bayerite was not detected after even 18 months [499]. SATO [895] reported that an amorphous phase precipitated first in the aluminium solutions (chloride and nitrate) he studied, and he concluded that this transformed o n l y to pseudoböhmite, and t h e n c e (optionally) to bayerite or gibbsite. The less crystalline phases acted as nucleating sites for bayerite formation [895]. Bayerite (formed at high pH) may transform to gibbsite upon ageing [895]. Amorphous aluminium hydroxide formed initially upon hydrolysis of aluminium isopropoxide, but transformed to pseudoböhmite upon ageing [222]. This occurred rapidly (within hours) when aged in the mother liquor, but was inhibited at low water activities [222]. Notwithstanding the limited ordering of pseudoböhmite, it appears that the presence of water is required to facilitate ordering through formation by hydroxyl-group condensation and polymerisation [222]. Ageing in aqueous mother liquor (pH ~ 7) of precipitate formed from aluminium secbutoxide led to transformation of amorphous phase(s) to pseudoböhmite and bayerite, but no gibbsite was detected after even one year [223, 224]. It was suggested that nordstrandite can appear under these conditions, but that gibbsite requires higher pH [223], which is contrary to the indications of more recent references (see also Table R1-5 and Table R1-6). Pseudoböhmite was first detected after only 2.5h under these conditions, and was itself fully transformed after 24h [223]. High concentrations of NaCl (3M) and dioxane (30%) resulted in the formation of pseudoböhmite from amalgamated aluminium at pH 8 instead of bayerite; increasing the dioxane concentration (90%) resulted in the formation of a completely amorphous precipitate [622]. The dioxane appears to have a greater effect, which may be due to the formation of an adduct with aluminium hydride in this system [622]. Acetone was found to have the same effect as dioxane [622]. It was reported that in this amalgamated aluminium–water system at pH 8 — with or without impurities — an amorphous † product always formed first (in the first 3 minutes), which then transformed to either bayerite or pseudoböhmite depending upon the concentration of ‘impurities’ in solution [622]. Pseudoböhmite began to show signs of transformation to bayerite upon heating in the mother liquor (pH 8) at 100°C for 4d [622]. Heating at only 80°C resulted in a sharpening of

*

This efficacy is associated with the ion sizes and hence hydration energies [499].

†

It is not clear whether the question of crystallinity in this early stage is valid, as it relies on the existence of large-scale precipitate structure (which is then assessed as either ordered or disordered).

676



the x-ray diffractogram peaks, and a marginal shift in the d020 peak [622] toward that of böhmite (see §4▪2▪1▪2(b)). Pseudoböhmite prepared from amalgamated aluminium in various solutions was found to be extremely stable when (air-)dried, with no detectable change after 15 years’ ageing [622]. The amorphous gels were similarly stable [622]. Differential thermal analysis (DTA) showed that pseudoböhmite had a high content of lowtemperature (~140°C) bound water, which was presumed to be associated with the surface [622]. Organic acids, and NOM in general, have a significant effect on the precipitation process [707]. These species “act as competitors against hydroxyls for the bonding sites” of Al, resulting in [707]: 1. reduction of the precipitation pH and higher supernatant turbidity; low amounts of Al13, and hindering of Al polymerisation generally; and 2. precipitation of polymorphic, amorphous hydroxides. 3. NOM typically forms complexes in solution and is incorporated into the precipitating material; e.g. much less fulvic acid is removed by adsorption on pre-formed and aged Al(OH)3 [300]. SINGER & HUANG (1990) [940] conducted a systematic investigation into the formation of aluminium hydroxides (from AlCl3) in the presence of various levels of soil * humic acid at three separate pH values. Their findings are summarised by Table R1-5. Both pH and humic acid level strongly affected phase formation. Table R1-5: Influence of humic acid upon aluminium (oxy)hydroxide formation from 1.1mM AlCl3 (30mg(AL)/L) after 80 days ageing in the mother liquor at ~25°C [940].

pH 6 8 10

0 G, P P, B, G B

2.5 G (P) P, B, G am.

Humic acid level [mg/L] 5.0 12.5 G (P) B P, B (G) P am. aq. (am.)

25 am. aq. aq.

37.5 am. aq. aq.

am. = amorphous; aq. = aqueous (no precipitate); B = bayerite; G = gibbsite; P = pseudoböhmite. Phases in parentheses indicate minor quantities.

In the absence of humic acid it is seen that gibbsite and pseudoböhmite formed at nearneutral pH, while bayerite was favoured as the pH increased. Humic acid generally favoured the formation of amorphous phases and ultimately The d020 spacing of pseudoböhmite (see suppressed precipitation altogether [940]. §4▪2▪1▪2(b)) was also found to increase with increasing humic acid concentration [940]. These effects can be attributed to complexation of Al by humic acid making the Al “unavailable” for precipitation [940]. The shift to formation of bayerite at pH 6 seems to go against the grain, given that aside from this the humic acid is apparently discouraging crystallisation. It was suggested that this may be due to an increase in the crystallisation rate due to the humic acid [940]. An analogy

*

An udic haploboroll (orthic black chernozemic soil) [940]. R1▪2 : Coagulation

677

D. I. VERRELLI

could be drawn to the action of oxalate on Fe, in which the metal ion spacing in the complex is hypothesised to be similar to that in the favoured hydroxide or oxide phase [583]. KODAMA & SCHNITZER (1980) [584] carried out a systematic study into the formation of aluminium hydroxides (from AlCl3) in the presence of various levels of soil * fulvic acid at three separate pH values. The fulvic acid sample was measured to have an indicative molecular mass of order 957g/mol, so that the m o l a r ratio of fulvic acid to Al varied from 0 to approximately 0.1 [584]. Table R1-6: Influence of fulvic acid upon aluminium (oxy)hydroxide formation from 0.9mM AlCl3 (24mg(AL)/L) after 70 days ageing in the mother liquor at 30°C [584].

pH 0 G N, B B

6 8 10

0.5 G (P) N, B (P) –

Fulvic acid level [mg/L] 1.0 2.0 3.0 5.0 G (P) P (G) – P N, B, P – P (N or B) – aq. – – aq.

10.0 P P (N or B) aq.

100 – am. aq.

am. = amorphous; aq. = aqueous (no precipitate); B = bayerite; G = gibbsite; N = nordstrandite; P = pseudoböhmite. Phases in parentheses indicate “trace” quantities. (No distinction shown between “major” and “minor” components — see original reference for details.)

The results in Table R1-6 are mostly similar to those of Table R1-5, which is not surprising, as fulvic acid is able to complex Al [584] † in a similar way to humic acids. The (fulvic acid) complex may be so strong that it prevents full hydrolysis to Al(OH)3 [584]. A key difference is the identification of nordstrandite instead of gibbsite at pH 8. This cannot be due to the fulvic or humic acid, as the undosed system shows the same difference — it must be due to either experimental technique or misclassification. The fulvic acid study also did not detect formation of bayerite at pH 6; this does suggest an inherent difference between humic and fulvic acids. Although an amorphous phase was not reported to form at either pH 6 or 10 at ‘appropriate’ organic levels, this may be simply because of the specific conditions covered. At pH 10 both the fulvic acid and aluminium ion are negatively charged, and so electrostatic repulsion may be responsible for the lack of precipitation [584]. As in the case of Al13 (§R1▪2▪5▪2(a)), precipitate formation can depend upon the details of chemical addition and mixing — or locally elevated concentrations [e.g. 499], cf. interfacial disequilibrium [148, 300, 675, 677]. Different results can be obtained by acid-neutralising an aluminate solution [see 982].

R1▪2▪5▪4

Reaction pathways

It is accepted that the nature, quantity and longevity of transient polymeric species, colloidal particles or amorphous solid phases formed is determined by the conditions of hydrolysis, *

An imperfectly drained podzol [583].

†

An alternative explanation proposed in terms of analogy to salt effects [584] seems implausible due to the higher concentrations required for salts (see above) and the inability of this mechanism to explain formation of bayerite at pH 6 and intermediate humic acid concentration (Table R1-5).

678



such as the composition of the solutions that are combined, the rate of combination, the temperature, and the amount of agitation [118]. Similarly, the conversion of these transient species to tridecameric aluminium (metastable) or gibbsite depends upon “the temperature, the pH, the amount of gibbsite already present, and perhaps on the anion present” [118]. BERTSCH & PARKER [146] present a model of reaction pathways for the precipitation of Al(OH)3 in hydrolysed aluminium solutions (to which base has been added), as per Figure R1-7. Not shown is the formation of precursors to the tridecamer, namely small oligomers such as a dimer or trimer * [146]. Reaction pathway I is said to be common when solutions are “brought to supersaturation through simple dilution or when rapid neutralisation occurs” [146]. In this regime little or no Al13 forms, and gibbsite crystals appear within days or weeks [146]. On the other hand, the insoluble, outer-sphere aggregates of Al13 formed by anion bridging are described as forming rapidly and predominating if the rate of neutralisation is rapid — although perhaps over only a narrow pH range [146]. Of the various species in which aluminium occurs, the condensation products are the least soluble (or “labile”), while the “tenuous” aggregates formed by anion-bridging can ‘dissolve’ into component Al13 units, which are soluble [146]. Reaction pathway II favours the formation of significant amounts of Al13. There are three possible ways in which reaction can then proceed [146]: Most of the soluble aluminium is present as Al13, and aggregation does not occur a. during neutralisation. In this case, the Al13 units may dissociate to form octahedral, mononuclear species over a period of months to years. If aluminium is predominantly present as unaggregated Al13, as in the previous b. case, then it is also possible for the Al13 units to undergo condensation reaction (via aggregation) over a period of months to years. If Al13 condensation products form during the initial hydrolysis in significant c. amounts, then these act something like nucleation sites for the deposition of further Al13 , which can take place over weeks or months. Transformation to the “poorly ordered solid phase(s)” is highly dependent upon the neutralisation conditions, and on the presence of anions, which facilitate bridging. Reaction pathway III seems to be similar in character to reaction pathway II.c, described above.

*

The concentrations of these species could be expected to decrease in more dilute aluminium solutions, favouring direct conversion of mononuclear aluminium to the solid phase [818]. This corresponds the most closely to reaction pathway I in the figure. R1▪2 : Coagulation

679

D. I. VERRELLI

[Al(OH)3]n

intermediate

Al(OH)3 (gibbsite)

II.a I SLOW

Al3+ + base

II

Al13a+

III [Al13a+.cXb–]n

Al3+

II.b VERY SLOW [Al13]nd+ [Al13a+.cXb–]n II.c SLOW

FAST

d+

[Al13]n

FAST SLOW

“Poorly ordered phase”

intermediate Al(OH)3 (gibbsite, bayerite)

Figure R1-7: Formation of Al(OH)3 species from Al3+ ions. Adapted from BERTSCH & PARKER [146]. Al13 represents the tridecamer, [Al13a+.cXb–]n represents anion bridging aggregates, and [Al13]nd+ represents the inner-sphere condensation products*. [Cf. 148, 1100.]

Much as the presence, early on, of insoluble condensation products serves to increase the rate of formation of crystalline phases, so too is it expected that nucleation of gibbsite in the field will be predominantly heterogeneous (i.e. occurring on suspended clays et cetera) due to the “greatly reduced” activation energy required in comparison to ‘homogeneous’ nucleation [146]. Specific ions (e.g. phosphate, silicate, and sulfate) are likely to significantly inhibit the formation of Al13, though not preventing it entirely [146]. Such observations have led to the common view that Al13 is “unlikely” to be formed in “measurable quantities” in soils and surface waters [146]. STOL, VAN HELDEN & DE BRUYN [978] claimed that amorphous precipitates tended to predominate at lower pH (pH ~ 6), where the orientation of platelets into ordered crystalline structures was less favoured — more ordered structures were observed at higher pH (pH T 10).

*

680

This is not a precise notation: due to the condensation, the formula for inner-sphere association of two Al13 units would be something like [146] 2AlO4Al12(OH)24(H2O)127+ → AlO4Al11(OH)22(H2O)11‒Al‒AlO4Al11(OH)22(H2O)119+ + Al(OH)4(H2O)22‒ Clearly, if the condensation ‘polymerisation’ produced very long chains, then the notation [Al12]nd+ would be more appropriate, but evidence of the occurrence of such production is not apparent. This is not in complete agreement with the proposal that the single-unit defect structure (“AlP1”) has the indicative formula Al12O39, and the double-unit defect structure (“AlP2”) has the indicative formula Al24O72 (described as “two AlP1 units”, although the stoichiometry doesn’t appear to work out) [146]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


R1▪2▪5▪5

Industrial practice

Aluminium sulfate coagulation is generally optimised between pH 5.5 and 7.5, with 7.0 a typical value [1113]. (Optimisation between pH 5.5 and 7.2 has been attributed to the minimum in solubility observed for aluminium hydroxide in this range [402]. KAWAMURA [557] gave 5 to 7.) United Utilities typically operates alum coagulation at pH 6.0 to 6.5 [436]. WILSON [1124] gave an example where at a Yorkshire Water plant treating highly coloured water A254nm reduction was optimised for alum at pH 5.9. BOLTO [171] specified pH 5.5 as typical. For comparison purposes COOK, CHOW & DRIKAS [276] adopted a constant pH of 6. LIND [668] notes that pH values above 8.5 for alum coagulation result in excessive formation of the aluminate ion, which will precipitate out only much further downstream. For enhanced coagulation especially, pH values of 5.5 to 6.5 are preferred [668]. EDZWALD & TOBIASON [335] suggest coagulation between pH 6 and 7 for low alkalinity waters with low to moderate levels of aquatic humics, with the lower end appropriate to ‘summer’ temperatures; water with higher levels of NOM may be coagulated better at still lower pH values such as ~5.5. The trend of decreasing pH with rising NOM levels was also reported by KIM et alia [569] and BOTTERO et alia [183]. Working on coloured, low-turbidity waters, BACHE et alia [116] identified 6.2 to 7.2 as an optimum pH range *, yielding the best colour removal as well as the largest aggregates. This corresponded to the pH of zero streaming potential. For precipitate formed in the absence of NOM the streaming potential was consistently higher, giving a larger i.e.p., and this was reflected in larger aggregate sizes as the pH increased up to 8. For similar waters DULIN & KNOCKE [331] found pH 6.0 to 6.5 to be optimal. In earlier work BACHE & HOSSAIN [494] identified pH 5.5 as optimal for the same type of raw water, based on minimising the supernatant aluminium concentration. AMIRTHARAJAH & MILLS [90] gave ‘theoretical’ ranges of aluminium dosages of about 0.045 to 2.7mg(Al)/L for charge neutralisation, and about 1.3 to 13mg(Al)/L for sweep coagulation. A common dose is ~2.7mg(Al)/L [90]. According to KAWAMURA [557], doses as low as 0.9 to 1.6mg(Al)/L are required for “good quality” raw water. Doses of e.g. 1 to 6mg(Al)/L have been suggested as appropriate for typical industrial application in combination with a polyelectrolyte [229]. In New Zealand alum doses would not normally be expected to exceed about 10mg(Al)/L [161, 797]. Some workers (e.g. PACKHAM [359]) have proposed an inverse relationship at l o w degrees of raw water contamination (especially with regard to particulate matter), wherein the paucity of contaminant is taken as implying a very low concentration of points from which the coagulation can be ‘nucleated’, yielding impractically slow kinetic behaviour. Montmorillonite clays have been singled out as an exception in this hypothesis, as the “exceptional degree of subdivision” with which montmorillonite clays are associated means

*

An earlier report by BACHE & HOSSAIN [111] shows a pH range of about 4.5 to 5.0 to be optimal for the coagulation of an apparently similar raw water — however the earlier report only considered pH values up to 6.0 with moderately low doses, operating primarily in a charge neutralisation regime. R1▪2 : Coagulation

681

D. I. VERRELLI

that they behave, in this respect, as if they were at a significantly higher concentration (by mass) in comparison to other clays [359]. The pH range in which coagulation (by charge neutralisation) occurs can both broaden and decrease in magnitude as the alum dose is increased [149]. This is not apparent from the stability–coagulation diagrammes published showing the solubility curves for the (amorphous) hydroxide precipitates of aluminium and iron(III) [90, 155, 326], which show a broadening range with increasing metal concentration, but not the decrease in pH. However, the coagulant precipitates will form at lower pH values as the metal concentration is increased [e.g. 894]. The solubilities of aluminium in coloured raw water and in distilled water are different [494].

R1▪2▪6

Iron

The chemistry of iron is even more complicated than that of aluminium, due chiefly to the existence of two common oxidation states (aside from the elemental form and perhaps two other less stable states) [1095] [see also 118] and the high reactivity or lability of many of the compounds [466, 539]. Hydrolysing iron salts used as coagulants include ferric chloride or ferric sulfate, and (chlorinated *) ferrous sulfate [94, 797, 879]. These have the respective formulæ: • Fe2(SO4)3·xH2O [28, cf. 281], with x = 0 [827, 854] or 9 [854] for the powder, and circa 36.9 [854] for the typical commercial stock solution used industrially, which is ~12.3%m Fe [668]; • FeCl3·xH2O, with x = 0 [827, 854] or 6 [854] for the solid, and circa 13.1 for the commercial liquid [854], which is ~15.8%m Fe [668] — but sometimes more diluted (e.g. ~40%m FeCl3 [93], i.e. ~8.3%m Fe); • FeSO4·xH2O, with x generally given as 7 [879], but sometimes 5 [94] or (presumably) 0. The ferric salts are much more commonly employed, and often called simply ‘ f e r r i c ’ . For reasons outlined in Appendix S23, and to simplify the analysis, in the present work iron is assumed to all or predominantly be present as Fe(III) [see also 118, 307, 536].

R1▪2▪6▪1

Hydrolysis

Similarly to the case for aluminium [90, 675, 786] (§R1▪2▪5▪1), the ferric ion may be expected to undergo a series of (reversible) hydrolysis reactions, in which co-ordinated water molecules are successively replaced by hydroxyl ligands [118, 533, 674], viz. Fe(H2O)63+ + H2O # Fe(H2O)5OH2+ + H3O+ et cetera — i.e. Fe(H2O)63+ # Fe(OH)(H2O)52+ # Fe(OH)2(H2O)4+ # Fe(OH)3(H2O)30 # Fe(OH)4‒ Although Fe(III) has historically been assumed to form only octahedral complexes [e.g. 118, 533, 1008], it implicitly follows the same transformation as aluminium to a tetrahedral complex at elevated pH [see 538, 674, 675]. The uncharged species might also be found as

*

682

Chlorinated ferrous sulfate produces ferric sulfate and ferric chloride in situ [797]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


Fe(OH)3(H2O)0 [cf. 466, 677]. supported.

The existence of Fe(OH)5(H2O)2‒ or Fe(OH)63‒ [118] is not

Assuming complete dissociation * applies to both ferric sulfate and ferric chloride, the important equilibrium reactions are then: ΔH°298 ~ 45kJ/mol † p∗β1 = 2.19±0.03 Fe3+ + H2O # Fe(OH)2+ + H+ Fe3+ + 2H2O # Fe(OH)2+ + 2H+ p∗β2 = 4.7 p∗β3 < 13.2 Fe3+ + 3H2O # Fe(OH)30 + 3H+ ΔH°298 ~ 143kJ/mol p∗β4 = 21.6 Fe3+ + 4H2O # Fe(OH)4‒ + 4H+ where cumulative equilibrium constants have been selected from the critical compilations of SMITH & MARTELL (1989) cited by BUTLER [219] at 298.15K and I → 0 [cf. 547]. Standard enthalpies of reaction are derived from various sources [280, 307, 662, 936, 947, 1094] ‡. The value for p∗β2 may be low. Good thermodynamic property data has been available for only Fe(OH)2+ [307]. Such aqueous hydroxide species are most important in aqueous solutions with low organic matter concentrations at pH > 2.5 [307]. Fe3+ exists for pH values below about 1 [118] to 3 [994]. Chlorido complexes, especially FeCl2+, may also be present in significant concentrations for ferric chloride solutions that have not been neutralised with base [994, 1008]. TAGIROV et alia [994] computed the following molal equilibrium constants for 298.15K and I → 0: ΔH°298 = 22kJ/mol pβ1 = ‒1.52 (±0.10) Fe3+ + Cl‒ # FeCl2+ 3+ ‒ + ΔH°298 = 44kJ/mol pβ2 = ‒2.4 (±0.3) Fe + 2Cl # FeCl2 Formation of FeCl30 is only significant at exceedingly high chloride concentrations [994]. There is significant variation in the ‘constants’ for these (and other) reactions with both T and I [see 994].

R1▪2▪6▪2

Polynuclear iron species

The above hydroxo complexes can condense to form dimers, trimers, tetramers and larger oligomers [280], similar to aluminium. However, due to the high lability of ferric species, these are less well characterised than the aluminium analogues [466, 539]. The precise speciation depends on many factors [533]; the diversity of species appears to decrease upon ageing [462]. Polynuclear species are less important in “dilute” systems [118]. Most evidence indicates that dimers are the dominant oligomer formed [280, 462], along with poorly ordered (“chaotic”) polymers leading to the formation of a solid phase likely to be 2line ferrihydrite [280]. Trimers [280] and tetramers [462, 573] have been observed. There is evidence for occurrence of [Fe2(OH)2(H2O)8]4+ and (cyclic) [Fe3(OH)4(H2O)9]5+ [118, 466, 538, 677].

*

At 25°C consideration of ferric–chloride species in solution is only required in highly acidic environments (pH < 3) with high chloride ion concentrations ([Cl‒] > 0.5M) [994].

†

Data quoted by CORNELL & SCHWERTMANN [280] imply ΔH°298 ~ 11kJ/mol.

‡

All but two [280, 307] of which quote data published decades ago, with some of the later works also citing the earlier references. R1▪2 : Coagulation

683

D. I. VERRELLI

The above leads to additional hydrolysis reactions [219, 1094]: ΔH°298 = 57kJ/mol 2Fe3+ + 2H2O # Fe2(OH)24+ + 2H+ 3+ 5+ + 3Fe + 4H2O # Fe3(OH)4 + 4H

p∗β22 = 2.9 p∗β34 = 6.3

The formula of a generic iron oxohydroxo polynuclear complex can be written as [FeIIIxOy(OH)z·nH2O](3x‒2y‒z)+ [280, 462]. If the water molecules are actually co-ordinated (in the inner sphere), then both olation and oxolation can occur (see §R1▪2▪4▪2). Specific complexes likely to form include [Fe2(OH)2(H2O)8]4+ and [Fe2O(H2O)10]4+ [466, 538]. In contrast to aluminium polycations, ‘oxo’ bridges are more common in polynuclear ferric species, possibly due to the higher electronegativity of iron [536, 539]. However it has been suggested that the iron complexes containing olation bridges are more stable than those containing oxolation bridges (when formed from dilute ferric chloride solutions) [462]. These condensation reactions can occur even in strongly acidic media (pH ≥ 1) for ferric species [536]. Goethite has been said to form through oxolation of “rutile-type” double-chain products of olation [466, 520, 536, 538, 539] — as proposed in the formation of pseudoböhmite (§R1▪2▪5▪3). The base unit for formation of the dioctahedral chains would most likely be the uncharged planar tetramer [Fe4(OH)12(OH2)4]0 [466, 536, 538, 539]. (Lepidocrocite may form from the skewed tetramer [Fe4O(OH)10(OH2)5]0 — analogous to the proposed formation of böhmite [466].) The akaganéite structure also contains double chains of octahedra, but they connect differently, leaving wide channels [538]. These channels initially contain chloride ions, which are n o t incorporated into the crystal structure, and can be exchanged [538]. Indeed the less compact final structure may be directly related to steric effects arising from the presence of these large (circa 181pm) ions [538]. A discrete Fe13 analogue of Al13 (§R1▪2▪5▪2(a)) does n o t form, as Fe(III) is not sufficiently polarising to deprotonate the μ3-OH group [466] and has difficulty adopting tetrahedral coordination (even without crystal field stabilisation [see 677], except in a mixed-valence system) [cf. 538]. In general, small polymers form rapidly by olation first, and large polymers are built through a slow transformation to ‘oxo’ bridges [325, 965] [cf. 466, 536, 539]. Thus 2-line ferrihydrite, which forms in rapidly neutralised systems, contains a greater fraction of OH than the 6-line form [965]. Ferrihydrite is most likely to comprise a “disordered stacking of Fe3+ ions surrounded by OH‒ and O2‒ anions” [466]. The ferric polynuclear species typically appear as a red to red–brown suspension of 2 to 5nm particles, which resists separation [279, 280, 325, 466, 573, 677, 767, 768]. An approximate formula of [Fe4O3(OH)4]n2n+ has been suggested, with n ~ 25 and a molecular mass of circa 104g/mol [677]; n ~ 250 has been reported [see 573]. The polynuclear species may precipitate under certain conditions, depending primarily upon the system pH and ionic strength [280]. At moderate Fe concentration (0.1M) in the presence of Cl, first dimers and then trimers form as the hydrolysis ratio increases to [OH‒]added/[Fe] ~ 0.7 , and these coalesce to form polymers when [OH‒]added/[Fe] > 1.5 [182]. These polycations are approximately 1.5nm in size, very stable, and have the structure of akaganéite [182, cf. 768].

684



Formation of polynuclear species is inhibited by NOM [583, 1082]. Only monomers, dimers and trimers were detected when ferric chloride was added to raw water at 14mg(Fe)/L and pH 5.5 to 7.5 with TOC = 4.0 to 8.4mg(C)/L [1082] *. The mechanism of inhibition appears to be formation of Fe‒O‒C bonds that block growth through (say) Fe‒O‒Fe bonds [1082]. The iron remained present as Fe(III) in octahedral structures bridged by ‘ol’ and ‘oxo’ linkages at corners † and along edges [466, 1082].

R1▪2▪6▪3

Solid iron phases

Crystalline, paracrystalline and amorphous forms of iron may precipitate. Important crystalline forms of iron include the following [280]: • α-FeOOH ( g o e t h i t e ) . This is the stable solid phase under normal atmospheric conditions (i.e. ambient temperature, at which liquid water would exist) [118, 280, 306, 459, 466, 547], with ΔfG° ≈ ‒492kJ/mol [280]. In fact, as a bulk material it is more stable than hæmatite, irrespective of the partial pressure of water, up to a temperature of around 100°C [280, cf. 633]. It is the most insoluble hydroxide of the ferric ion [118], with the region of minimum solubility at around pH 7 to 8, near the point of zero charge [280]. However, “the attainment of equilibrium and interconversion of various other phases are very slow in this system, requiring several years at 25°C” [118]. Yet in some cases (slow hydrolysis at very low pH) it is the first oxide to form [279, 280]. Goethite forms by direct precipitation of Fe3+ species [280] or polycations [767]. This species forms in sulfate [118] and nitrate [573, 675, 767] solutions. Goethite has the same structure as diaspore (α-AlOOH) [280], viz. orthorhombic with hexagonal closepacking of oxygen atoms [1130]. It principally forms acicular crystals [280], e.g. with dimensions from circa 3nm×30nm [573], to 50nm long [910], to ~20nm×73nm [1131]. Goethite precipitated from acid ferric solutions may be acicular, rod-like [cf. 547] or < 100nm cubes depending upon pH (or [OH‒]added/[Fe] ratio) and temperature [280]. At elevated ionic strength (I ~ 0.2M) in acid media acicular goethite crystals slowly align and aggregate to form rafts of parallel rods [280, 767, 1130, 1131]. Multidomainic goethites tend to form at high ionic strength as well as at low synthesis temperature (< 40°C) [280]. • β-FeOOH ( a k a g a n é i t e ) . This species forms in (slightly reducing) chloride or fluoride media [118, 280, 573, 677] (rarely in nature [280]), though it may redissolve to precipitate hæmatite [792], as it is considered “highly active” [118] (it is certainly highly soluble [280]). Thus, despite the chemical formula commonly given, it may actually contain the halide, e.g. up to 7% chloride [280]: the ions may be an “essential constituent” [520] of the crystal [573], or they may be exchangeable species occupying nanometre-scale channels through the structure [538]. Akaganéite principally forms somatoids (e.g. 200 to 500nm long and 20 to 100nm wide) and rods [280], which may aggregate to form ‘rafts’ [388, 767, 768]. At room temperature the crystals take a month to grow, and exhibit a square cross-section, whereas at higher temperatures crystal *

Considering the molar ratio of the organic matter and Fe indicates that Fe was not in excess.

†

Normally edge sharing is favoured thermodynamically over corner sharing [466] octahedra, although corner sharing can be stabilised by cyclisation [535, 538]. Corner-sharing prevails in tetrahedral species [535, 538]. R1▪2 : Coagulation

685

D. I. VERRELLI

growth is measured in days and the cross-section is circular [280]. However in partially neutralised ferric salts (0 < [OH‒]added/[Fe] < 3) rod-like crystals are formed that are usually monodisperse and measure about 6nm×50nm [280]. Akaganéite has apparently been trialled as an adsorbent in drinking water treatment, with results comparable to activated carbon [360]. • Fe16O16(OH)x(SO4)y·nH2O ( s c h w e r t m a n n i t e ) . This is a related compound to akaganéite. It occurs in media of high sulfate concentration, but is “unstable under most conditions”, transforming spontaneously (albeit slowly) to goethite in solution at room temperature [279, 280]. Schwertmannite forms “spherical hedge-hog–like [...] aggregates” composed of long, radially-oriented, filamentous crystals [280]. • γ-FeOOH ( l e p i d o c r o c i t e ) . This typically forms in nature as an oxidation product of Fe2+, but may also form by direct precipitation of low-molecular-mass ferric species [280, 767] at low concentration and pH [466, 573, 677]. It transforms readily to αFeOOH on heating in alkaline or FeSO4 solutions [118], and is usually associated with goethite [279, 280]. Lepidocrocite has the same structure as böhmite (γ-AlOOH) [280, 536, 539]. It principally forms lath-like (thin, narrow, and elongated) crystals [279, 280]. • α-Fe2O3 ( h æ m a t i t e ) . This is the most thermodynamically stable form of iron(III) species [118] in ‘dehydrolysing’ conditions [306, 459] (ΔfG° ≈ ‒744kJ/mol [280]). It may be formed from amorphous ferric gels [118]. Hæmatite is known to form in aqueous media from ferrihydrite by combined dehydration and internal reorganisation [280]. Hæmatite is isostructural with corundum (α-Al2O3) [280]. It principally forms hexagonal plates and (at higher temperatures) rhombohedral crystals [280]. In the absence of additives, hæmatite “grows from suspensions of ferrihydrite at temperatures < 100°C as hexagonal or subrounded plates” [280]. The plate diameter increases with pH and temperature from < 100nm (at pH 8) to > 5μm [280]. Idiomorphic hæmatite crystals can be produced from ferrihydrite in neutral to alkaline media [280]. References are often made to iron(III) hydroxide in the general literature. Crystalline Fe(OH)3 does exist, and is called bernalite, however it is exceedingly rare in nature [280, 520, 538]. What is usually meant is an a m o r p h o u s * o r p a r a c r y s t a l l i n e - t o - c r y s t a l l i n e material of uncertain structure and composition [118, 279, 280, 520]. The paracrystalline forms are correctly termed f e r r i h y d r i t e [280], but use of imprecise historical terms — amorphous ferric hydroxide, colloidal ferric hydroxide, hydrous ferric oxide (or HFO) †, and the “TOWE–BRADLEY phase” [520] — persists. Likewise, use of the simple, nominal formula am-Fe(OH)3 has persisted, although it is certainly incorrect; the best formula at present is Fe5HO8·4H2O [279, 520]. Alternative formulæ are given in Table 4-4. Much of the uncertainty stems from the ability to prepare ‘ferrihydrite’ specimens with far less water (or OH) than this [520, 910, 965]. A molar ratio of OH to Fe between 0.15 and 3 is expected, with a recommended value of 0.86 [280]. The structure was originally described as a sort of ‘defective’ hæmatite type, with hexagonally close-packed anions (O2‒ and OH‒), randomly distributed FeIII ions with a *

The existence of complete amorphicity in any solid phase has been disputed [373, 1109] [cf. 374]. The contention is that some degree of local ordering is always present, and apparent amorphicity is often a consequence of very small sizes of individual crystalline domains (i.e. crystallites) [1109].

†

This description has been more commonly applied to 2-line ferrihydrite [279, 280].

686



number of vacant sites, and a considerable amount of H2O [280], however studies have superseded this. Recent x-ray spectroscopic studies indicate that the local structure is closer to the FeOOH polymorphs goethite [957] and akaganéite [520, 538]. For 6-line ferrihydrite, another recent model consists of three intergrown structural constituents comprising a defect-free ABACA component, randomly ordered ABA and ACA fragments (defective), and around 25% ultradispersed 1 to 2nm hæmatite — the main difference from the 2-line form is the increased crystal domain size [280]. (An alternative study indicated the ultradispersed hæmatite need not be present [280].) Although all forms of ferrihydrite are poorly ordered, the degree of ordering does vary between the “ 2 - l i n e ” form and the more ordered “ 6 - l i n e ” form [280] *. The two forms precipitate under different conditions, and the 2-line form d o e s n o t transform to a more ordered or crystalline form of ferrihydrite with time [280] †. Historically a distinction was also drawn between forms in an ‘ a c t i v e ’ or ‘ i n a c t i v e ’ state [118] — alternatively, ‘freshly precipitated’ or ‘aged’ (respectively) [280]. Both forms are thermodynamically unstable with respect to the crystalline forms, and the active form is considered unstable with respect to the inactive form, as the latter undergoes a much slower transformation to FeOOH [459]. MISAWA’s data gives ΔfG° ≈ ‒760±10kJ/mol for ferrihydrite taken as Fe(OH)3 [279]; LANGMUIR’s value was around ‒700kJ/mol [280]. The thermodynamically less stable 2-line form is the type of ferrihydrite that is produced initially by rapid hydrolysis of ferric solutions [258, 280, 520], following OSTWALD’s ‘rule of stages’ (§R1▪2▪4▪4). 6-line ferrihydrite forms upon thermolysis (heating) of acidic ferric solutions (pH ≤ 3) at low concentrations of chloride (C < 10‒3M) [520, 536] [cf. 280]. Ferrihydrite formation is favoured when the supply (rate) of iron and hydroxide is high, and in the presence of silicates [258] or organic matter ‡ (which suppress formation of crystalline phases) [280], or at “high” ratios of C/Fe [520]. Ferrihydrite principally forms spheres [280]. While the 6-line form shows indications of hexagonal outlines in single crystals of 4 to 6nm [cf. 965] in size and has “appreciable internal order”, the 2-line form (as produced by fast hydrolysis of ferric salt solutions in neutral media) is heavily aggregated, comprising single particles (or crystallites, perhaps 2 to 3nm in size [cf. 397, 398, 520, 910, 965]) that are difficult to discern and have less internal ordering [279, 280]. These poorly-crystalline fine grains are the main reason for the difficulty in determining the structure of ferrihydrite [520]. Ferrihydrite has been found in significant concentrations in the sediments at the bottom of cool to warm (5 to 80°C) natural water bodies of near-neutral pH (around 6 to 7); it is commonly produced by aeration processes (high oxidation rate) [520].

*

The numbering of the lines follows the number of peaks counted on an x-ray powder diffractogram of the sample [520]. Although the 2- and 6-line forms are most often referred to, in fact a range of intermediate crystallinities can form, including 2-, 3- [1053], 4-, 6-, 7- and 9-line forms [280, 520].

†

Hence the term “protoferrihydrite” [cf. 258] for the less crystalline form has not been accepted [520].

‡

At very high levels of NOM only organic iron complexes form [280]. R1▪2 : Coagulation

687

D. I. VERRELLI

Aside from ferrihydrite, the stable ferric (oxy)hydroxides * can also exist in poorly crystalline forms, including poorly crystalline akaganéite [768] and poorly crystalline goethite [280, cf. 910]. The properties of these forms are generally variable and not well known. In nature hæmatite and goethite are the most commonly occurring of the above iron (oxy)hydroxides, followed by lepidocrocite and ferrihydrite, with akaganéite the least Most of these iron (oxy)hydroxides are detected in soils (except common [520]. akaganéite/schwertmannite), usually as extremely small crystals and/or with low crystal order [633], with typical Fe/soil mass fractions being of order 0.01 [280] [for ferrihydrite see 258, 520]. A review of the literature by CORNELL & SCHWERTMANN [280] indicates that in wastewater and water treatment applications — including the case of FeCl3 dosing and (partial) neutralisation with Ca(OH)2 — it is usually p o o r l y - c r y s t a l l i n e iron oxide, chiefly 2-line ferrihydrite, that forms and adsorbs unwanted species due to its high surface area and affinity for many ions †. While normally the ferrihydrite would be expected to form from solution, it could also be produced through transformation from another poorly ordered phase (e.g. akaganéite) and there are also cases in which naturally-formed ferrihydrite has been directly added for treatment of water and wastewater [279]. Pre-formed natural ferrihydrite and p o o r l y c r y s t a l l i n e akaganéite have both been used as alternatives to dosing ferric salts in water and wastewater treatment [280].

R1▪2▪6▪3(a)

Formation of important phases

Kinetics typically determine the phase that forms initially, rather than thermodynamics, and that phase may persist for long times due to the slow rate of subsequent transformation to a more stable phase. If the hydrolysis ratio, [OH‒]added/[Fe], rises above a “flocculation threshold” of 2.7 to 2.8, then rapid polymerisation occurs, yielding a poorly ordered precipitate [182, 184, 279, 573, 1008]. In particular, the first phase to form in response to rapid hydroxylation of ferric ions at room temperature is 2-line ferrihydrite, at pH > 3 [536]. For partial hydrolysis of ferric chloride, when the flocculation threshold is reached, there is a sudden increase in ‘particle’ size from order 101 to 102nm (at 24h), and the local-range ordering continuously [279] approaches that of goethite as the ratio is increased [1008]. This contrasts with partial hydrolysis of ferric nitrate, where the ‘particle’ size decreases from order 102 to 101nm [184]. Below a lower limit in the hydrolysis ratio of about [OH‒]added/[Fe] = 1, slow formation of more-crystalline FeOOH compounds (or α-Fe2O3, or mixtures thereof) dominates over the poorly-ordered precipitation of polynuclear species (precursors to ferrihydrite) [280, 573]. Small, rod-like goethite crystals slowly formed in dilute ferric nitrate solutions with a

*

The use of ‘ox(yhydrox)ides’ [cf. 536] or “(hydr)oxides” [e.g. 817, 957] are alternatives. ‘Hydrous oxide’ is less general and for iron connotes ferrihydrite. ‘((Oxy)hydr)oxide’ would be most general, but in the present text ‘(oxy)hydroxide’ is used for simplicity.

†

The claim by JOHNSON & AMIRTHARAJAH [533] that it is lepidocrocite that forms in a WTP is not supported elsewhere in the literature.

688



hydrolysis ratio of just 0.35 while ageing for ~2y at room temperature [1131]. The predominant phase is a strong function of the rate of hydrolysis, and hence the rate of generation of solid phase, based in part on the degree of supersaturation and solubility product with respect to each solid phase [280]. According to CORNELL & SCHWERTMANN [280]: The observed morphology of a crystal is usually the g r o w t h morphology. equilibrium morphology [where total GIBBS energy is minimum] is rarely observed.

The

The morphologies (or habits) of the iron (oxy)hydroxides given above are subject to the ‘driving force’, or chemical potential difference (Δμ / kB T ) — i.e. the degree of supersaturation in the case of precipitation and crystallisation [280]. A low driving force allows the formation of polyhedral crystals, whereas a very high driving force can induce the formation of dendritic, spherulitic, or “bow-tie” morphologies [280] — that is, morphologies with a lower fractal dimension, Df (see §R1▪5). Other environmental conditions can also affect the observed morphology, including local currents in solution, changes in the nature of the solvent, and the presence of foreign ions [280, 466, see also 675]. Even the “ageing history” of the ‘parent’ iron solution can have a bearing, due to the increased hydrolysis, formation of more nuclei, and hence reduction in crystal size and extent of crystal twinning [280, cf. 573]. These conditions also affect the available surface area (and porosity), due to changes in particle size; high growth rates or low temperatures “may lead to poorly ordered crystals” with surface areas of order 1002m2/g [280]. On average, specific surface area increases in the order hæmatite < goethite < schwertmannite < ferrihydrite for formation from solution at ambient temperature; the surface area of lepidocrocite is highly variable; akaganéite is somewhere in the range spanned by hæmatite and goethite, depending on the morphology [280]. GAN et alia [388] proposed a direct link between crystal morphology and dewaterability, suggesting that platy morphologies would tend to release surrounding water easily, while acicular morphologies would tend to ‘trap’ water.

R1▪2▪6▪3(b)

Solubility and stability

The rates of dissolution of iron oxides are generally extremely slow in natural systems, where the aqueous phase tends to be almost completely saturated with iron [280], and hence also in drinking water treatment. However (surface) structural defects, which are usually present to a greater or lesser extent [280], can serve to significantly increase (initial) dissolution rates [279] — even if only for a small fraction of the mass [280]. The solubility products given generally apply to equilibrium systems, where the timescale may be on the order of years [280]. Reduction is typically the most rapid dissolution mechanism, provided the conditions allow it [280]. Dissolution is generally faster for less-crystalline oxides [280]. The dissolution rate of 2-line ferrihydrite (in 0.2M oxalate) has been reported to increase as the original formation rate of the precipitate is increased [280]; rather than a decrease in crystallinity, this more likely suggests the formation of smaller solid domains, smaller aggregates, or more open aggregates. Ferrihydrite is 2 to 3 orders of magnitude more soluble than goethite at a given pH, with solubility decreasing when aged [280]. 2-line ferrihydrite dissolves in preference to goethite R1▪2 : Coagulation

689

D. I. VERRELLI

or hæmatite, often by a factor of order 103, with rapidly precipitated material dissolving somewhat faster than more slowly precipitated samples [280]. It is at least an order of magnitude more soluble than any of the other, more stable oxides [280]. Solubility products of the selected iron (oxy)hydroxide species at 25°C are given below [280]: ΔH°298 ~ ‒62kJ/mol p∗Ks0 ~ ‒1.4 α-FeOOH + 3H+ # Fe3+ + 2H2O 0.5α-Fe2O3 + 3H+ # Fe3+ + 1.5H2O ΔH°298 ~ ‒65kJ/mol p∗Ks0 ~ ‒1.7 ΔH°298 ~ ‒66kJ/mol p∗Ks0 ~ ‒2 γ-FeOOH + 3H+ # Fe3+ + 2H2O p∗Ks0 ~ ‒3 Fe(OH)2.7Cl0.3 + 2.7H+ # Fe3+ + 2.7H2O + 0.3Cl‒ 2 + 3+ fh-Fe(OH)3 + 3H # Fe + 3H2O * p∗Ks0 = ‒4.0 (‒3.6 aged) where 2fh- denotes 2-line ferrihydrite, and Fe(OH)2.7Cl0.3 is used here (perhaps incorrectly) to represent akaganéite. (Enthalpies from two references [280, 1094].) Further estimates for select parameters can be obtained from the literature [e.g. 547, 994], however the values given above are more self-consistent. The values given here indicate that hæmatite is less soluble than goethite — experimentally both have been identified as the least soluble under different conditions [280]. Hæmatite is normally up to an order of magnitude more soluble than goethite at a given pH, and frequently dissolves somewhat more rapidly than goethite [280]. The data suggest akaganéite is more soluble than ferrihydrite [280]. For 6-line ferrihydrite ∗ Ks0 is likely to be an order of magnitude † smaller (implying lower solubility) than that of 2line ferrihydrite: a value of p∗Ks0 ~ ‒3 would be consistent with the data tabulated above [280]. Predicted solubility is a function of temperature and ionic strength, and the actual solubility may differ further due to complexation, particle size, crystal defects, or ageing [280]. Particle size can greatly alter the solubility: for both hæmatite and goethite the solubility increases by about two orders of magnitude as particle size decreases from 1μm to 10nm [280]. As an example of complexation, normally positively-charged ferrihydrite becomes more soluble as the concentration of organic carbon is increased, as this counters the positive charge (and may even reverse it) [520]. The relative stability of hæmatite and goethite is a complicated topic. Salient details are discussed in Appendix S24. A key conclusion is that hæmatite is predicted to be thermodynamically more stable than goethite if the goethite particles are small [see also 280, 306, 307, 633, 634, 1109].

R1▪2▪6▪3(c)

Formation and transformation

The foregoing discussion brings up the point that stability diagrammes (e.g. POURBAIX Eh‒pH diagrammes) simply provide “a guide to what compound may form under any particular conditions” [279, 280]: • the kinetics of transformation from a metastable to a more stable phase may be very slow;

*

The formula is indicative only, and other researchers have variously proposed that for ∗Ks0 = [Fe3+][OH‒]x, x = 2.35 or 2.86, rather than 3 [280]. JUNG, JAMES & HEALY [547] quoted ΔH°298 ~ ‒83kJ/mol for am-Fe(OH)3.

†

Assuming a misprint in the text.

690



• values of standard GIBBS energies of formation reported in the literature vary considerably; • even the available thermodynamic data may not apply to metastable species actually present; and • stability may be affected by particle size through surface energy. The mechanism of precipitation of dissolved ferric ions as either amorphous or crystalline solids has been debated by various research groups. Evidence apparently supporting the growth of particles by aggregation of the initially-formed (‘primary’) particles, or by diffusion of solute to the surface of particles *, or by some combination of these has been reported [792]. SUGIMOTO & MURAMATSU [986] presented compelling arguments a g a i n s t the aggregation model for formation of hæmatite particles: Formation of monodisperse hæmatite particles argues against essentially 1. probabilistic aggregation processes. Dissolution–recrystallisation has “completely been proved” to be the formation 2. mechanism of condensed ferric gels. Observation of polycrystalline and porous structures consisting of a number of 3. subcrystals [792, 793] is due to the interruption (“blocked fusion”) of epitaxial † deposition of monomeric solvent by strongly adsorbed anions such as chloride (Cl‒) or sulfate (SO42‒), and they have also been seen in condensed ferric gels. 4. Dissolution and recrystallisation would have to occur to form the primary particles. The final number of particles was concordant with the initial number of nuclei. 5. 6. It is “geometrically impossible to form the nearly perfect monocrystalline lattice structure[s] [that have been observed] by aggregation of primary particles”. The observed surface roughness of some hæmatite particles [792, 793] can be 7. attributed to aggregation of co-existing β-FeOOH (akaganéite) in dried TEM specimens and to non-uniform adsorption of phosphate ions. The dissolution–recrystallisation process generally proceeds as [986]: The cation (Fe3+) is assumed to dissociate completely and essentially 0. instantaneously hydrolyse to form various ‘monomers’, possibly alongside some oligomeric species ‡. Particles of the less-stable phase (e.g. akaganéite, amorphous gel) precipitate. 1. 2. Primary particles of the more-stable phase (e.g. hæmatite, goethite), with lower solubility [280], crystallise out of solution. These grow by the deposition of monomeric solute in five elementary steps that occur in sequence [280]: a. Bulk diffusion of solvated ions or molecules to the surface of the crystal.

*

Such as according to the LA MER model [792].

†

Crystal growth on a crystalline substrate, where the substrate determines the orientation of the newly deposited crystal.

‡

The presence and nature of oligomers is not definitely known. SUGIMOTO & MURAMATSU [986] noted: Incidentally, if the dimensions of the primary particles are assumed to be as small as the level of oligomers similar to the monomeric solute in chemical nature, [then] we may have no reason to discuss the particle growth mechanism in distinction from the deposition of the monomeric solute. R1▪2 : Coagulation

691

D. I. VERRELLI

b. c.

Adsorption at and diffusion over the crystal surface. Partial or total dehydration, dehydroxylation, decharging and/or rearrangement of the ions at the surface [see also 573]. d. Integration of the ions into the structure. Counter-diffusion of released solvent from the crystal. e. Particles of the less-stable phase dissolve to balance the monomer being 3. deposited in point 2 — i.e. quasi ‘steady state’. (Oligomers may also be decomposed [573].) Eventually all of the less-stable phase has dissolved and recrystallised. 4. KNIGHT & SYLVA [573] also favoured a dissolution–re-precipitation process to explain FeOOH formation from ferric polycations. The size and shape of the particles changes progressively, influenced by OSTWALD ripening [986], which states that solubility is enhanced where the curvature (convexity) of the solid is higher (§R1▪2▪4▪5). The rate of ‘ripening’ is reduced as solubility decreases (here e.g. for high pH) [108]. For the system studied by SUGIMOTO & MURAMATSU [986] (solute at 100°C), the kinetics of akaganéite dissolution were faster than the deposition process, and the surface reaction was found to be the rate-limiting step. This implied that the ‘sharpening’ (or narrowing) of the size distribution was due only to the increase in mean size (with constant standard deviation), rather than any decrease in the standard deviation of particle size (“selfsharpening”) which is found for diffusion-controlled growth [986]. See also §R1▪2▪4▪4, OSTWALD’S rule of stages. According to MURPHY, POSNER & QUIRK [767]: Goethite forms by aging of the polycations under conditions where there is no anion penetration of the polycations or precipitates. Where penetration does occur β-FeOOH is formed. Lepidocrocite grows from the unpolymerized ferric species. High total ionic strength or the presence of anions with a strong affinity for ferric ions, e.g., chloride, will prevent its formation.

As noted earlier (§R1▪2▪4▪1(a)), iron may also be complexed by ‘foreign’ anions in solution. Experiments on monodisperse α-Fe2O3 particles produced from ferric chloride solutions have shown that the m o r p h o l o g y can be greatly altered in the presence of phosphate ([PO43‒] T 10‒4M) [986] and sulfate ([SO42‒]/[Fe] ~ 0.03, circa 90% incorporated) [929, 985]. It is unclear how relevant these results are to drinking water systems (e.g. [PO43‒] ~ 10‒7M [744]). The shape of iron precipitates has been found to be more irregular at lower concentrations (e.g. [Fe] < 0.1M) [792]. The shape may also be expected to be affected by the rate of formation of the particles. An indicative summary of formation pathways for selected solid iron phases is given in Figure R1-8. Other transformations are possible under specific conditions, e.g. β-FeOOH to α-Fe2O3 at elevated temperature [929, 985, 986].

692



VERY FAST pH ≥ 3

2-line Fh

I.a ?

I

NOT OBSEVRED FAST

Fe3+

II

I.b d.–r. SLOW

hydrolysis IV

II.a

Cl– or F–

III

pH ≥ 1

Very low pH VERY SLOW

IV.a SLOW

SLOW

6-line Fh

pH ~ 2, ~100°C

β-FeOOH

I.c

II.b SLOW

d.–r. SLOW

α-FeOOH

III.a ? SLOW V.a ?

α-Fe2O3

NOT OBSERVED

Figure R1-8: Summary of the formation of more stable phases upon the precipitation of iron from solution under environmental conditions. From information in CORNELL & SCHWERTMANN [280] and DIAKONOV et alia [307]. “Fh” is ferrihydrite. “d.–r.” denotes an ‘indirect’ mechanism of dissolution followed by re-precipitation as a different phase.

The surface Fe atoms of an iron oxide are LEWIS acids and quickly (within minutes to hours) co-ordinate with hydroxyl ions or water molecules, which share their ‘lone pair’ electrons [280]. Adsorbed water molecules usually dissociate to form hydroxyls, which thus cover the whole surface, and to which further water molecules form hydrogen bonds [280]. The exposed hydroxyl functional group makes the iron oxides amphoteric [280, 538, 924] [cf. 537]: bFe(OH)2+ # bFeOH + H+ bFeOH # bFeO‒ + H+ where b signifies a surface group *.

R1▪2▪6▪3(d)

Transformation of ferrihydrite

Ferrihydrite is a metastable phase, and is thermodynamically inclined to transform into goethite or hæmatite; the resultant phase depends upon the prevailing conditions and also kinetics [280, 395]. Goethite is formed via an ‘indirect’ dissolution–re-precipitation process (a “reconstructive” transformation) [280, 536, 539]. Until recently it had been accepted that hæmatite formed (more) directly through a (mostly) internal, solid-state process involving a sequence of aggregation, dehydration (or rather, oxolation) and pseudomorphic rearrangement (short-range crystallisation) [258, 280, 536, 538, 539, 910, 1053]. This was based on the proposed similarity of the ferrihydrite structure

*

In fact the hydroxyls may be singly, doubly, triply, or even geminately co-ordinated with surface Fe atoms [280, cf. 370, 537, 538]. In such cases amphoteric behaviour need n o t be assumed [537]. R1▪2 : Coagulation

693

D. I. VERRELLI

to the crystal structure of hæmatite [258, cf. 520]. Further evidence indicating that the ferrihydrite structure comprises dioctahedral chains of Fe (which ‘cross-link’ upon ageing) [520] and highlighting the essential role of water in the process * [280] (perhaps promoting prerequisite aggregation of ferrihydrite [280, 910]), suggests the importance of a “short-range via-solution” component of the process [279, 910] along with loss of hydroxyl [520, cf. 965]. (The latter structural model structure is similar to that of FeOOH [520, 536, 539], cf. §R1▪2▪6▪2, and thus resembles also pseudoböhmite [cf. 504], §R1▪2▪5▪3.) Following from the difference in mechanism, formation of goethite tends to be favoured when overall ferric solubility is higher [536, 910]. The localised, internal nature of the transformation to hæmatite means that this route typically leads to the formation of very small particles with very small crystalline domains [536]. In both cases there is normally an ‘induction period’ where a nucleation process precedes the main transformation [280]. A summary of some factors affecting the transformation of ferrihydrite (especially the 2-line form) to a more stable phase is presented here: • p H . The pH affects the ferric hydrolysis species present; monovalent species (dominant at neutral to alkaline pH) are believed to be the most suitable growth units for goethite [280]. The rate of transformation of ferrihydrite to goethite and hæmatite increases monotonically as pH increases from 2 to 12, being of order years at pH 2, months at pH 7 to 8, and days at pH 10 (at 24°C) [280, cf. 583]. Near the p o i n t o f z e r o c h a r g e (p.z.c.), at pH approximately 7 to 8 [cf. 325], aggregation of ferrihydrite is promoted over dissolution, and so transformation to hæmatite predominates [280, 538]. The proportion of hæmatite formed is maximised in the pH range of about 6 to 8 (or 5 to 8 [536]), comprising about 20% of the total at 4°C, 40% at 15°C, 60% at 20°C, up to about 70% at 30°C [280, 910]. At pH values further from the p.z.c, approaching 4 or 12, ferrihydrite solubility increases and more goethite forms [280, 910]. At pH values between 2 and 5.5, goethite predominates regardless of temperature (below 30°C) [280, 910]. At the extremes of pH (i.e. pH < 4 or pH > 14) the proportion of hæmatite formed begins to rise again, although (below 30°C) goethite still predominates [cf. 258]; the increasing concentrations of multivalent ferric ions may account for this change [280, 538]. • T e m p e r a t u r e . The rate of transformation increases with temperature [280]. As suggested above, increasing temperature promotes dehydration and thus the formation of hæmatite [280, 910]. At temperatures below about 18°C, goethite predominates regardless of pH [280, 910]. Retardation due to foreign species (see below) becomes weaker as temperature increases [280]. Various investigations have shown the transformation of ferrihydrites into hæmatite under dry heating at 127°C (requires months, i.e. order 103h), 227°C (order 101h), and 327°C (order 100h) † — interestingly, 6-line ferrihydrite was found to be less prone to structural transformation than the 2-line form under these conditions [280] (no change observed at 300°C [258]); furthermore, if the heating reduces available water sufficiently (below approximately 10 to 15%m), then transformation to hæmatite will be prevented [280].

*

Adsorbed water is sufficient for this, although ‘free’ bulk water can also be used [280]. At temperatures >300°C hæmatite is able to form in the absence of water through an alternative mechanism [520, 910, 965].

†

The presence of foreign elements reduces the transformation rate [280].

694



• W a t e r a c t i v i t y . A reduced water activity, such as at high i o n i c s t r e n g t h or for a i r - d r i e d samples, decreases the rate of transformation in favour of hæmatite [279, 280, 306]. Unit water activity does not prevent dehydration, and in fact may aid iron mobility [279]. • I o n i c s t r e n g t h . Apart from its effect on water activity, a high ionic strength promotes aggregation of ferrihydrite via electrostatic attraction over dissolution, and so transformation to hæmatite predominates [279, 280]. • F o r e i g n s p e c i e s . Ions in solution typically retard nucleation or growth of goethite through competition for available surface sites on the crystal or nucleus, favouring transformation to hæmatite [280, 520]. The model of ferrihydrite in which the surface Fe species are tetrahedrally co-ordinated * [cf. 573], rather than the more usual octahedral co-ordination, suggests an especially high amenability to adsorption of foreign species at these ‘co-ordination–unsaturated’ sites [520]. Anions, ligands, and cations may be adsorbed onto or incorporated into ferrihydrite, and most commonly suppress its reactivity toward internal ordering and/or dissolution [280]. Hæmatite formation can be retarded if adsorbed species hinder the ferrihydrite aggregation [280]. “The effects of foreign species (especially retardation) are particularly strong at room temperature where the transformation may be retarded for months or even years; they become weaker as temperature rises.” [280, see also 520]. Retardations up to 105y have been proposed [536]. o NOM species including fulvic [583] and humic [520] acids inhibit the transformation of ferrihydrite, and increase the p r o p o r t i o n of hæmatite formed. The effect is strong at a molar ratio, fulvic acid to Fe, of 0.2 [583]. When fulvic acid was added before precipitation there was greater Fe complexation and greater inhibition of crystallisation [583]. The mechanism is probably similar to certain small hydroxy–carboxylic polybasic acids (e.g. citrate, tartrate) which complex ionically through dissociated ‒COOH moieties, and especially where the groups are vicinal (e.g. oxalate) [583] [see also 536, 538, 539, 675]. Oxalate (specifically) also promotes hæmatite crystal nucleation; it was proposed that the Fe–oxalate complex acts as a “template”, with similar Fe–Fe distances to hæmatite [583]. o Silicate has a high affinity for the ferrihydrite surface and strongly retards its dissolution and transformation, with hæmatite being favoured in the resultant phase [280]. Silicate levels of [Si]/[Fe] = 0.0001 are sufficient to obtain this outcome [280]. (In solution silicate can also inhibit nucleation of goethite [280].) The presence of pedogenic minerals, in particular various clays, tended to slow ferrihydrite transformation under ambient conditions (pH 5) and promoted the formation of hæmatite over goethite [279]. “Natural ferrihydrites precipitated in cold surface waters frequently contain a few per cent Si which may [...] be the reason for their long-term stability” [280]. The magnitude of retardation caused

*

The presence of tetrahedral ferric iron has been widely disputed [520] (cf. aluminium [1100]); according to LIVAGE [674]: “Precipitation from FeIII solution always leads to hexacoordinated FeIII species [...]”. However the leading alternative model, comprising dioctahedral chains of Fe (which ‘cross-link’ upon ageing), can be similarly reconciled except that in this case the labile sites are assigned to locations with “lesser [...] than average Fe–Fe octahedral coordination” (at the ends of the chains) [520]. This model structure is similar to that of FeOOH [520], and thus resembles also pseudoböhmite [cf. 504]. R1▪2 : Coagulation

695

D. I. VERRELLI

by the presence of silicon is significantly greater when the silicon is incorporated into the ferrihydrite structure (during formation), rather than being adsorbed onto the surface (i.e. added to the outside of pre-formed ferrihydrite) [280]. o Soil minerals generally behave similarly to silicates, in that they tend to retard or inhibit transformation (except muscovite), and favour hæmatite over goethite (except “soil clay”) [520]. The effects roughly follow the order: allophane > (smectitic) soil clay > smectite > kaolinite > illite ~ gibbsite > quartz [520]. Part of the effect is due to aluminium [520]. o Aluminium is sometimes added in a ‘mixed’ coagulant. Aluminium at levels of around 5% relative to the sum of the two metals retards the transformation of ferrihydrite to more stable phases such that it takes years to occur at room temperature at pH 5 to 7 [279] (again the effect is stronger in the case of coprecipitated aluminium [280]). Aluminium especially hinders the dissolution and nucleation/growth processes, and a level of 2.5% was sufficient to fully suppress goethite formation at room temperature at pH 4 to 7 [279]. o Chloride ions have been linked to retardation of the transformation to goethite [see 388], but have also been claimed to favour goethite over hæmatite [see 1053]. Sulfate ions have been reported to retard transformation to goethite and hæmatite even more strongly [520]. • S e e d c r y s t a l s . The presence of seed crystals of either goethite or hæmatite (and possibly even the more ordered regions in ferrihydrite [279]) promotes the formation of goethite (not hæmatite) [280], as these seed crystals act as nucleation sites and enhance the kinetics (or rather, minimise the ‘induction’ time).

R1▪2▪6▪4

Industrial practice

Coagulation with either ferric sulfate or ferric chloride is generally optimised between pH 5.0 and 8.5, with 7.5 a typical value [1113]. The Macarthur Water Filtration Plant (United Utilities Australia) supplying Sydney is running at around pH 9.0, just outside the suggested range (see §3▪2▪6▪2). In contrast, United Utilities finds pH between 4.5 and 5.5 is typically optimal [436]. WILSON [1124] gave an example where at a Yorkshire Water plant treating highly coloured water A254nm reduction was optimised for ferric sulfate in a broad range around pH 4.9. For enhanced coagulation especially, pH values of 4.0 to 5.5 are preferred [668]. BLACK et alii [159] identified 3.6 to 4.1 as typical values for the optimum coagulation pH. BOLTO [171] identified pH values “slightly less” than those for alum as typical, i.e. <5.5. JARVIS et alii [525] showed a pH between 3.5 and 6.0 to be optimal. BLACK and co-workers [159] reported that optimal coagulation with ferric sulfate achieved superior colour removal compared to aluminium sulfate, and occurred at a lower pH value, namely 3.5 compared to 5.0 (approximately), respectively [155]. This difference is attributed to the ferric ion being a stronger acid than the aluminium ion [159]. Interestingly, BLACK et alii [159] recommend that, subsequent to coagulation at some optimal pH, the pH then be raised (if necessary) above 6.0, followed immediately by filtration, in order to maximise the removal of colour and (residual) iron. Orica (Melbourne, Australia) claim optimal performance of FeCl3 for 4.5 ≤ pH ≤ 8.5, which they compare to 5.5 ≤ pH < 7.5 for alum [294, 858]. An advantage of ferric coagulants over aluminium sulfate is that they are less sensitive to pH in terms of removal of colour or organics [1124]. 696



The dose of ferric chloride (FeCl3) added varies from around 2 to 4mg(Fe)/L in conventional coagulation up to 11mg(Fe)/L in enhanced coagulation [854]. Doses may be up to 18mg(Fe)/L in waters that are difficult to treat [1124]. BLACK et alii (1963) [159] reported that no flocs and ineffective colour removal were observed from coagulating highly coloured waters (e.g. > 300mg/L Pt units) at ferric sulfate doses less than about 12mg(Fe)/L — at intermediate raw water colour (around 80mg/L Pt units), about 5mg(Fe)/L sufficed. Extrapolation of the (nearly linear) relationship suggests that for raw waters of low colour the minimum ferric dose may be on the order of 3.5mg(Fe)/L [159]. Doses of e.g. 1 to 6mg(Fe)/L have been suggested as appropriate for typical industrial application in combination with a polyelectrolyte [229]. JARVIS et alii [525] quoted a one-to-one ratio of raw water TOC and Fe dose as a rule of thumb for optimal treatment of coloured water. BLACK and co-workers found that, for m o d e r a t e l y t o h i g h l y coloured waters, the required ferric sulfate dose increased approximately linearly with colour, and that there was a gradual decrease in the coagulation pH at which the greatest colour removal was achieved, e.g. (for one raw water) from around 3.8 to 3.45 [155, 159]. Published stability–coagulation diagrammes showing the solubility curves for the (amorphous) hydroxide precipitates of aluminium and iron(III) [90, 155, 326] support this notion, as an increase in the coagulant dose leads to a decrease in the lowest pH at which precipitation may be attained, provided that re-stabilisation, i.e. charge-reversal, of the raw water contaminants does not intrude [90, 155] (say, because the coagulant dose is very high — as consistent with the original research). However the principle could not be taken as universal, due to the different types of natural organic matter (NOM) which contribute to colour, some of which are more highly coloured than other types, whereas the coagulant demand may not depend upon the degree of colouration [359].

R1▪2▪7

Magnesium

The chemistry of magnesium is more straightforward than that of iron or aluminium. As magnesium is not a commonly-used coagulant, it is helpful to first review the historical context.

R1▪2▪7▪1

Application

Magnesium chloride was used as a coagulant in the mineral industry circa 100 years ago [857]. Much of the pioneering work on drinking water treatment coagulation using magnesium was carried out by BLACK, leading to several patents [e.g. 156]. Part of the motivation for this was to “avoid environmental contamination” due to conventional water treatment sludges “mainly composed of water, clay and the coagulant used in the treatment” (especially alum) [156]. It was also hoped to realise financial savings [1022] and provide a means of controlling alkalinity and hardness [1021]. R1▪2 : Coagulation

697

BLACK envisaged a flexible system wherein operation would be determined by natural magnesium (and calcium) levels in the raw water: • L o w levels of magnesium imply low water hardness, which can exacerbate corrosion * [34, 156]. Addition of lime (CaO) and magnesium in a “suitable reactive form” (see below) causes in situ precipitation of m a g n e s i u m h y d r o x i d e and calcium carbonate in the raw water, which coagulates turbidity elements and occludes or adsorbs colouring matter [156]. Carbonation † of the sludge allows recovery of a basic m a g n e s i u m h y d r o g e n c a r b o n a t e (Mg(HCO3)2) solution, which is directly recycled to provide a portion of the magnesium for coagulation and to avoid water wastage [156]. Insoluble calcium carbonate and associated turbidity elements may be disposed of, or a portion of the lime may be recovered [156]. Some magnesium remains in the water to increase its hardness [156]. • I n t e r m e d i a t e levels of magnesium imply that the operation is approximately selfsufficient, in that the recovered magnesium is just enough for the water treatment process without significant surplus or deficit. • H i g h levels of magnesium indicate that the water is too hard, meaning that it will form scale and will not lather readily, and requires softening [34]. Conventional treatment with lime results in the formation of a waste lime sludge in which “sizeable amounts of treated water” are also entrapped [156]. Carbonation of the sludge as above effects a phase separation of the calcium and magnesium components. The recovered magnesium hydrogen carbonate solution may be decarbonated to provide a (hopefully! [1022]) saleable magnesium carbonate solid product — as a normal hydrate, MgCO3·3H2O, or as a basic form [cf. 942] — and to reduce the environmental burden [156]. In all cases a portion of the sludge generated, containing precipitated Mg(OH)2, will be recycled to the coagulation chamber, which can ‘seed’ further precipitation and coagulation [156]. Recovery and recycle are more difficult at extremely high levels of colour (say, above 150mg/L Pt units) [1022]. BLACK [156] claimed that the sludge arising from coagulation with magnesium would “usually have a solids content ranging from about 2 to 8% solids”. The fresh sludge is a slurry of CaCO3·Mg(OH)2 with clay and other siliceous material, but this will be modified if magnesium recovery units are operated. It is not clear whether the susceptibility of the magnesium components of the sludge to dissolve upon carbonation represents a benefit, in ensuring carry-over ‘disappears’ [cf. 1021], or whether in certain circumstances it may be problematic in releasing contaminants back into solution. Typical characteristics of raw water in each of the above three categories are outlined in Table R1-7.

*

More recently low water hardness levels have been linked with adverse health effects in humans (see §R1▪2▪7▪6), although the latest Australian Drinking Water Guidelines [34] do not impose any health guideline values.

†

In practice the temperature of this process is closely controlled (in the range 15 to 21°C) so as to avoid the contamination of the lime components with magnesite and allow recovery of a useable product [156].

698


Table R1-7: Characteristics of raw waters containing various levels of magnesium [156].

Characteristic Calcium [ppm of Ca2+] Magnesium [ppm of Mg2+] Total hardness [ppm as CaCO3] Non-carbonate hardness [ppm as CaCO3] Turbidity [JTU *]

Low 1–29 0–6 5–87 0–25 0–1000

Magnesium level Intermediate 15–62 5–12 60–187 5–115 0–1100

High 15–120 5–34 60–428 5–174 0–4800

A desirable level of magnesium in municipal drinking water is up to 9ppm (as ion) [156]. There is currently no specific guideline value given in any of the well-known national or international recommendations [34, 39], but see also the discussion under ‘Health aspects’ in §R1▪2▪7▪6. Magnesium has been used to perform coagulation on full-scale treatment plants. One such plant was at Kansas City, where the raw water quality (~66mg(Mg)/L) meant that magnesium did not need to be added, and the process functioned essentially as a watersoftening operation allied with a high-pH (~11.4) recirculation loop [227].

R1▪2▪7▪2

Reagents

Magnesium species suggested as being in a reactive form suitable for use as make-up material include [156]: • hydrated normal magnesium carbonate (MgCO3·3H2O [also 28]), • dolomitic hydrate, • dolomitic quick lime, • magnesium oxide (MgO) [1021], and/or • magnesium hydroxide (Mg(OH)2). The species are listed in approximate order of decreasing favourability. Normal hydrated m a g n e s i u m c a r b o n a t e is more favoured [156], but may not be readily available commercially [1021]. In 1974 BLACK & THOMPSON [160] reported using Mg(HCO3)2 at plant scale. Other potentially suitable species include: magnesium chloride (MgCl2), which acts in the same way as a raw water of high magnesium content, (this may result in increased residual hardness) [166, 1021]; and magnesium sulfate (MgSO4) [449, 711, 916]. In some locations magnesium salts may be conveniently and economically available as either seawater (more useful for wastewater treatment) or bitterns (residual concentrated liquor remaining after solar drying of seawater in table salt production) [916, 1001]. Addition of pre-formed Mg(OH)2 (as by recycle) provides some enhancement by increasing the availability of adsorption sites and acting as a nucleation site to promote co-precipitation of Mg(OH)2–NOM [166] (see below). Basic, light magnesium carbonate (4MgCO3·Mg(OH)2·3H2O) has also been successfully used — at least in laboratory studies [251]. In this case stock solution was prepared in distilled

*

Jackson Turbidity Units are an obsolete measure of similar magnitude to NTU (see §3▪4▪3▪1). R1▪2 : Coagulation

699

water at approximately 90mg(Mg)/L * for doses up to about 3mg(Mg)/L; for higher doses magnesium would have to be added as a slurry [251]. Laboratory studies have demonstrated that recycled magnesium carbonate was comparable in performance to the fresh chemical [251, 1021]. Hence a suitable source of magnesium would be from WTP’s treating (or softening) hard raw waters [156, 1021]. Due to the convenient or economical use of dolomitic lime [166, 711] it may be seen that magnesium coagulation is closely associated with softening processes (lime itself being the main chemical used in conventional softening). It has been shown that the Mg(OH)2 precipitate is a much more effective remover of NOM [166] and (other) colloidal matter [711] than CaCO3 . A potential issue with dolomitic quick lime (largely CaO and MgO) is that the magnesium may not become completely hydrated to Mg(OH)2, and therefore not all be available, lessening the enhancement of DOC removal [166]. When added as a magnesium-containing (dolomitic) lime, or through separate addition of a magnesium compound and lime, effective proportions of Ca and Mg (in the precipitate) have been reported with wide variation: from 40%m Mg [711] to only a small fraction (say 2%m) Mg [166]. It should be noted that what are sometimes called “magnesium carbonates” are in fact “hydrated basic magnesium carbonates” containing approximately 40 to 45% MgO [180, 563]. These are typically available in two classifications, namely “light” and “heavy” which both conform to the general formula xMgCO3·Mg(OH)2·yH2O [563] — the reason that they are also termed “magnesium hydroxy carbonates” [180]. The light form (magnesia alba levis) has x = y = 3 (or similar †) and exists as a voluminous powder [563, 716]. The heavy form (magnesia alba ponderosa) has x = 3 and y = 4 (or similar ‡) and is about 2 to 2.5 times denser than the light form [563]. Both are classified as practically insoluble in water § [716], but may be dissolved readily in dilute acid [563]. The key chemical equations involving magnesium are [156, 1021]: + CaCO3 (s) + 2H2O Mg(HCO3)2 + Ca(OH)2 # MgCO3 + Ca(OH)2 # Mg(OH)2 (s) + CaCO3 (s) MgCO3 MgSO4 + Ca(OH)2 # Mg(OH)2 (s) + CaSO4 Magnesium sulfate as in the last equation is assumed to be present naturally in hard waters [156]. The carbonation proceeds as [156]: Mg(OH)2 (s) + CO2 + xH2O # MgCO3·yH2O # Mg(HCO3)2 + zH2O MgCO3·yH2O + 2CO2 An undesirable competing reaction here is Mg(OH)2 (s) + Mg(HCO3)2 + xH2O # 2MgCO3·wH2O (s) ,

*

This is consistent with the solubility in cold water of “natural hydromagnesite” (3MgCO3·Mg(OH)2·3H2O) given in WEAST [1106] as 0.04g/100mL, or the equivalent of roughly 106mg(Mg)/L (this data removed from later editions [662]).

†

For example x = y = 4 (hydromagnesite) [180, 563], or x = 4 and y = 3 [251].

‡

For example x = 4 and y = 5 (dypingite) [180, 1021], cf. x = y = 3.2 [716].

§

The heavy form may be slightly more soluble [716], cf. CHITRANSHI & CHAUDHURI [251] (cited pp. 699f.).

700


where w may be 3 or 5, which occurs when the addition of magnesium hydroxide is too rapid and results in precipitation of magnesium carbonate [156]. In line with this, the magnesium content of the sludge prior to recovery is to be limited to less than the equivalent of 6.5g(MgO)/L [156], i.e. 3.9g(Mg)/L. It is suggested that the above procedure is more compatible with froth floatation * to separate (coagulated) turbidity elements [156].

R1▪2▪7▪3

Hydrolysis, polymerisation, and solubility

Significant hydrolysis of magnesium occurs only under alkaline conditions, according to Mg2+ + H2O # MgOH+ + H+ p∗β1 = 11.44 (±0.1) 2+ 4+ + p∗β44 = 39.71 (±0.1) 4Mg + 4H2O # Mg4(OH)4 + H at 25°C in the limit of zero ionic strength (estimated standard deviation in parentheses) [118]. The above tetramer likely has the formula [Mg4(OH)4(H2O)12]4+, corresponding to a compact, symmetrical tetragonal cluster of Mg species surrounded by four μ3-OH groups (Mg retains 6-fold co-ordination) [466, 538]. It is expected to form following olation of [Mg(OH)(H2O)5]+ to edge-sharing dimers, [Mg2(OH)2(H2O)8]2+, containing two μ2-OH groups, which condense to the tetramer [466, 538]. If hydrolysis to [Mg(OH)2(H2O)4]0 is possible at high pH, then rapid and infinite olation will result in precipitation of Mg(OH)2 [466]. This would proceed through olation to a compact planar tetramer, [Mg4(OH)8(H2O)8]0, followed by bidimensional olation of the tetramers to yield the l a m e l l a r structure of b r u c i t e , Mg(OH)2 [538] [cf. 466]. The solubility is given as [118] pK = ‒p∗Ks0 = 16.84 Mg2+ + 2H2O # Mg(OH)2 (s) + 2H+ with interpretation illustrated by Figure R1-2. (KVECH & EDWARDS [614] cited values of 17.68 for “fresh Mg(OH)2” and 17.12 for brucite at 20°C — i.e. decreasing solubility.) This data supports the status of pH 8.5 to 9 as a critical threshold, above which magnesium almost entirely precipitates, and below which it is almost entirely dissolved (predominantly as Mg2+) — at equilibrium, in the absence of confounding ions [614, 1022]. In practice precipitation is shifted up by about 1 pH unit (perhaps due to enhanced solubility of the initial phase [614]), with onset at pH ≈ 9.5, significant generation at pH > 10.5, and essentially complete precipitation at pH ≥ 11.0 to 11.5 [916]. (An old tabulation listed 10.5 as the pH for precipitation of 0.2M Mg solution [505].) Equivalently, more magnesium remains in solution if either insufficient time (e.g. < 4h) is allowed to reach equilibrium or other ions that are present enhance solubility [1022]. The solubility of magnesium carbonate is of order 1.2g/L, so for practical doses it must be fed as a slurry [1021].

*

Using agents such as tall oils or organic amines, in particular fatty acid amines such as dodecyl amine [156]. R1▪2 : Coagulation

701

R1▪2▪7▪4

Solid phases and transformation

It has been reported that colloidal matter, including NOM and silicates (or silica), is adsorbed onto the magnesium hydroxide precipitate, which forms particles of 30 to 40μm size [711] of positive superficial charge [166, 916]. The mechanism of magnesium coagulation is described as predominantly an enmeshment action, as in conventional sweep coagulation [251]. Pre-formed magnesium hydroxide aggregates are only about half as effective at removing bacteria or turbidity [251]. The initial hydrolysis of magnesium is expected to yield a m o r p h o u s hydroxide precipitates of magnesium at high pH (although it is possible that n a n o c r y s t a l l i n e domains may be present [890]), so the formula Mg(OH)2 may be taken as i n d i c a t i v e only. The precipitates have a high specific surface area, typical of an aggregate structure [166]. The literature [e.g. 890] indicates that these amorphous (or paracrystalline) magnesium hydroxides are more susceptible to transform to a crystalline phase (namely brucite) upon ageing than for either aluminium or iron [see also 556]. Prior to ageing they may be slightly more hydrated than brucite [556, 890]. Brucite tends to form hexagonal platelets with (001) basal plane [537]. SAKHAROV et alia [890] describe a “memory effect”, whereby the “crystallisation ageing” of magnesium chloride (MgCl2·6H2O), magnesium nitrate (Mg(NO3)2·6H2O), and magnesium sulfate (MgSO4·7H2O) in excess potassium hydroxide (KOH) over a period of hours to days proceeded in different ways. Specifically, magnesium hydroxide synthesised from the sulfate exhibits uniform growth, whereas for the chloride or the nitrate crystal growth is favoured along certain axes [890]. In these systems, the crystalline phases took on the form of “porous brecciated aggregates” [890], i.e. loose aggregates of angular crystal ‘fragments’. It is important to note that crystallisation was not observed to progress during storage in air [890]; a strongly alkaline environment appears to be required.

R1▪2▪7▪5

Industrial practice

Recommended doses are typically in the range 0.6 to 1.3mg(Mg)/L [251], depending upon raw water quality, and may be estimated based on the correlation [1022]: Dose [mg(Mg)/L] = [R1-1] 1.46 + 0.005 Θ + 0.081C ‒ 0.005 alkalinitytotal + 0.025 hardnesstotal , where Θ is the turbidity and C is the “organic colour” (presumably equivalent to true colour), which had R2 = 0.68 *. THOMPSON, SINGLEY & BLACK [1022] used higher doses of approximately 2 to 7mg(Mg)/L in laboratory studies on 17 natural waters, and a higher dose still in pilot-scale testing (~11mg(Mg)/L †). MAVROV et alia [711] apparently used a much higher dose, of order 100mg(Mg)/L, with a reaction time of about 2.5h.

*

The independent variables are given in the correlation in d e c r e a s i n g order of statistical influence on the dosage; however, the predicted dose based on the correlation will usually be dominated by C [1022].

†

With approximately 8mg(Mg)/L naturally present in the raw water [1022].

702


In laboratory studies TAMBO & WATANABE [997] used approximately 2.4mg(Mg)/L as magnesium chloride to treat a turbid water (50mg/L kaolinite clay), and 24mg(Mg)/L to treat a naturally coloured water (C ~ 77mg/L Pt units). In treating h i g h l y - c o l o u r e d textile dyeing effluent TAN, TENG & OMAR [1001] used doses of MgCl2 at about 400 to 1000mg(Mg)/L and pH 10.5 to 11.0, with negligible colour removal at pH ≤ 9, and decreasing efficacy above pH 11. The response at both of these extremes of pH is explained in terms of solubility, with minimum solubility occurring around pH 11 (depending upon Mg dose) [1001]. Some wastewater treatment plants coagulating with ferric chloride have found their dosages can be reduced by spiking the influent to the plant with magnesium-laden seawater (or bitterns) [916]. Aside from precipitation of Mg(OH)2, it has been speculated that double layer compression resulting from increased ionic strength may be a second mechanism for enhancing colloid destabilisation and aggregation [916]. (A ‘ballast’ effect may also occur [cf. 1128, 1129], as in §8▪3▪5.) CHITRANSHI & CHAUDHURI [251] found that the effectiveness of magnesium in removing turbidity and bacteria increased as the pH increased from 9.0 to about 12.0. The incremental benefits of operating above pH 11 were small, except at the lowest of doses, because most of the magnesium precipitated as Mg(OH)2 in the pH range 10.5 to 11.0 [251]; moreover, extra operational difficulties may be anticipated when running at such an alkaline setting. Thus, an optimum pH of 11.0 was nominated. BOB & WALKER [166] also referred to the need for an increase in operating pH above conventional levels, again in the range 9 to 11 (preferably at the higher end), depending upon dose; advantages were said to be increased Mg(OH)2 precipitation and enhanced NOM adsorption. MAVROV et alia [711] maintained pH values at around 11.1. SEMERJIAN & AYOUB [916] recommended pH values of 11.0 to 11.5 for magnesium coagulation. In laboratory studies TAMBO & WATANABE [997] reported optimum coagulation of kaolinite clay from water at a pH of 11.6, and used pH 11.4 for coagulation of naturally coloured water. In 1971 THOMPSON, SINGLEY & BLACK [1022] reported that WTP costs were minimised for magnesium coagulation by operating at a pH between about 11.0 and 11.4, depending on relative chemical purchase costs. At an AWWA seminar in 1973, THOMPSON & BLACK [1020] claimed that magnesium coagulation operated optimally at pH 11.2 to 11.5, which produced a n o n - c o r r o s i v e treated water. (This may have implicitly included ‘restabilisation’ of the water with CO2 to a pH of 10.5, or ‘stabilisation’ to pH 9.0 [1022].) 1972 studies were carried out with a target pH of 11.00 to 11.25, however values as low as 10.75 still gave adequate treatment [1021], and pH 10.50 is apparently high enough for certain raw waters [1022]. For comparison, the current ADWG [34] give æsthetic guideline values for drinking water pH as 6.5 to 8.5, with no health-based range. Below this range or for pH > 11 water is likely to be corrosive, above the range it is more likely to cause scaling, taste and odour problems, or chlorination inefficiencies — up to pH 9.2 at the customer tap “may be tolerated” [34]. It is suggested that pH values outside the range 4 to 11 may be harmful to health [34]. Nowadays the process has fallen out of favour due to economic considerations, and no existing full-scale WTP’s are known to practice magnesium recovery any longer [cf. 282] — it is practised in the pulp and paper industry, however [289], and occurs incidentally in lime– softening plants practising lime recovery [282]. Also, renewed interest appears to have been generated in the technology of late, perhaps sparked by a series of papers published by R1▪2 : Coagulation

703

DZIUBEK & KOWAL through the 1980’s [e.g. see references in 916], just as the early champion was BLACK. The cost of magnesium chloride as a coagulant is intermediate to that of conventional alum and PACl (polyaluminium chloride) [1001]. Lime costs were reported to halve by THOMPSON & BLACK at a 1973 AWWA seminar [1020]. The technology is most cost effective for low-alkalinity raw waters [1022].

R1▪2▪7▪6

Health aspects

Magnesium is one of the two predominant components of water ‘hardness’, and has been associated with a protective effect against a variety of diseases, primarily cardiovascular disease (CVD), with anecdotal and scientific reports dating back to 1957 [7, 68, 288, 938, 939]. While previous WHO guidelines had judged that the evidence of a c a u s a t i v e association was not yet conclusive [7], the mounting body of evidence has been proving more and more persuasive, so that a subsequent WHO meeting of experts (Rome, 2003) reached a consensus that: On balance, the hypothesis that consumption of hard water is associated with a somewhat lowered risk of CVD was probably valid, and that magnesium was the more likely contributor of those benefits.

as reported in 2005 [288]. A minimum (guideline) level of magnesium in drinking water of 10mg/L was mooted [288] [cf. 939]. The scientific community has not universally accepted this conclusion [288, 938, 939], and debate and research are ongoing [63, 68].

R1▪2▪8

Alkalis

Alkalis include [28]: calcium carbonate (CaCO3); dolomitic lime (58% CaO, 40% MgO); hydrated lime (Ca(OH)2); magnesium oxide (MgO); sodium carbonate (Na2CO3); and sodium hydroxide (NaOH). NaOH and varieties of lime appear to be the most popular. Each substance has advantages and disadvantages, and the ultimate choice will also be influenced by local conditions [see e.g. 486, 754, 916]. Addition of liming agents for alleviation of acidity and aluminium toxicity problems may provide an interfacial disequilibrium such as to favour the formation, even if only transiently, of tridecameric aluminium (i.e. the Al13 species) [146]. When alkali is dosed into a turbulent fluid the mixing processes typically have a timescale of order milliseconds [cf. 804], which is much slower than the timescale for proton exchange [538].

R1▪3

Flocculation

As stated (§R1▪2▪1), flocculation generally involves the addition of polymer, which may be ionic or non-ionic, to achieve essentially the same result as in coagulation. Under appropriate conditions the polymer binds to one or more particulates, leading to

704


aggregation. The polymer may also bind to other polymer strands, forming larger, stronger flocs. Polymer treatment can be applied both to raw water colloids at the head of the WTP and to the settled or dewatered sludge further downstream. Strictly both of these applications are forms of flocculation. Yet in practice they use different polymers and yield qualitatively different materials: where it is useful to draw a distinction, in the present work the former procedure is called ‘flocculation’ and the latter is called ‘ p o l y m e r c o n d i t i o n i n g ’ .

R1▪3▪1

Sequence of events

GREGORY [428] outlined a comprehensive theory for dynamic aspects of polymer flocculation [see also 80]. In summary the key steps are [cf. 428]: 1. mixing of polymer into the suspension; 2. adsorption of polymer moieties onto the particles; 3. re-conformation of the polymers (generally resulting in a less-extended conformation, i.e. through adsorption at additional moieties); 4. floc formation by interactions of colliding particles with adsorbed polymer; and 5. rupture of flocs. These steps do not necessarily occur in the sequence listed above [428]. Rather, there is competition of steps 3 and 4, which may both occur following the initial adsorption; also, rupture and formation will eventually establish a dynamic equilibrium which may involve re-conformation as well. This is shown schematically in Figure R1-9. Externally-applied shear enhances the rate of polymer mixing (step 1), particle collision (3 or 3′), rupture (5 or 5′), and desorption (‒2); in the absence of significant shear gradients, these processes occur by BROWNian motion and thermodynamics [see 428]. However the enhancement of shear is only significant above a certain size range, roughly on the order of the KOLMOGOROV turbulence microscale (see §R1▪4▪2 and §R1▪4▪4▪3) [cf. 428]. Although not shown in the diagramme, it is possible at high shear rates for polymer chains to be broken [428, 491]. Mechanisms such as this or re-conformation of polymer chains after rupture imbue a degree of irreversibility. In the present work polymer ‘size’ is likely to be of order 102nm (Zetag 7623) to 103nm (Magnafloc 338) [cf. 512, 565, 861], depending upon extension in the fluid [428] (the cited flocculants are not highly charged). Following GREGORY’s [428] simple application of SMOLUCHOWSKI’s equations for perikinetic and orthokinetic collision frequency — assuming equal (perfect) bonding efficiencies and ignoring hydrodynamic effects — transport by shear processes is dominant for particles larger than 100nm (G = 1000s‒1) to 102nm (G = 10s‒1) given a polymer ‘size’ of 1000nm, or for particles larger than 102nm (G = 1000s‒1) to 103nm (G = 10s‒1) given a polymer ‘size’ of 100nm. These dimensions are all much smaller than the respective dKolmogorov. (This lengthscale and the characteristic velocity gradient, G, are explained in §R1▪4▪1▪1 and §R1▪4▪2.) Under normal circumstances polymer–particle encounters will be more common than particle–particle encounters (polymer–polymer encounters are ignored) [cf. 428].

R1▪3 : Flocculation

705

1

2 –2

4′

3

5′

4 3′

5

Figure R1-9: Schematic of polymer flocculation dynamics; extended version of GREGORY’s [428] diagramme. Circles represent particles; wriggly lines represent polymers. See text for meaning of numbers.

Experimental studies indicate that the initial adsorption upon polymer–particle collision is very rapid, but the re-conformation time could be on the order of seconds, minutes [1138] or hours (or even days [80]) [cf. 804] depending on surface coverage (longer for higher coverage) and polymer size [428]. The frequency of particle–particle encounters is enhanced (step 4′) if polymers extend out from the surface, as would occur when re-conformation is slower than the particle–particle collision rate [80, 428]. (The effective layer thickness following re-conformation at the surface can be an order of magnitude smaller [80].) High particle concentrations and long polymer chains favour this ‘non-equilibrium’ pathway [80, 428]. The mechanism is expected to be less important for cationic polymers adsorbing onto negatively charged particles, where the conformation would be rather flat [428, 538], and charge-neutralisation would be more important. The ionic strength affects the polymer conformation in the bulk, and hence also the extent of relaxation upon adsorption [80]. This effect on its own indicates slower aggregation at high ionic strength [80], unlike charge-driven mechanisms (cf. §R1▪3▪2▪3). Evidently the initial mixing and adsorption are on the critical path to building flocs.

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Under (in)appropriate conditions, adsorbed polymer species including polyelectrolytes can stabilise particles of e.g. iron oxide through “steric stabilisation”, which works through two recognised mechanisms [280]: • v o l u m e r e s t r i c t i o n , wherein interpenetration of adsorbed polymer tails would cause an unfavourable loss in conformational freedom; and • an o s m o t i c e f f e c t , wherein the high concentration of species in the narrow gap between two particles leads to the creation of an osmotic pressure directing solvent into that gap, forcing the particles apart.

R1▪3▪2

Flocculation regimes

In the industrial context two flocculation mechanisms are important: • bridging flocculation — polymers span the gap between particles [80, 333, 511]; or • charge-neutralisation mechanisms — principally ’charge patch’ [426]. Of the alternative modes of interaction [see 80, 510, 511], only depletion flocculation is worth mentioning, in which low osmotic pressures in small gaps not accessible to polymers pulls particles together. In depletion flocculation an equilibrium state exists that is independent of path, and the process is reversible [80]. For bridging flocculation the dynamics (e.g. mixing protocol) control the end-point, and the process is irreversible [80, 428]. Charge patch flocculation is also expected to be irreversible. In the presence of c h a r g e d macromolecules (i.e. polyelectrolytes, NOM) electrostatic effects usually dominate particle–particle interactions [1031]. However, often the flocculants employed are only weakly charged or of the same charge (sign) as the particles. Hence non-charge mechanisms of flocculation (i.e. bridging flocculation [333, 511] rather than charge-patch flocculation) are important. Bridging is the dominant mechanism in the industrial context. Long-range interparticulate bridging is dominant even for slightly cationic (say up to 15% charged) polymers, given the usual system of negatively-charged particulates [333, 620, 1101]. Experimental work indicates that in typical water treatment operations flocculation is dominated by interaction with precipitated coagulant, rather than materials removed from raw water [113]. The smaller particle size and greater surface area of the precipitate [113] may be responsible for this dominance. The process of flocculation is often assumed to occur after the particulate suspension has been coagulated to form “colloidal bundles” [816]. In such cases, the polymer bonds to the “colloidal bundles” formed through the coagulation process [816] and forms bridges between the clumps of coagulated particulates. The polymer may also wrap itself onto a single clump of particulates, strengthening the aggregate. This interpretation implies that within each coagulated clump of particulates, “the colloidal material will have a composition reflecting the polymer-free floc and should retain much of its original fractal structure” [816]. In that case, similar principles should apply to polymer conditioning of pre-formed sludge further downstream in the processing.


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R1▪3▪2▪1

Charge-driven mechanisms

Highly charged cationic polymers adsorb quickly, practically irreversibly, and ‘saturate’ the (negative) surfaces at low concentrations [333, 1101]. Typically equilibrium is achieved in less than 20min for charge densities greater than 5% [333]. They essentially operate by a charge neutralisation mechanism [cf. 1101]. Cationic polymers of low charge, on the other hand, only approach “quasi-irreversible” adsorption at large molecular masses [1101]. This can be understood as a stochastic process, where the likelihood of the multiple polymer adsorption sites detaching at the same time becomes vanishingly small as the size of the molecule — and hence number of sites — increases. An important flocculation mechanism is called ‘ c h a r g e p a t c h ’ . Here the particulates are partially covered in patches of (charged) polymers [326, 426, cf. 813]. Interaction between the patches on one particulate and the bare surface on another particulate can lead to aggregation [426]. This mechanism is limited to systems in which the radius of gyration [see e.g. 636, 1004] of the polymer is smaller than the particulate [459, cf. 1140]. When the radius of gyration of the polymer is larger than the particulate, then e n m e s h m e n t may be expected to be the dominant mechanism [459].

R1▪3▪2▪2

The hydrophobic effect

Typically the particulates found in natural waters will have an overall negative surface charge (as measured by ζ-potential) at typical treatment pH values [511], and may be considered slightly hydrophobic (with respect to water) [898]. Increasingly, typical polymeric flocculants used will not be cationic, but rather anionic or non-ionic [898]. Often the flocculants have both hydrophobic and hydrophilic groups [898]. The blocks of hydrophobic groups bind onto particle surfaces (forming ‘trains’ on the surface [364, 511]), while the hydrophilic groups are necessary to allow the molecule as a whole to dissolve [898]. The hydrophilic groups will therefore not be inclined to attach to the particle surface, but instead will form ‘loops’ (between two points of attachment) or ‘tails’ (at the end of a polymer molecule) [364, 898]. The tails can then adsorb onto nearby particulates, forming a polymer ‘bridge’ [364, 511]. Interaction between opposing loops is also possible; however the tails tend to dominate the particle’s ‘effective surface’ characteristics as ‘seen’ by other particles, simply because they extend further out from the (otherwise) bare surface [364]. This was shown schematically in Figure R1-9. (Although the mechanism driving adsorption is not charge-based, in practice interaction of the non-ionic polymer with a metal oxide surface ultimately occurs through hydrogen bonds between p o l a r functional groups on the polymer and h y d r o x y l a t e d and p r o t o n a t e d groups on the surface [538]. While the interaction energy at each connexion is very small, the large number of contact points yields good adsorption [538].) Water forms a “highly structured” liquid due to the influence of hydrogen bonds [538, 1002]. The isotropic, l o c a l l y tetrahedral arrangement of water molecules is disturbed by the presence of solute species [538, 1002]. Ionic or strongly polar species can form strong bonds to water molecules which “more than compensate” for the disrupted or distorted water– water bonds, but this is not the case for non-polar species [1002].

708


A series of investigators [637, 1002] explained the effect with reference to a water–water ‘attraction’ or ‘cohesion’ that is much greater than (say) water–hydrocarbon or hydrocarbon– hydrocarbon interactions. The hypothesis is extended to argue that proximity to any nonpolar surface imposes on neighbouring water molecules an ‘unfavourable’ local ordering [511, 637, 1002]. The experimental evidence indicates that interactions between hydrophobic moieties and water molecules must be of short range [1002]. The driving force for hydrophobic attachment is entropic [459, 1002]. A typical polymer with alternating blocks of hydrophobic and hydrophilic groups will be in a ‘random coiled’ state in solution, with water in the ‘gaps’ between hydrophobic blocks on the polymer chain [459]. If the hydrophobic groups attach to the surface of a particle, then some of the formerly associated water molecules will be free to attain more configuration states [459]. Although there is a small decrease in entropy contribution due to the constraints on the newly-attached non-polar hydrophobic groups, this contribution is negligible in comparison to the large increase in entropy contribution due to the ‘freed’ water molecules; hence the change in entropy for hydrophobic attachment as described is large and positive [459, 1002]. The change in enthalpy for hydrophobic attachment varies from positive to negative for aliphatic hydrocarbons * (near room temperature) as the length of the chain increases [1002]. However the change in entropy dominates (and also compensates for the variation of enthalpy change with chain length [1002]), so that the change in GIBBS energy is negative, indicating that equilibrium also favours the attachment [459, 1002]. As an order-of-magnitude computation, the change in GIBBS energy for adsorption of a hydrocarbon chain is approximately ‒3600J/mol times the number of CH2 groups per chain [1002]. Aside from added water treatment chemicals, it should be recalled that even trace impurities are “often concentrated at an interface” [1002].

R1▪3▪2▪3

Flocculation conditions

TILLER & O’MELIA [1031] summarised the expected effect of several changes in flocculation conditions: • p H . The charge on a polyelectrolyte will vary depending upon the pH of the bulk solution and the functional groups on the polymer [see also 170]. • Polymer charge. Highly charged polyelectrolytes adsorb in very flat conformations (mostly ‘trains’), while less charged polymers will have more ‘loops’ and ‘tails’ (extending out from the surface [1101]) [see also 170, 333, 364, 538, 1138], cf. Figure R1-9. This reflects their extended or coiled conformations in ‘solution’ [538, 766, 1138]. • I o n i c s t r e n g t h . As the ionic strength is increased, the intermolecular electrostatic forces of repulsion are ‘screened’ more effectively [1101], so that they act over a shorter

*

For aromatic hydrocarbons the change in enthalpy is slightly negative [1002]. There is a large, positive change in enthalpy associated with removal of water molecules from around the p o l a r blocks on the flocculant polymer chain [459] [see also 700], indicating that an energy input would be required to achieve this. R1▪3 : Flocculation

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distance. This allows closer packing and greater polymer adsorption onto a surface (or adoption of a coiled conformation in ‘solution’ [766]). Divalent cations such as calcium can ‘enhance’ the ionic strength effect (cf. §R1▪2▪2▪1 and §3▪4▪6), manifest as increased polymer adsorption and enhanced aggregation (or “attachment efficiency”). The magnitude of the surface charge of materials such as hæmatite (positive charge) will also be increased as the ionic strength increases. However these factors are less important than surface affinity and chain length for polymers that are not highly charged (e.g. at low values of pH). • S u r f a c e c h a r g e . As the magnitude of the surface charge increases, the electrostatic attraction between that surface and (oppositely charged) polyelectrolytes will increase, yielding an increase in polymer adsorption. (Yet the t h i c k n e s s of the adsorbed polyelectrolyte layer may not be greatly affected by the sign of the surface charge [cf. 170, 1138].) Surface charge can also have a highly localised effect of increasing the degree of dissociation of parts of the polyelectrolyte close to the surface. • F l o c c u l a n t c h a i n l e n g t h . This parameter is not relevant when the polymer adsorbs predominantly in a quite flat conformation (i.e. for high charge densities, say >30% [333]) — unless the particle concentration is high [620]. When the adsorbed polymer forms a significant proportion of loops and tails, the extent of adsorption increases with increasing chain length. For bridging flocculation (low polymer charge), long chains are more easily able to span interparticle gaps and form robust flocs — without requiring the particles to approach close enough to experience significant electrostatic repulsion [1101]. These predictions are predominately based on a charge-driven mechanism of adsorption, although contributions of other mechanisms such as hydrophobic interactions (§R1▪3▪2▪2) and/or bidentate complex formation may be important, especially for NOM polymers [1031]. As suggested in §R1▪3▪1, lower particle number concentrations (cf. solidosity) correspond to lower particle–particle collision rates, so that flatter polymer conformations are attained and charge-neutralisation or charge patch aggregation would be favoured over bridging [812, 1140].

R1▪3▪3

Flocculants

Flocculants include activated silica, anionic and cationic polyelectrolytes, and non-ionic polymer [28]. They are often added from shortly after addition of coagulant (circa 5 to 600s [1113]), and so are sometimes called “coagulant aids” [e.g. 28]. Yet when dosed in sufficient quantity they can obviate the need for any (other) coagulant to be added [28, see also 106, 142, 289, 444, 576, 654]. Early flocculants included inorganic polymers (activated silica [see 654]) and natural organic polymers (starches, alginate [436], et cetera [171, 505]), but for decades these have been largely replaced by synthetic organic polymers, which tend to be cheaper or more effective and are more widely available [289]. Nevertheless, interest in natural polymers such as chitosan [e.g. 339] persists [171, 289], primarily motivated by situations where acrylamide-based polyelectrolytes are not desired or permitted for health or environmental reasons [436], based on toxicity of residual acrylamide monomer [505]. 710



(It should be noted that acrylamide has been shown to readily biodegrade in natural waters [797], and it is susceptible to ozone or other oxidants [315]. Furthermore, regulations in the U.K. (effectively ~0.1μg/L) [see e.g. 315] are much more restrictive than the WHO guideline (0.5μg/L) [59], and still around twice as restrictive as the Australian guideline (0.2μg/L) [34]. Use of polyelectrolytes by WTP’s is banned in Switzerland and Japan [171].)

R1▪3▪3▪1

Polymer classification and dose

The key parameters in polymer specification are average molecular mass and charge density distribution [505]. Many workers categorise these polymers based on their size as either coagulation aids (or, indeed, primary coagulants), or flocculants. They may also be categorised based on their application in drinking water treatment as either clarification aids (flocculants or coagulation aids), or dewatering aids (conditioners). See Table R1-8. Table R1-8: Processes following from polymer addition according to polymer properties and addition point (or purpose).

Location (purpose) Species Small, charged polymer Small, uncharged polymer Large polymer

Head of plant (to remove colloids from raw water) Coagulation

Downstream (to improve sludge dewatering) Conditioning

Flocculation

Organic c o a g u l a t i o n a i d s tend to be cationic (of opposite charge to the particulates) and of relatively low molecular mass [171], namely 104 to 105g/mol [142]. They are used chiefly for coagulation at the head of the plant, where clarification is carried out, and are usually specified in order to reduce the amount of inorganic coagulant used [see 142, 161, 289], although occasionally they may be used as sole coagulants [142]. Less sludge is produced, and it is denser and also ‘stickier’ [142, 289, cf. 1101]. The three main groups of coagulation aid are [142]: • polyDADMAC (polydiallyldimethylammonium chloride) • epichlorohydrin dimethylamine (epi-DMA) • melamineformaldehyde. These first two are the most widely used [cf. 94], and contain quaternary amines [cf. 505], whose positive charge is not sensitive to solution pH [654]. Dosage rates are on the order of 5 to 15mg/L for commercial products [142] (or 1 to 10mg/L [171, 289]). Addition of excess coagulating polymers can lead to suspension restabilisation [654], as overall aggregate charges become dominated by the polymer and are no longer neutral. Natural polymers, as in chitosan [339, 340], can also be employed. Polymer coagulation occurs predominantly by adsorption and charge neutralisation, not by enmeshment [654]. The low molecular mass favours charge patch aggregation over bridging, and this results in the formation of strong flocs [1140]. For this reason these polymers used as sole coagulants tend to produce relatively small, high-density aggregates from dilute suspensions, making them suited for direct filtration processes, but not


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sedimentation processes [289, 654]. They are also ill-suited to removal of dissolved substances, either organic or inorganic [289]. While the polymers are significantly more expensive on a mass basis than conventional coagulants such as alum (of order 10 times more), dosage rates are less, and plants can either achieve better quality product water or reduce overall operating costs while maintaining the same quality of water (due to reduction in coagulant dose) [335]. Organic f l o c c u l a n t s have much greater molecular masses, of order 106 to 107g/mol, tending also to be larger than natural polymers [142]. These polymers may be used for clarification or for ‘conditioning’ sludge prior to dewatering [142]. Their main benefit is increasing the size and/or strength of particle aggregates, which is primarily by a bridging mechanism [654]. The three main groups of flocculant are defined according to charge [142]: • non-ionic — e.g. polyacrylamide (poly(1-carbamoylethyelene)), [‒CH(CONH2)‒CH2‒]n [see also 280, 807] • anionic — e.g. acrylamide and acrylic acid copolymers; the carboxyl groups hydrolyse in solution, [‒CH(COO‒)‒CH2‒ran‒CH(CONH2)‒CH2‒]n [465] • cationic — e.g. copolymers of acrylamide and a cationic monomer; usually dimethyl-aminoethyl-methacrylate (DMAEM) or dimethyl-aminoethylacrylate (DMAEA) [142]. As implied, the most commonly used flocculants are derived from acrylamide (2propenamide), and sometimes this is ‘functionalised’ by copolymerisation with other monomers [807]. For details and alternatives see BOLTO [171]. Any of these, aside from moderately- or highly-charged cationic polymers, is suitable for clarification; doses usually are of order 0.05 to 0.5mg/L (commonly at the lower end [161, 229]), although they may be up to 2mg/L for highly turbid waters [142]. The cationic flocculants are usually less charged than the coagulation aids [171]. Where regulations permit, cationic flocculants are often economically favoured [557]. Large anionic polymers of lower charge can be used for (bridging) flocculation or conditioning, as they adsorb onto the positive sites of metal (oxy)hydroxide coagulum [171]. Non-ionic polymers are not frequently used in water treatment [505]. Suggested dosage ranges for anionic and non-ionic polymers (0.2 to 0.3mg/L [161]) show less variation than for cationic polymers (0.1 to 1.5mg/L [161] or 0.25 to 4.0mg/L [557]). Very low doses of 0.005 to 0.05mg/L of non-ionic polymer may be applied just upstream of granular bed filtration [289, 654]. Higher doses are used for conditioning [161]. For sludge conditioning, anionic polymer may require somewhat higher doses than cationic polymer for a given amount of dry solids to be treated [911]. The Degrémont Handbook [142] claims that inorganic sludges require the use of anionic flocculants [cf. 191], with doses of 0.5 to 7g/kg(dry solids). MWH’s ‘Water Treatment’ [289] suggests that most polymers will be effective (although longer chain lengths are generally the most effective), with doses of order 100 to 101g/kg(dry solids) appropriate for inorganic metal hydroxide sludges; likewise QASIM, MOTLEY & ZHU [854] gave 1 to 10g/kg(dry solids) as typical for conditioning. BELLWOOD [134] and SCALES [898] gave similar recommendations of 2 to 5g/kg(dry solids) (or about 0.05 to 0.10mg/L for clarification) and 3 to 4g/kg(dry solids), respectively. BOLTO [171] cited a range of 102 to 103mg/L for “sludge conditioning”, or specifically 1.5 to 3.0g/kg(dry solids) for centrifugation. Similarly, NIELSEN [781] gave 2 to 3g/kg(dry solids) as the “expected” range (for centrifugation), or up to 712



6g/kg(dry solids) when in “overload” condition. ZHAO [1145] obtained 2.2g/kg(dry solids) for an anionic polymer with a ~4.5g/L alum sludge. Amphoteric polymers, with both positive and negative sites, may also be used, and the charge on some polyelectrolytes is a strong function of solution pH [654]. Multiple polymeric conditioners of different charge can be added in immediate succession [911]. Polymer dosage is directly related to the surface area of the solids which it is intended to aggregate. BACHE et alia [113] suggested that the polymer dose would scale linearly with the mass of precipitated coagulant, on the basis that interaction with this phase dominates [cf. 815]. Optimum doses corresponded to roughly 75% of saturation (<100% to encourage interparticle bonding) [815]. In order to bond primary particles (or ‘primary clusters’ produced by coagulation) a relatively large amount of polymer is required due to the large number of particles (and hence bonds) involved, and the high ratio of surface area to volume; however, to build these small aggregates up into larger flocs requires only a small increment in polymer dosage, due to the decreased number involved, the reduced ratio of (external) area to volume [807], and indeed the fact that the exposed surfaces would already be largely covered with polymer.

R1▪3▪3▪2

Polymer stability and activity

There are a number of practical difficulties associated with the preparation and use of polymeric flocculants: • dissolution/hydrolysis • shear degradation • ageing • deactivation by (cation) complex formation OWEN et alia [807] concluded that ideal polymer ‘dissolution’ occurs in a few distinct phases: 0 (10 h: polymer grains take up water and form swollen lumps of gel. Less than 1. half of the polymer chains have dispersed into solution. Flocculant efficacy is very low. 100 to 101h: the gel lumps break up into supramicron agglomerates containing up 2. to order 103 chains, which coexist with discrete unaggregated chains as well as submicron clusters containing very few (<10) polymer chains. Flocculant efficacy is improved. 101 to 102h: all of the polymer is present as either discrete chains or submicron 3. clusters containing only a small number of entangled chains. Flocculant efficacy is optimised. 102 to 103h: the remaining clusters disentangle and the polymer chains undergo 4. conformational changes in solution, typically adopting more compact, coiled structures due to the solvation of intra-polymer hydrogen bonds. Flocculant efficacy is slightly reduced. Somewhat different outcomes may be observed when flocculating ‘real’ slurries [see 465]. In the laboratory it is common practice to first ‘wet’ the dry polymer (of order 10‒1 to 100g) with a solvent such as acetone [388, 1141] or ethanol [105, 807] or methanol [465] (2 to 3mL) R1▪3 : Flocculation

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and make up with purified water (total 100 to 200mL). However the practice of ‘wetting’ is by no means universal in the laboratory [e.g. 239], and can be omitted by (say) adding the polymer gradually to a swirling volume of water [807] to avoid forming a massive gel agglomerate. ‘Wetting’ is not performed in industry, and optimal mixing and dissolution/hydrolysis — or ‘activation’ [e.g. 93, 879] — is regularly not attained. Exposure to excessive shear degrades polymers [240, 491, 807]. Under industrial pumping conditions (G ~ 104s‒1) [465] significant polymer degradation can occur in less than 3s [465]. Laboratory operations such as prolonged shaking at 145rpm [807] and peristaltic pumping [465] appear tolerable. Susceptibility increases with concentration, low ionic strength, and (surprisingly) decreased anionicity [465]. Polymer stability depends upon water content: at least 12 months for dry powders; 4 to 12 months for concentrated liquids and emulsions; up to one or two weeks for ~5g/L stock solutions (cationic or anionic) when kept away from heat, light, and air, or as little as 2 to 3 days; and no more than one day for diluted (0.5 to 1g/L) solutions [134, 315]. C a t i o n i c polyacrylamide copolymers are more susceptible to degradation through hydrolysis of ester groups, crosslinking and formation of anionic carboxylates [171]. This degradation is very slow (timescale of months) at low charge densities (say, <6%) or low pH (say, <6); salt or alkaline conditions accelerate degradation [171]. More generally, degradation is known to occur upon exposure to UV light or strong oxidants [240], and radical attack from residual catalyst [807] or initiator [465] has also been proposed. The hypothesis of radical attack is supported by the observation that the presence of 3% alcohol is able to stabilise polyacrylamide solutions against degradation — for over one year [465]. N o n - i o n i c polyacrylamide flocculants are very stable [171] and are unaffected by the presence of a range of ions, however a n i o n i c species are prone to forming complexes that effectively ‘deactivate’ the polymer, and may cause it to precipitate [465]. The deactivation occurs through chelation of a single cation by multiple carboxyl ligands; it is especially likely in the presence of either Al3+ or Fe3+ ions [465]. Almost complete deactivation was induced at concentrations of about 3mg(Al)/L or 6mg(Fe)/L (without alkali addition) [465]. The equilibrium solubility of aluminium and iron under conditions typical of WTP coagulation and flocculation tends to be significantly less than this (given 5 ( pH ( 8½ for aluminium [90, 155, 326], or pH T 3 to 4 for iron [155, 326]; see Figure R1-1, p. 648). There is little to no published data on the degradation of flocculant a f t e r adsorption has occurred and flocs have been formed. There has been some limited research in the case of biosolids [reviewed in 240]. Some papers suggested that polymer degradation may be significant in flocculated biosludges, but such results have not been confirmed by subsequent studies [239]. Pendant groups appear more susceptible [239] than a polyacrylamide backbone [171, 240]. This could make a cationic polymer either non-ionic or anionic, which would “likely” affect the flocculating capabilities of the polymer [240]. Nevertheless, the degradation must be assumed to be less in the case of WTP sludges.

714



R1▪3▪3▪3

Industrial practice

As far back as 1982, over 50% of American WTP’s used at least one polymer to improve treatment efficiency [654], following introduction in the early 1950’s [289]. Later research indicated that usage was greatest at plants producing very high quality filtered water and those operating rapid sand filtration processes [654]. According to BOLTO [171], sludge conditioning typically consumes more polyelectrolytes than flocculation or primary coagulation. The traditional industry procedure for testing flocculant performance is to compare the settling rate of suspensions flocculated in graduated cylinders. The dispersion of flocculant is achieved through either a few manual oscillations of a ‘plunger’ or through inversion of the sealed cylinder. Both of these mixing techniques are simple and convenient, but offer illdefined mixing subject to operator variability, and can yield polymer-rich and polymer-poor regions, decreasing reproducibility [807]. Another source of variability may be ambient temperature fluctuations, likely to be of magnitude several degrees Celsius [465]; this would be a greater concern in the comparison of tests conducted at different times than for tests conducted in parallel. It is not vital to work at the optimum polymer conditioner dose: deviation from the optimum by ±50% should not cause problems [315] — greater excess can lead to steric stabilisation. Polymer treatment is also claimed to be able to tolerate wider ranges of pH and raw water quality than conventional coagulation [171]. Different dewatering operations are optimised by different flocculants [e.g. 171, 505]. For example, settling rates tend to increase using polyelectrolytes with higher molecular masses (and the same charge density) [505]. An overview is provided in Table R1-9 for key operations. Table R1-9: Optimal polyelectrolyte sizes for assorted dewatering operations [505].

Process type Low-solids clarification Sedimentation Centrifugation Pressure belt filtration Vacuum filtration Pressure filtration

Optimal molecular mass range Very low to high High a High Medium to high b Medium to high Low to medium

Notes a Assisted by dosing highly cationic polyelectrolyte. b Assisted by dosing low-molecular-mass, highly cationic polyelectrolyte.

R1▪4

Mixing

As seen earlier (e.g. §R1▪2▪8) the mixing effectiveness can control the extent of interfacial ‘disequilibrium’, influencing the chemical species formed. Mixing also alters the overall shear environment, and so helps determine the mode of aggregation, and thus the final aggregate structure.

R1▪4 : Mixing

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R1▪4▪1

Characterisation

It useful to describe mixing processes in terms of dimensionless variables for two reasons: a given condition can be described more concisely, and scaling up or down is possible through similarity arguments. Dimensional analysis of mixing processes typically yields equations between the dimensionless Power, REYNOLDS and FROUDE numbers. Important dimensionless numbers in mixing include [484, 485]: • Power number Po = P / ρL N3 Da5 ratio of exerted to applied forces • REYNOLDS number Re = ρL N Da2 / η ratio of applied to viscous drag forces [cf. 433] • FROUDE number Fr = N2 Da / g ratio of applied to gravitational forces 2 3 • WEBER number We = ρL N Da / σ ratio of applied to surface tension forces • PÉCLET number Pé important in two-phase systems, see §R1▪5▪6▪4(a) • assorted geometric ratios (shape factors) — see §3▪3▪2▪1, §S6▪1 In the above list the ‘applied force’ can be taken as ‘inertial force’. The ‘exerted force’ can be taken as ‘resistance forces’. P is the power input to the fluid (after losses); ρL is liquid density; N is the rotation speed of the agitator in revolutions per second; η is viscosity; g is gravitational acceleration; and σ is surface tension. We is only important in the case of two-fluid systems [484]. Fr can also be ignored if no “stratification” effects [650] — principally vortexing — occur at the free surface, as in a fullybaffled system [484, 623] or when Re is small (e.g. less than 300) [485]. For a particular geometrical configuration the simple correlation Po ≈ c Rex Fry [R1-2] applies, in which c, x, and y are fitting parameters [485]. Although c, x and y are regularly taken as constant, in fact they can vary from one flow regime to another, and even within the same flow regime [see 485]. The Power function is defined as Λ ≡ Po / Fry [485]. In the case of non-vortexing systems — i.e. fully baffled system, or with low REYNOLDS number (e.g. Re < 300) — the FROUDE number exponent can be taken as zero (Fry = 1) [199, 485], leaving Λ = Po ≈ c Rex . [R1-3] Plots of log(Λ) versus log(Re) have been published for a wide variety of mixing configurations [see e.g. 485], although results from different sources vary [see e.g. 144, 199] *. For the “Standard Tank Configuration” (see §3▪3▪2▪1) defined by HOLLAND & CHAPMAN [485] there is a “gradual” transition over 20 ( Re ( 2000 from viscous to turbulent flow.

The power consumption can be estimated from: • measurement of the shaft torque [144, 228], T [N.m], and rotation rate, so that [485, 518, 854]

*

716

Furthermore, BUJALSKI et alia [199] found weak (but significant) power-law correlation against relative blade or disk thickness (exponent ≈ –0.2) and absolute system size, DT (exponent ≈ +0.065). Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


P ≈ 2π N T ; [R1-4] • a similar dynamometric measurement of torque at an external thrust bearing [96, 283, 485, 784]; or • correlations involving the so-called impeller ‘power number’ or drag coefficient (cf. §R1▪4▪1▪1) — which itself depends on N and Da [283, 467, 518, 623, 854, 913] [cf. 960]. There are at least three other important parameters associated with mixing that are not dimensionless. The duration of mixing time, t, is self-explanatory. The characteristic velocity gradient, G, describes the (‘average’) shear intensity, as shown below. (The product of these two variables, G.t, i s dimensionless — it is sometimes called the CAMP number [427, 441, 518, 587, 1018] [cf. 283].) Finally, §R1▪4▪2 discusses dKolmogorov as a characteristic lengthscale of turbulence.

R1▪4▪1▪1

Characteristic velocity gradient

The power loss per unit fluid volume *, P/V, and the viscosity of the fluid being mixed, η, were related to a “root-mean-square” (or “rms”) velocity gradient, G [s–1], by CAMP & STEIN [228], building on STOKES’ theory [266, 518, 623, 834, 854, 1113]: P/V  dv  G=  ~ , [R1-5a] η  dz  rms in which v is the linear velocity of the fluid perpendicular to the z-direction [m/s], and V is the volume of fluid [m3]. This was intended to apply to both laminar and turbulent flow [228, 834]. NEWTONian fluid behaviour is assumed [228, 518]. The averaging refers to both space and time [228, 518]. In practice the derivative † is not evaluated, and it is a s s u m e d that [266, 602]

G=

P/V . η

[R1-5b]

It has been recommended that the quantity in equation R1-5b be referred to as a volumeweighted power input, as the strain rate distribution can vary greatly in different flow geometries even when P/V is fixed [600]. Similarly, it is sometimes convenient to use the mean energy dissipation rate per unit mass, ε [W/kg], and a s s u m e [110, 116, 266, 328, 368, 834, 1018] ρL ε G= . [R1-5c] η (The energy dissipation rate can also be computed from the cube of a characteristic

*

This is taken as equal to the “dissipation function” averaged over the tank volume [623, 834].

†

The derivative term is indicative only: the expression originally derived contains several partial derivatives, but improperly assumes a three-dimensional flow field can generally be reduced to a twodimensional (viz. pure shear) flow field [266] — a corrected form with three more terms [cf. 593, 602, 743] has been presented [266, 600, 834], however it is likewise not used in most practical analyses, and neglection results in only minor errors for practical flocculation processes (as these operate outside the laminar regime) [1018] [cf. 743]. KRAMER & CLARK [600] stated that only shear strain or normal strain can induce particle collision — and that rotation cannot; however, they neglected to consider the possibility that rotation may affect collision e f f i c i e n c y . R1▪4 : Mixing

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D. I. VERRELLI

turbulent * velocity fluctuation divided by a characteristic length [cf. 266, 602, 743, 921] [see also 968].) CLARK [266] recommended that the quantity in equation R1-5c be called the (spatially averaged) characteristic velocity gradient [cf. 962]. In the present work the term ‘ c h a r a c t e r i s t i c v e l o c i t y g r a d i e n t ’ is adopted for G, with calculation generally via equation R1-5b. Two correlations due to CAMP indicate that for laminar flow G2.η = P/V ∝ N2, whereas for turbulent flow G2.η = P/V ∝ N3 [269, 623]. CAMP noted that although flash mixing and flocculation always occurs in the turbulent regime on the industrial scale, laminar conditions may occur in jar testing at commonly used speeds [623].

R1▪4▪2

Turbulence Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is the problem to be solved. — LESIEUR (1987) [650] [See also 381, 964]

In the isotropic model of turbulence large eddies accomplish most of the momentum transport and may be affected by system geometry; little energy is dissipated in these eddies, and the energy cascades down to eddies of smaller size; at the smallest eddy size all of the remaining energy is dissipated by viscous forces, and these eddies are assumed to be independent of the bulk flow — i.e. l o c a l l y i s o t r o p i c [120, 269, 476, 509, 593, 602, 650, 834, 964, 1018]. The lengthscale of the largest eddies can be called the ‘integral’ scale, while the smallest eddies are found at the ‘dissipative’ scale [592, 650, 925, see also 959]; the former scale is also known as the m a c r o s c a l e of turbulence [269, 299, 743] [cf. 368], while the latter is also commonly called KOLMOGOROV’s t u r b u l e n c e m i c r o s c a l e (or similar) [cf. 269, 299, 326, 328, 368, 613, 834, 921, 964, 968, 1018, 1140], denoted here as dKolmogorov, referring to the widely-used model of KOLMOGOROV † (1941) [translations in 508, 593] [see also 509, 959]. The KOLMOGOROV microscale indicates the size of the smallest turbulent eddies [650, 774, 921, 964] [cf. 476]. This was originally defined as [592, 593] 1/ 4

 (η / ρL ) 3   , dKolmogorov ≡  [R1-6]  ε   in which ε is the time-average (or ensemble-average [110]) energy dissipation rate per unit mass. For convenience it is often computed as

*

CLARK [266] states that ε strictly only includes dissipation from turbulent fluctuations. At large REYNOLDS numbers this is not a problem, but at low REYNOLDS numbers the gradient of the time-averaged velocity (i.e. with fluctuations smoothed) contributes significantly to particle collision, which would not be accounted for in the formal definition of ε, leading to underestimation of the total energy dissipation [266].

†

А. Н. КОЛМОГОРОВ.

718



1/ 4

 ( η / ρL ) 3   , dKolmogorov =  [R1-7a]  ε   in which ε is the volumetric average of ε — to which it is (roughly) proportional [110]. By comparison with equation R1-5c this may be conveniently rewritten as [114]: ( η / ρL ) dKolmogorov ≈ . [R1-7b] G KOLMOGOROV’s model has since been further developed and critiqued, and alternatives have been proposed [see 123, 650, 964], yet it remains in many ways an excellent, intuitive description of the concepts in turbulence [368, 381, 509, 650, 925, 964]. The inertial (sub)range describes eddies with a moderate lengthscale: m u c h l e s s than the largest scale of the flow (viz. the boundary dimensions, i.e. the integral scale) but m u c h g r e a t e r than the smallest eddies (i.e. dKolmogorov) [123, 381, 476, 509, 581, 925]. The special feature of the inertial scale is that the fluid dynamics are “independent of viscosity and largescale forcing and boundary conditions” [925]. The ‘universal equilibrium’ range of isotropic turbulence is expected to apply to all eddies on the scale of the inertial subrange and extending down to dKolmogorov (and below) [cf. 269, 476, 819, 968]. The lower portion of the universal equilibrium range can be termed the ‘viscous subrange’ [110, 581, 672]. The dissipation range covers all scales below dKolmogorov, where eddies are rapidly (perhaps exponentially) damped [650]. Hence this range makes a practically negligible contribution to the turbulent energy spectrum [e.g. 476]. Precise specifications of the endpoints of these ranges and subranges are not generally possible, and several alternative nomenclatures are in use — cf. §S25 [469, 763, 776]. Although several turbulence scales have been defined, dKolmogorov appears most suitable to characterise aggregation processes [see 774, 963] [cf. 123, 785]. Refinement to dKolmogorov, i (see §R1▪4▪4▪3) may be advantageous if geometric similarity is not maintained [602]. Turbulence can be classified as primarily a system of ‘deterministic chaos’ [cf. 120, 433, 650, 906], described in terms of a fractal dimension [cf. 366, 509, 650], or multifractals [123, 906] or ‘local’ * fractal dimensions [see 381]. The multifractal scaling accounts for temporal intermittency, which leads to additional fluctuations in space and lengthscale — i.e. a breakdown in the presumed isotropy [123]. It is most important for non-linear processes occurring on ‘short’ timescales †, such as (irreversible) aggregate rupture, on lengthscales from the inertial scale down to dKolmogorov [123]. Single-fractal models and KOLMOGOROV’s theory tend to underestimate the strength of intermittent ‘violent’ events [123, cf. 743].

*

Self-similarity, manifested as power-law correlation [119, 120, 906], has been observed for turbulence in water over around t h r e e d e c a d e s of lengthscale (i.e. reciprocal frequency) under given conditions [650] [cf. 602] — and even wider in other media [509] — so ‘localisation’ may not always be important.

†

Less than the LAGRANGian time microscale in the viscous subrange and less than the LAGRANGian timescale of change of the turbulent field in the inertial subrange [see 123] [cf. 602, 743]. These are roughly of order 100 and 101s in the present work, much slower than the coagulation processes (cf. R1▪5▪6▪1(b), p. 764). R1▪4 : Mixing

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D. I. VERRELLI

The foregoing analysis is strictly only valid for fully-developed turbulence, though in practice it is often applied in transitional flow regimes too [cf. 602]. Although the pipeline transition to turbulence is taken as occurring at Re ~ 2100, this value is ill-defined * and is not characteristic of other geometries [see 433, 650]. For a baffled stirredtank geometry (as per §3▪3▪2▪1), turbulent effects commence at Re ~ 20, although the flow regime is primarily laminar at Re ~ 400; fully-developed turbulent flow is obtained at Re T 10000 [485]. Generally the fluid motion in the upper part of the tank is the least turbulent [743].

R1▪4▪3

Velocity and shear distribution

Mixing with high-speed agitators occurs by momentum transfer, with high-velocity streams formed by the impeller entraining slower-moving or stagnant fluid [485]. Particles less than about 100μm are affected primarily by only the turbulent component of the flow — the fluctuating velocity component [293] (cf. §R1▪4▪4▪2, §R1▪4▪4▪3). The amplitude and frequency of velocity fluctuations may be greater for a RUSHTON turbine impeller as compared to a propeller [293]. However for small particles (10μm or less) and for chemical reactions, the actual impeller type is irrelevant, provided that the necessary macroscale mixing conditions have been set up [293]. It is clear that the highest shear rates exist in the immediate vicinity of the agitator [cf. 968]. NORWOOD & METZNER found that the shear strain rate, γ , decays exponentially with distance from the agitator [485]. (More recent work suggests logarithmic decay of ε [743].) Also, METZNER & OTTO proposed that the average shear strain rate is directly proportional to the stirring rate, viz. [485] ( γ )ave. ∝ N . [R1-8] Rather than attempt to model the entire distribution of velocities or shear rates or local velocity gradients continuously throughout the system volume, it has been found to be convenient to consider separate zones of greater or lesser agitation, each with their own characteristic G value, and track the time spent by the particles in each zone [266, 328, 587, 600, cf. 834]. Simple rules of thumb have been developed which suggest the dimensions of ‘spheroids of agitation’ [see 485, 919]. For example, in water adequate circulation may be expected at vertical distances (4Da from the impeller [485]. Some of the most rigorous measurements have been carried out by MICHELETTI et alia [743], and show that at high Re the blades of a RUSHTON turbine impeller generate trailing vortices which propagate radially outward toward the baffles, and are then directed vertically up and down the wall, creating the characteristic circulation pattern [see also 144, 199, 968, 980]. The lowest shear is found in an annulus centred in the middle of the top half of the tank. At lower Re secondary circulation patterns may be set up [743]. (Changes in mode such as this can be problematic in scale up.)

*

720

More generally the transition occurs in the range 2000 ( Re ( 2400 [476] [see also 433]. REYNOLDS’s (1883) original paper noted that special effort was required to destabilise the flow [650] — although wall roughness apparently does not affect the threshold Re [476] [cf. 433]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


The main criticisms of the multiple-compartment approach are l i n k e d to the assumptions that (i) aggregates are only influenced by eddies in either the viscous or inertial subrange, and (ii) that the turbulence is isotropic [328]. (DUCOSTE [328] cites experimental work showing turbulence in the impeller discharge region n o t to be isotropic — at least on the macroscale [see also 144, 774, 785] — but other experiments [602, 963] indicate the opposite result for local isotropy [see also 743, 968]. Improved isotropy is obtained in pipe flow [299].) On the other hand, it would be theoretically p o s s i b l e to implement a multiplecompartment approach that did not make these assumptions, and which may therefore even improve upon the accuracy of DUCOSTE’s method. The remaining obstacle would then be specification of the numerous model parameters [cf. 330]. The approach of DUCOSTE and co-workers is generally considered superior [328]. Accurate estimation of the shear distribution is difficult [cf. 602], leading to large discrepancies in the results obtained by different groups [see 743]. The l o c a l ε can vary as much as three orders of magnitude in a RUSHTON turbine agitated tank [743]. DUCOSTE and co-workers defined a variable Ki as the ratio of the local energy dissipation rate in the impeller discharge zone to the mean for the entire volume [328], which can be written Ki ≡ εi / ε . Published values of Ki range from 1.7 (the 95th percentile in ‘reasonably uniform’ turbulence) [116], to ~5 (paddle in square jar [110, 968] and Lightnin A310 foil impeller discharge zone [328]), to 14 (RUSHTON turbine discharge zone) [328]. Higher factors are obtained for the small “impeller-tip zone” [see 368]. Ki itself is also a weak function of ε [963]. According to DAHLSTROM et alii [293], in the impeller zone — typically about 5% of the tank volume — the specific mixing energy dissipation is on the order of 100 times greater than for the rest of the vessel, and the root-mean-square turbulent velocity fluctuations are of order 5 to 10 times larger than for the rest of the vessel [see also 963] [cf. 980]. MÜHLE [763] also cites dissipation rates 102 times greater in the “impeller stream” than elsewhere, implying G to be a factor of order 101 greater [cf. 490]. Note that the preceding discussion normalised by the mean for the e n t i r e volume. The distinction is important if the energy dissipation o u t s i d e the impeller discharge region is significantly different from the average for the entire tank [cf. 743]. In a stirred tank of more-or-less ‘standard’ configuration (§3▪3▪2▪1) KUSTERS, WIJERS & THOENES (1991) found that G, calculated by volumetric averaging, is a good estimate of the time-averaged value of rms velocity gradient (cf. §S26▪1▪2) experienced by a circulating aggregate [613, 1018]. This had been predicted by KOH, ANDREWS & UHLHERR [587], given a high circulation rate (cf. volumetric flow, §R1▪4▪4▪1) [613]. CAMP & STEIN [228] also defined an “absolute” (local) velocity gradient, which can be arrived at by reducing the volume under consideration in equation R1-5 (including equation R1-5c) to ‘local’ scale * [834]. PEDOCCHI & PIEDRA-CUEVA [834] present a critical listing of the

*

In fact the absolute velocity gradient was originally defined in two non-equivalent ways [834], as reflected in equation R1-5. The form used in the text relating the power input (or viscous dissipation rate) is the more satisfactory and more practically applicable; the alternative form can be more directly interpreted as a physical velocity gradient [834]. R1▪4 : Mixing

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D. I. VERRELLI

assumptions both explicit and inherent to CAMP & STEIN’s [228] derivation of the rms and local velocity gradients. CAMP & STEIN’s [228] formula for G has been criticised as overestimating the true rms velocity gradient due to the way in which local velocity gradients typically vary within a tank [1018]. In fact, the degree of overestimation increases as the shear distribution broadens [600], showing that G (as computed by equation R1-5b) is actually a w e i g h t e d mean *. This can be attributed primarily to the fact that the spatial averaging implicit in equations R1-5b and R1-5c is applied to ε , rather than G [587]. The correction factor has been estimated to be of order ~0.7 to 0.9 [587] [cf. 613, 996]. Importantly, provided the tank geometry and flow regime do not change, and circulation rates are high (all reasonable assumptions in practice), then the correction factor for G is predicted to be nearly constant when the tank dimensions are scaled [587]. Despite a range of criticisms, as indicated above, use of the characteristic velocity gradient as a scaling parameter remains popular. This may be partly because the criticisms often focus on the ‘appropriate calculation’ of an average velocity gradient, rather than its inherent validity [cf. 600] †. However an alternative motivation is exemplified in the explanations of ARGAMAN & KAUFMAN of their analysis [269]: The reason G was introduced into the flocculation equation was the relative ease in which it is estimated and its acceptance by sanitary engineers.

and [96]: Despite its theoretical deficiencies, [use of G to obtain the collision frequency] has found wide application [...] and has been validated under certain circumstances [...].

A further problem, notwithstanding the critiques of G, is that the alternatives seem to be either [266, 600]: • complicated formulæ that do not have an immediate practical application; or • of an identical or (superficially) similar functional form to the CAMP & STEIN result [cf. 80]; or • based on their own problematic assumptions; suggesting that “we might as well just accept the [CAMP & STEIN] analysis” [266].

R1▪4▪4

Scale-up

The scale-up problem relates to the need to proportionally match the conditions in a larger vessel to those in a smaller vessel. The motivation in the present work is to ensure that bench-scale laboratory methods are consistent with tank-scale methods, and that both are valid representations of the full-scale process.

R1▪4▪4▪1

General principles

As mentioned, scaling is often carried out by maintaining dimensionless ratios constant. This is known as the principle of ‘ s i m i l a r i t y ’. HOLLAND & CHAPMAN [485] describe three

*

This would seem more reasonable if the SMOLUCHOWSKI equation were defined as non-linear in the strain rate (whereas in fact it is linear) [600] — cf. p. 726.

†

CLARK, who authored one of the first [834] comprehensive critiques (1985) [266] (submitted before CLEASBY (1984) [269]) continued to use G in his own later work [e.g. 329, 330].

722



levels of similarity: • g e o m e t r i c s i m i l a r i t y , where dimensions remain in proportion (e.g. constant aspect ratios); • k i n e m a t i c s i m i l a r i t y , where, additionally, “the ratios of velocities between corresponding points in each system are the same”; and • d y n a m i c s i m i l a r i t y , where, additionally, “the ratios of forces between corresponding points in each system are equal”. It is generally necessary for the regime (e.g. laminar or turbulent) to be the same in both vessels [485]. In practice it can be difficult or impossible to maintain all of the governing ratios constant. In that case a good compromise is to concentrate on the term(s) involving the dominant force(s) or dominant resistance(s) [484, 485]. When this is not possible, the system is said to operate in a “mixed regime” [485]. Where pure similarity proves impossible to attain, results may be extrapolated using the “extended principle of similarity” [485]. Instead of keeping the individual dimensionless ratios of applied to opposing forces (Re, Fr, We) constant, a parameter proportional to powers of those ratios is held constant [485]. For the case of liquid mixing, this could mean that the Power number is held constant, according to equation R1-2. Some other possible criteria for scaling are [485, see also 963]: • constant agitator tip speed [484, 962, 968], vtip ∝ N Da — see Table R1-10 • constant power per unit volume [484, 968], P/V ∝ N3 Da2 • constant volumetric flow per velocity head *, V /Hvel. ∝ Da / N • constant volumetric flow per volume [490, 962] [cf. 587, 968], V /V ∝ N (For comparison, G ∝ N3/2 Da for turbulent operation in a fully-baffled tank.) In a suspension of particles, volumetric flow is “of great importance”, and the developed head is a measure of shear [485]. The last two points are more relevant to b u l k mixing [963]. Use of global scaling parameters such as these implicitly relies on a correlation with the underlying local-flow behaviour controlling the process of interest on the microscale [963]. Table R1-10: Typical agitator tip speeds [484, 485].

Mixing regime Low agitation Medium agitation High agitation

*

Typical tip speed [m/s] 2.5 to 3.3 3.3 to 4.1 4.1 to 5.6

The volumetric flowrate and velocity head are related by P = ρ V Hvel. , where velocity head is given by v2 / 2 g, in which v is a linear velocity [485]. The volumetric flowrate may typically be obtained by considering a propeller as a “caseless pump”, such that V = э Vd N , in which Vd is the volumetric displacement per revolution, and the efficiency factor, э, is ~0.6 for a typical propeller [485]. A simple alternative correlation has V ≈ э∗ Da3 N, with э∗ a parameter of order unity for a RUSHTON turbine [see 144, 587, 962, 963, 980]. R1▪4 : Mixing

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D. I. VERRELLI

Additional considerations apply to more complicated systems, such as those in which reactions, heat transfer or mass transfer occur. For example, it is desirable to maintain the same temperature and contact time for reacting systems [485]. Two further types of similarity that may be considered in such systems are [485]: • t h e r m a l s i m i l a r i t y , where, in addition to being geometrically and kinematically similar, the ratios of temperature differences between corresponding points in each system are the same; and • c h e m i c a l s i m i l a r i t y , where, additionally, the ratios of concentration * differences between corresponding points in each system are the same. For continuous-flow, reacting systems, two ratios which represent possible scaling criteria are [485]: • rate of chemical conversion : rate of bulk flow • rate of chemical conversion : rate of molecular diffusion The latter ratio “can usually be neglected” in comparison to the former [485] (presumably assuming effective mixing with large Pé). An equivalent ‘bulk flow’ can be defined for batch mixed systems (see p. 723 footnote). The rate of reaction is governed by the equilibrium between the driving force and the resistances, and hence may be a function of temperature, concentration, and turbulence [485].

R1▪4▪4▪2

Turbulent coagulation and flocculation

It has been common to scale industrial coagulation and flocculation processes based on a constant value of G [328, 968] †. For fully turbulent baffled tanks (where Po reaches a constant asymptote [485]) with a given fluid this is equivalent to holding the dimensionless term ε / N3 Da2 constant (see §R1▪4▪1 and equation R1-5b) [cf. 743, 968]. This scaling is often employed or justified in the context of the ideal correlation [96, 110, 116, 123, 328, 329, 369, 763, 819] [cf. 915] dmax = м G–ш [R1-9] where dmax is the maximum ‡ aggregate size at steady-state §, м is a coefficient related to the strength of the aggregates, and ш is an exponent related to the particle breakup mode, the size of eddies that cause the disruption, and the fractal dimension of the aggregate; in general, 0 ≤ ш ≤ 2. Some experimental studies support a value of ~0.5 for ш, with the simple, intuitively appealing implication that (maximum) aggregate size is directly — i.e. linearly — proportional to dKolmogorov (see equation R1-11) [e.g. 116].

*

Or, more accurately, mole fraction.

†

Re is a poor means of scaling in comparison to dKolmogorov [774], which is simply related to G through

‡

Or volume-mean diameter [see 368, 369]. Or 95th-percentile size (by volume) diameter [see 114].

§

According to DUCOSTE [328] 20 to 30 minutes is generally sufficient time for steady-state to be reached.

equation R1-7b.

724



However a wider literature survey reveals estimates of ш from 0.2 to 2.7, with a lack of consistency in the failure modes and mechanisms (e.g. particle erosion, cluster erosion, floc splitting) proposed for various lengthscales and flow regimes [see 114, 116, 367, 413, 469, 523, 763, 776, 799, 819, 921, 953, 960, 996, 1018, 1069] [see also 301, 997, 1084]. These are examined in more detail in Appendix S25. The investigators used different materials, different shear geometries, and different means of estimating G. The studies involve different distributions of aggregate size and of local shear stress (or local G) [523]. The case for using equation R1-9 to gauge or achieve similarity in scale-up is not immediately compelling. While the definition has been sensibly constructed to ensure that comparisons of dagg are made at steady-state, to avoid errors based on slower or faster kinetics, unfortunately it may not be sufficient to ensure only that the same final state is attained (implying, perhaps, the same ratio of aggregating to disaggregating forces). The main impediment lies in the typically multilevel structure of real aggregates (§R1▪5▪7▪4) [see also 367]. Thus, it is eminently conceivable for two systems to ultimately yield the same dmax, and yet be characterised by different Df, and to have been ‘assembled’ from respectively denser or more open clusters — or indeed by a different mode of aggregation altogether (see within §R1▪5, e.g. §R1▪5▪3 and passim). DUCOSTE [328] has presented an improved model of particle aggregation and subsequent floc break-up under turbulent conditions, based on that of DUCOSTE & CLARK [330]. In summary, the implication is that it is acceptable to scale up coagulation and flocculation processes by holding the characteristic velocity gradient, G, constant, provided that [328]: the vessel and agitator shape and proportionality are not changed and 1. any one (or more) of the following conditions are met [see also 490]: 2. a. the fluid volumes are ‘large’, or the characteristic velocity gradients are ‘large’ *, or b. the concentration of particles is ‘low’, or c. d. the concentrations of coagulant are ‘low’. The last two points imply that only small aggregates would be formed. The second point additionally implies that any flocs that are formed would be dense. In both cases it may be expected that the aggregates would be relatively strong, due to the greater contact between primary particles [328]. It is believed that these two requirements will be met in the operations described for the present work.

*

High values of G avoid problems of particle concentration correlation effects [266]. At low values of G large fractal-shape particles may be formed by cluster–cluster aggregation at the boundaries between ‘islands’ of regular flow within a ‘sea’ of chaotic flow in the bulk region (away from the agitator) where break-up may not be significant [328, 490]. These large, highly porous aggregates would typically be weak and subject to rupture in the impeller discharge zone when exposed to larger-scale turbulent fluctuating velocities [328, 490]. Furthermore, large values of G are associated with shorter tank circulation timescales [490]: §R1▪4▪4▪1 indicates that V / V ∝ (Da / G)2/3 at large Re in a fully-baffled tank. More spatial variation is expected when recirculation to the impeller zone is slow compared to the aggregation kinetics [490, 587, 613]. Equivalently, mixing improves as N increases with G constant [cf. 587]. Note that this simplified analysis predicts superior spatial uniformity for s m a l l e r volumes. In the present work the circulation timescale varies from ~10s (rapid mixing) to ~60s (slow mix) — see Table 3-5 (cf. Table 7-1) — while the aggregation timescale appears to be of magnitude 101 to 102s. R1▪4 : Mixing

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D. I. VERRELLI

As a separate point it is assumed that the particle mass (or velocity) is sufficiently low that inertial effects may be neglected and the particles can be assumed to follow the turbulent motion [299] [cf. 613]. A remaining concern with the concept of scaling based on constant G is that often the smallscale testing is done in batch mode, which might not satisfactorily replicate all of the hydrodynamic features of full scale continuous flow units [518]. It should also be acknowledged that some models of orthokinetic flocculation yield rates that are not directly proportional to G (e.g. HAN & LAWLER [439], cf. VAN DE VEN & MASON [1071]) [1018]. Nevertheless, G is a highly useful practical parameter.

R1▪4▪4▪3

Model mechanisms of aggregation and disaggregation Neither aggregation nor breakup is a completely understood process and their modelling is highly empirical. — PEDOCCHI & PIEDRA-CUEVA (2005) [834]

DUCOSTE’s [328] key assumption is that two lengthscales are important for aggregation and break-up in turbulent flow. The two scales are defined as being either a b o v e or b e l o w the KOLMOGOROV microscale in the impeller discharge region, dKolmogorov, i [328]. (Numerous other researchers recommend a similar division [e.g. 116, 269, 299, 1140].) Furthermore, the large scales of turbulent motion are assumed to affect only the large aggregates, while small scales of turbulence are assumed to affect only the small aggregates [96, 328]. The pivotal role of a turbulence microscale — and its magnitude relative to that of the particles (and their spacing) — in determining the mechanisms of aggregation and rupture was recognised in the 1970’s [e.g. 299, 819], and notably employed by KUSTERS (1991) [328]. (DUCOSTE [328] described eddy scales larger than dKolmogorov as the “inertial subrange”, and those below dKolmogorov as the “viscous subrange” [cf. 819]. ARGAMAN & KAUFMAN [96] even interpreted the “inner or microscale of turbulence” as the u p p e r end of the universal equilibrium range. Such terminology * is not consistent with the accepted notation presented in §R1▪4▪2: this raises the concern that the value of critical lengthscale indicating the changes in mechanism may be misspecified [cf. 116, 996]. This would be problematic only for models that rely on the presence of turbulent eddies below the critical lengthscale; otherwise the concept remains valid.)

*

726

It appears to derive from the usage of PARKER et alii [819] and TAMBO & HOZUMI [996]; these authors cited LEVICH as a source, but he made no such definitions [656]. It is pertinent that LEVICH, along with LANDAU (& LIFSHITZ), proposed that turbulent eddies smaller than dKolmogorov are only “gradually” damped, whereas PRANDTL and KÁRMÁN’s hypothesis of much more rapid damping is widely accepted [see 656] — including in modern scholarship [e.g. 650]. LEVICH [656] relied on empirical evidence indicating the presence of turbulence in the viscous sublayer, but this behaviour can be explained by the “dual role” of the wall in both damping and p r o d u c i n g turbulence (recovery from a ‘disturbance’ is s l o w e r at the wall; an exchange of fluid elements — or surface ‘renewal’ — between the viscous sublayer at the wall and the outer layers can exist) [476]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


dKolmogorov, i is defined as [328] 1/ 4

 (η / ρL ) 3   , dKolmogorov, i =  [R1-10]  K ε i   in which ε is defined as the mean energy dissipation rate per unit mass, and hence the product K i ε represents the energy dissipation rate per unit mass in the impeller discharge

region (see §R1▪4▪3). From equation R1-5c we can more conveniently find [114]: 1/ 2

 (η / ρL )   , dKolmogorov, i ≈   K G i   showing more clearly the relative importance of G and (un)importance of Ki.

[R1-11]

DUCOSTE’s model includes five empirical constants, as follows [328, see also 329]: • Ki — see p. 721. It affects aggregate breakup only *. • α0 is a factor to account for reduced collision efficiency † due to “residual” electrostatic repulsion forces. It affects aggregate formation only. • Df is the fractal dimension of the aggregate. It affects aggregate formation only. • C1 is a constant in the large-scale breakup frequency function, and is a function of floc strength (through vessel and impeller configuration, coagulant type and water chemistry). • C2 is the analogue of C1 in the small-scale breakup frequency function. Key details of DUCOSTE’s [328] model are presented below.

R1▪4▪4▪3(a)

Agglomeration

DUCOSTE’s model

Agglomeration is described by the integral form of the SMOLUCHOWSKI rate equation using a modified collision frequency kernel based on turbulent shear and the coalesced fractal sphere formulation [328]. The turbulent shear is represented by G [299, 328]. A collision efficiency factor is included to account for collisions that are “unsuccessful” (i.e. do not lead to aggregation) due to electrostatic repulsion or hydrodynamic retardation [328]. This is a function of both aggregate size and structure [328]. For dissimilar aggregate sizes, collision efficiencies were computed using a modified version of ADLER’s flow number equation described by KUSTERS, WIJERS & THOENES [613], which represents the ratio of hydrodynamic shear forces to VAN DER WAALS forces [328]. ADLER’s approach does not rely on all of the assumptions made by SMOLUCHOWSKI (reviewed by THOMAS, JUDD & FAWCETT [1018]), and is considered to be the most detailed work on this subject [439]. For aggregates of similar size the shell–core model of KUSTERS, WIJERS & THOENES [613], which treats primary particles as though they comprise an (impermeable) hard core

*

Aggregate growth has been claimed to be better modelled by ε rather than εi [110, 996].

†

Given the uncertainties in some other parameters, α0 can also be viewed as a combined collision efficiency factor and overall empirical correction factor [1018]. R1▪4 : Mixing

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D. I. VERRELLI

surrounded by a (completely permeable) soft shell [cf. 1047], was used to calculate collision efficiencies [328]. Alternatives

CLARK [266] gave the most concise appraisal of G as a parameter to estimate coagulation: [...] while there must for a given steady turbulent flow be a specific value of velocity gradient which can be substituted in the Smoluchowski equation to yield the exact average collision rate, no one has ever shown that this velocity gradient is simply related to the average energy dissipation.

CLEASBY [269] had suggested that scaling with G is inappropriate for “particles” larger than dKolmogorov. Instead he concluded that coagulation of such particles would depend upon ε to the +2/3 power (not ε +1/2, as in equation R1-5c) and be independent of viscosity, η, (not η‒1/2) [269]. Furthermore, for “particles” of size d [ dKolmogorov the turbulence could not be isotropic (i.e. the eddies would not fall within the ‘universal equilibrium’ range), and would be geometry-dependent [269, cf. 600]. This relied on the proposition that “the important eddies causing flocculation [are] about the same size [as] the particles being flocculated” [269]. This topic has still not been resolved [834]. CLEASBY [269] stated that “particles” in water (and wastewater) treatment are typically larger than dKolmogorov. This is not generally true initially, as the first coagulant precipitates are forming. CLEASBY [269] did implicitly recognise this, but stated that the initial period in which particles would be smaller than dKolmogorov would be of order only a few seconds (in any case, it is unclear whether even this could affect macroscopic aggregate properties). This argument implicitly relies on a cluster–cluster mechanism of aggregation, and would not apply to predominantly particle–cluster mechanisms. In a number of cases the maximum aggregate size in WTP coagulation has been related to dKolmogorov, and indeed found to be of the same order of magnitude [e.g. 110, 116, 581]. This suggests that CLEASBY [269] overstated the size of typical WTP ‘particles’: if his analysis is correct, it may not be very relevant to WTP coagulation. (Although larger flocs tend to form when flocculant is added, the mixing intensity is also typically decreased, so that dKolmogorov is also larger.) DELICHATSIOS & PROBSTEIN [299] had earlier suggested that the aggregation rate ought to take into account the size of the aggregating particulates relative to the KOLMOGOROV microscale. It can be safely assumed for the systems presently of interest that d0 / dKolmogorov, but this is not necessarily true for the aggregates subsequently formed. ARGAMAN & KAUFMAN [96] had also criticised the failure of G to include information on the lengthscales and timescales over which turbulent velocity fluctuations occur *. Furthermore, G fails to account for the distribution of mixing intensities within the volume, which is especially important when comparing different geometries [96, 97, 403, 602].

*

728

They preferred the mean s q u a r e velocity fluctuation — although they ultimately claimed that this was directly proportional to G [96]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


HAN & LAWLER [439] combined the models of aggregation by BROWNian motion (perikinetic), shear (orthokinetic), and differential settling to investigate the relative importance of these mechanisms under various conditions (particle size, polydispersity, G, temperature). Two cases were considered: where hydrodynamic effects are significant, in which case the motion was referred to as ‘curvilinear’; and where hydrodynamic effects are negligible, in which case the motion was referred to as ‘rectilinear’ — the original derivations used this latter assumption [439, see also 489, 709, 804]. When hydrodynamics were ignored shear seemed to be the dominant mechanism for all but the smallest or largest particles, however, ‘curvilinear’ modelling predicted that shear would be dominant only for nearly monodisperse systems of intermediate to large particles if hydrodynamic effects were accounted for [439]. (Interestingly, a lot of experimental investigation is carried out on monodisperse systems of intermediate size particles, which would thus be unable to distinguish the importance of hydrodynamic effects.) Although experimental evidence was inconclusive, they suggested that G was not as important a control parameter as traditionally believed [439]. HAN & LAWLER [439] retained several assumptions in their modelling: they treated aggregates as coalesced spheres (Df = 3); they neglected break-up; and they neglected repulsive ‘double layer’ effects. It is accepted that in reality the aggregates are fractal-like objects, with some degree of permeability, such that the true behaviour would be intermediate between the ‘rectilinear’ and ‘curvilinear’ limits [429, 531, 1018]. The larger aggregates may be more permeable, and hence follow more closely the rectilinear limit [80]. The model used by DUCOSTE [328] treats an aggregate as a “coalesced fractal sphere”, following the formulation of LEE et alii [644]. This more realistically describes the aggregation process, although it does not specifically include aggregate permeability effects and does still assume additivity of cluster volumes [644] (which does not hold for true fractals). The ‘fractal rectilinear’ model was found to provide a slightly better description of experimental results for aggregation of estuarine sediment particles (d0 ~ 100μm, dagg ~ 102μm) than the conventional rectilinear model [644, 645] *. Curvilinear effects were not compared [644]. Treating the aggregates as true fractals would reduce the hydrodynamic ‘retardation’ for all mechanisms (perhaps inconsequentially for BROWNian motion) [439]. Moreover, the dependence of (terminal) settling velocity upon aggregate size, dagg, becomes weaker as the fractal dimension (Df) is reduced [644]: correspondingly, the importance of the differential settling would be reduced. This supports the view that perikinetic aggregation would dominate when at least one of the particles is ‘very small’ and otherwise orthokinetic aggregation would likely dominate (for conditions encountered in drinking water treatment, at least). Two possible issues with the derivation of HAN & LAWLER [439] are apparent from comparison with the earlier publications of VAN DE VEN & MASON: • The assumption of independent linear additivity of aggregation due to perikinetic, orthokinetic and differential settling modes [see 1071]. • The conflation of the concepts (and values) of ‘capture efficiency’ (bonds formed per collision) and ‘encounter efficiency’ (collisions per encounter) [see 1070]. *

The fractal rectilinear model contains an extra adjustable parameter, Df, and so it should outperform the non-fractal ‘EUCLIDean’ rectilinear model if variation of Df is physically important to the process (or if the additional model flexibility permits improved predictions, despite a lack of physical meaning) [645]. R1▪4 : Mixing

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D. I. VERRELLI

The implications of these two simplifications for the accuracy of the HAN & LAWLER’s [439] overall treatment cannot be determined a priori. The hydrodynamic radius and collision, or ‘capture’, radii are assumed to be the same in the SMOLUCHOWSKI theory. However the former is smaller than the latter for fractal objects, which suggests that the importance of perikinetic aggregation may be underestimated [429]. VAN DE VEN & MASON [1070] concluded that the success of SMOLUCHOWSKI’s model of orthokinetic aggregation could be attributed to substantial cancellation of errors due to neglecting the contrary effects of hydrodynamic resistance and VAN DER WAALS attraction. (GREGORY [427] quoted the same conclusion.) When hydrodynamic effects were included (but without double-layer repulsion) it was predicted that aggregation would scale with G0.82 (rather than G) [1070]. Nevertheless, holding G constant would still be predicted to maintain the same rate of aggregation.

R1▪4▪4▪3(b)

Break-up

DUCOSTE’s model

As stated, disaggregation of flocs is separated into two terms depending upon the size of the aggregates [328]. Due to variation in mixing intensity throughout the tank volume, it is likely that aggregates will grow to large sizes in the bulk regions of the tank, where dKolmogorov is large, before circulating to the impeller discharge region, where dKolmogorov is smaller [330]. Break-up of aggregates smaller than the KOLMOGOROV microscale in the impeller discharge region, dKolmogorov, i, is controlled by viscous forces [328], which e r o d e the surface of the aggregate [1018] [cf. 819]. It is a function of the velocity difference across the aggregate, which at this scale is proportional to the energy dissipation rate, and εi ∝ G2 [328]. Break-up of aggregates larger than dKolmogorov, i is controlled by larger-scale turbulent fluctuations [328] (of velocity, pressure, et cetera), which lead to d e f o r m a t i o n and f r a c t u r e [1018] when the inertial stresses exceed the limiting failure strength of the floc [330]. It is a function of the root-mean-square velocity difference across the aggregate, approximated at this scale as the product of impeller tip speed (vtip = N.Da) and the square root of the dimensionless impeller power number (Po1/2) [328] — that is, P1/2/ρL0.5.N1/2.Da3/2 *. Alternatives

YUKSELEN & GREGORY [1140] state that the size of the aggregates relative to the turbulence microscale determines the mode of breakage. One problem with the specification of a single value to represent the flow field is that different aggregates may be susceptible to different rupture mechanisms (e.g. shear, tension), and the intensity of each of these stresses can vary independently in different flow configurations and flow regimes [cf. 955].

*

730

The actual correlation with tank size may be weaker than implied by this [330]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


A number of alternative power-law correlations were presented earlier by CLEASBY [269], but a conclusive recommendation could not be made. The break-up rate is dependent on fluid shear, collisions between aggregates, and the probability of disaggregation after collision [921] (related to bond strength, or reversibility). BACHE et alia [116] attempted to show that dKolmogorov, i has even more direct application: for aggregates obtained through coagulating coloured water with alum (in the charge neutralisation regime) they found that the ratio of d95/dKolmogorov, i was nearly constant, and of order 100 (actual values ranged from 1.7 to 1.8, with dimensions of order 10–4m), for velocity gradients between 50 and 230s–1, where d95 is the 95th percentile by volume [see also 110]. The implication is that a direct proportionality exists between the two quantities. It certainly seems reasonable to believe that the largest aggregates could not possibly be much larger than the scale of turbulence — the larger they are compared to the turbulence scale, the more different parts of the aggregate will be exposed to hydrodynamic forces acting in different directions, imposing more stress upon the aggregate. It is not clear whether the implication would have been the same had a different percentile of the size distribution been considered. Indeed, for fractal aggregates, not only are the forces larger at larger lengthscales, but also the structure is weaker [666]. If the particle scale and microscale of turbulence are of the same order, then limiting theories Instead local acceleration, regarding particle breakup are precluded [110, 116]. 3/4 ‒1/4 3 ε (η / ρL) , and local characteristic turbulence velocity, (ε η / ρL)1/4, may be calculated [116]. On this basis BACHE et alia [116] found the following approximate relationship d ∝ (ξ Ebond )1 / m d0 ( 3−m) / m ε ( m−2 ) / 4 m . [R1-12] dKolmogorov where Ebond is the energy required to break a bond between the primary particles (of size d0), and ξ is the ratio of bonds broken per primary particle * (expected to be < 1). Given that they also indicated 1.8 ( m ≈ 3 – Df ( 2.0, then defining m ≡ 2 – δ in which δ is a small positive number and using volume averages yields d ∝ (ξ Ebond )1 /( 2 − δ ) d0(1+ δ ) /( 2 − δ ) ε − δ /( 8 − 4 δ ) dKolmogorov [R1-13]

→ (ξ Ebond )1 / 2 d01 / 2

as δ → 0 .

Interestingly, the specific energy dissipation does not need to be considered (to a first approximation). Ebond and d0 could be taken as constant, and BACHE et alia [116] also suggest parameter ξ may not vary greatly †; this is consistent with their claim that the ratio of particle size to turbulence microscale is approximately constant. This theory was extended and refined by BACHE [110] to include additional model parameters and with separate cases for the viscous subrange and the inertial subrange. The extension is at once an improvement, in terms of physical context, and a hurdle, in terms of

*

Roughly: the proportion of bonds broken [116].

†

With the product ξ Ebond ~ O(10–22)J [116]. R1▪4 : Mixing

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D. I. VERRELLI

the extra inputs required. For the 16 data sets considered, the exponent on d0 was estimated as 0.4±0.2 in the viscous subrange, consistent with the above [110]. In the viscous subrange the dependence of the ratio on ε was again very weak, but a significant decreasing tendency was predicted in the inertial range [110]. In the absence of significant hydrodynamic stresses, the maximum aggregate size will be governed by either thermal fluctuations or gravitational distortion [551, 666, 697] (§R1▪5▪1▪1). SONNTAG & RUSSEL [953] proposed that aggregate break-up could occur by two means: • An ‘equilibrium’ mode. In this mode it was envisaged that aggregates respond ‘almost instantaneously’ to increases in shear rate, i.e. due to hydrodynamic velocity gradients. • A ‘kinetic’ mode, associated with collisions between aggregates. This was hypothesised to progress slowly toward a steady state. Each of these could involve shear or normal (i.e. extensional or compressive) stress mechanisms. Shear was believed to be a more common mechanism of failure for “cohesive solids” [954]. SONNTAG & RUSSEL [954] developed a theory to model the rupture of a fractal aggregate. This theory relied on a series of assumptions, such as application of the VON MISES yield criterion, and azimuthal averaging [954]. (The VON MISES yield criterion itself is strictly valid only for incompressible, isotropic materials [151].) They predicted that the rupture site underwent a transition in location from the centre (small aggregate sizes) to near the surface (larger sizes) [954]. Although they implied that the rupture site continues to approach the surface as aggregate size increases, in fact this is only true of the dimensionless radius [954]: the absolute depth of the site below the surface seems to be more constant. Rupture was predicted to occur nearer the surface for lower fractal dimensions [954], i.e. where there is greater variation in intra-aggregate solidosity. A lot of the theory developed to model aggregate rupture assumes — either explicitly or implicitly — that individual bonds break due to the applied stress surpassing their tensile strength [cf. 151]. Such assumptions may not be valid: FURST and PANTINA [385, 813, 814] found that standard theories (e.g. DLVO) can underestimate tensile s t r e n g t h on the one hand, while also underestimating resistance to tangential or ‘bending’ s t r e s s e s . This combination suggests that failure of the interparticle bonds is likely to occur when a critical bending moment is exceeded [385, 386, 814]. PERRY’s Handbook [293] follows the traditional thinking that particle breakage is dependent upon the shear stress, to be obtained from the equation: σ = η γ . [R1-14] However [293]: In the equation referred to above, it is assumed that there is 100 percent transmission of the shear rate in the shear stress. However [...], at high concentrations of slurries there is a slippage factor. Internal motion of particles in the fluids over and around each other can reduce the effective transmission of viscosity efficiencies from 100 percent to as low as 30 percent.

In laminar flow the t y p e of shear is crucially important in determining the mode and speed of aggregate breakup [709]. The classification of shear was illustrated by KAO, COX & 732



MASON to encompass a continuum from pure rotation to simple shear (as in planar COUETTE flow) to pure shear (viz. extensional flow) [709]. Under turbulent conditions all of these types of shear will exist, although different set-ups may affect their relative importance.

R1▪4▪5

Industry

Mixing may be achieved by one of four groups of operation [518]: • paddle stirrers o revolving on horizontal or vertical axes o oscillating vertically or pendulum-like o propeller or turbine blades (or jet mixers, high-speed blenders, et cetera [1113]) • stationary elements (“hydraulic mixing” [1113]) o planar baffles fixed in channels or tanks o weirs [1113] o orifices [1113] o modular labyrinth or ‘honeycomb’ structures in tanks or pipes (‘static mixers’) • pipes (or channels) • particles o fixed beds o fluidised beds o bubble swarms o differential settling Traditionally the degree of mixing in water treatment has been measured by the characteristic velocity gradient, G = ( P / V ) / η , [854] and the duration of exposure, t. The dimensionless product G.t is also commonly quoted [427, 441, 1018]. This product has a neat similarity to the C.t product commonly used as a convenient measure of disinfection ‘energy’ [e.g. 7, 39, 827]. Optimum values of G, t, and G.t vary depending upon the WTP configuration. In Table R1-11 values relevant to coagulation ahead of a clarifier are presented [cf. 475, 1113].

R1▪4 : Mixing

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D. I. VERRELLI

Table R1-11: Typical values of G, t and G.t for coagulation–flocculation operations on full-scale WTP’s ahead of clarifiers.

Process

G [s–1]

t [s]

G.t [–]

Reference

Distribution channels 100 to 150 Rapid mix / chemical addition (“microfloc formation”) 300 (“polymer addition”) 50 to 100 up to 150 100 to 1000 (mechanical) 600 to 1000 (in-line mixers) a ~1000 Slow mix (“flocculation”) 10 to 20 10 to 50 (paddle ‘flocculators’) (paddle ‘flocculators’) (baffled channels) (basins)

20 to 75 10 to 55 10 to 50 15 c to 60 10 c to 60

[1113] 120 to 180

36000 to 54000

10 to 300 10 to 60 <1 240 to 1800 b

1200 to 1800 1800 to 2400 1800 to 2700 1200 c to 3600 1000 to 1500 c

[475] [475] [503] [854] [1113] [1113]

[475] [439] 4 5 10 to 10 [518] [cf. 431] [518] [557] [557] c 10000 to 150000 [854] 30000 c to 60000 [1113]

a

Notes: Jet mixers, high-speed blenders, and static blenders [1113]. b The slow mixing time is estimated based on a settling velocity of 0.01m/min to 0.05m/min [cf. 282, 557, 754] over 0.2 to 0.3m [475]. c Inconsistent.

The above values are not valid for floc blanket clarification and other such processes where the particle concentration is much higher, while G may be quite low (e.g. 5s–1) [518]. For this reason, it has long been known that a more general parameter is the product φ.G.t [431], in which φ is the system solidosity — this result can be taken from the derivation of SMOLUCHOWSKI (1917) [518, 639] (cf. §R1▪5▪6▪4(a)). Ideally 100 ( φ.G.t ( 500 for most dewatering operations [518], in which φ ≡ (φ/φagg) is the ‘apparent’ solidosity. Solids recirculation and ‘seeding’ can enhance performance by increasing φ for the system [518]. O’MELIA (1972) proposed incorporation of the bond-forming efficiency, э, to obtain a comprehensive parameter э.φ.G.t [439, 1018] [cf. 639]. In situations where pre-formed, settled sludge is sheared at high intensities — i.e. to describe breakup — the weighted parameter Gx.t may be appropriate; in correlations with CST, x decreased from ~2.8 to (1.0 with increasing polymer conditioning [788, 789]. In order to avoid excessive shear, which can damage the flocs and reduce the settling rate, the speed of the mixer tip in the second regime should be limited to about 0.4 to 0.5m/s [557, 854] (or below 0.8m/s [518]). Higher tip speeds are allowable in direct filtration configurations [1113] *, or in the first stage(s) of a tapered-mixing scheme (up to 2m/s) [557]. (For paddle mixers tip velocities from 0.15 to 1.0m/s are allowable [557].)

*

734

Values specified here by WESNER [1113] cannot be quoted with confidence due to an apparent error in his SI conversions. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


The horizontal flow velocity should be about 0.25 to 0.4m/s, and the area of the paddle blades should be less than 20% of the tank cross-sectional area (to minimise the amount of ‘dead’ liquid ‘carried’ around the tank by the blades) [518]. Velocities in baffled channels are typically between 0.25 and 0.5m/s, with retention time 10 to 60min [518]. A disadvantage is that G cannot be controlled independently of the flowrate [518]. The recommendation has been made [871]: Paddles or mixers in the flocculation basi[n]s should be provided with variable-speed drives so that operators have the ability to change the mixing energy to meet different water conditions and thus produce an effluent with the best settling characteristics.

Although mixers on plants may well be fitted with variable-speed drives (VSD’s), industrial experience indicates that the speed of mixing for (say) flocculation is likely to have been set during commissioning and thereafter maintained constant by the operators, irrespective of changing raw water (or other) conditions [475]. §R1▪4▪1▪1 presented formulæ for computation of G in the general case, with emphasis on stirred tanks. Appendix S26 provides guidance on estimating G for a range of other scenarios encountered on WTP’s, as in pipeline flow, clarification, and filtration.

R1▪5

Aggregate structure and fractal dimension

The problem of predicting sludge dewaterability has been tackled from different ends by different researchers. Some researchers tried to reach general conclusions about dewaterability by observing performance in individual unit operations. Other workers examined the aggregate microstructure under varying coagulation conditions; however, understanding how this relates to dewatering is currently poor [467]. The present work approaches the problem somewhere in the middle of these two extremes: the dewaterability parameters are inherent material properties that can be applied to any unit operation (provided shear is not significant), and must be fundamentally related to the component aggregate microstructure (although this has not been directly investigated). The porosity of a settled sediment of large particles is principally dependent upon particle size [1035]. As particle size decreases below about 10μm, surface and interparticle forces begin to control behaviour [1035, cf. 1107]: • When the attractive forces dominate, open, dendritic structures (fractal aggregates, §R1▪5▪1▪1) are formed with low solidosities of order 0.10 [1035]. • Somewhat weaker attractive forces give rise to less porous structures, reaching a maximum solidosity of about 0.60 to 0.65 [1035]. • When repulsive surface forces dominate (surface charge T 50mV), then particles settle past one another and deposit into a relatively dense, incompressible structure [1035].

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The primary particle size for WTP coagulant precipitates is of order 10nm [112] or smaller (cf. §R1▪2▪5▪3, §R1▪2▪6▪3, §R1▪5▪7, §4▪2▪3) *, and attraction is promoted to achieve acceptable process kinetics and robustness.

R1▪5▪1

Fractal objects

Conventional physics and mathematics follows E U C L I D in defining the d i m e n s i o n of a s p a c e as an i n t e g e r . By extension, in everyday parlance we describe objects as threedimensional (e.g. a mountain), two-dimensional (e.g. a coriander leaf), or one-dimensional (e.g. a hair). What we intuitively do in determining this classification is to estimate the smallest dimension of EUCLIDean space into which the object could be ‘embedded’. For example, the coriander leaf can be (more-or-less) embedded in a plane. Although this simple usage is generally adequate, more information can be obtained by directly considering the dimension of the o b j e c t itself. This is especially useful because it turns out that most natural objects — and many mathematical constructions — have a noninteger dimension: that is, a fractional, or ‘ f r a c t a l ’ †, dimension, D f [694, 906]. Fractal dimensions can take on any non-negative, real number value, including integer values [906], that is less than or equal to the EUCLIDean dimension of the embedding space [217, 906]. For the physically-relevant case of a single c o n n e c t e d ‡ object in three-dimensional EUCLIDean space 1 ≤ Df ≤ 3 [217, 404, 694, 966]. A key feature of fractal objects is that they exhibit ‘scale invariance’ [670, 730]: they are ‘self similar’ [906] in that the large-scale structure is replicated on all smaller lengthscales (and vice versa). Consequently many of a fractal object’s properties can be correlated by power laws [906]. In regular (mathematical) fractal objects scale invariance is seen unambiguously upon magnification (cf. Table R1-12). This is generally not the case for (real) natural fractals, where adherence to power-law correlations on physically-relevant scales tends to serve as an indicator of fractal character [906]. Their self-similarity is statistical only [730]. Mountains and (coriander) leaves are in fact excellent examples of natural non-EUCLIDean fractal objects §, as their topologies manifest rugosity [217] on a wide range of scales [see e.g. 694, 906]. This alludes to a further distinction in that pure mathematical fractal objects possess “scaleindependent correlations over an arbitrarily large range of distances” [1126], while for natural fractal objects the correlations break down at very large and small lengthscales.

*

For a primary particle size of 10nm for coagulation with alum this equates to a primary particle concentration of order 1015/mL at a dose of 5mg(Al)/L, typical of a WTP [112].

†

The word “fractal” was coined by MANDELBROT from the Latin fractus, meaning “in irregular fragments” [694].

‡

By “connected” it is assumed that the solid elements of the entity are contiguous. This would not strictly be true for an aggregate formed by coagulation in the secondary minimum [e.g. 838].

§

Strictly the fractal surfaces of these objects may be classed as ‘self-affine’, rather than self-similar [see 730].

736



R1▪5▪1▪1

Fractal aggregates

In 1964 BEECKMANS [132] developed a theory predicting a power-law dependence of aggregate density upon size with a single numerical parameter representing the “fluffiness” [cf. 730] (cf. equation R1-18 and Df), which was cleverly illustrated by an aggregate consisting of a number of clusters that are in turn composed of smaller clusters and so on. TAMBO & WATANABE (1967, 1979) [see 997] and LAGVANKAR and LAGVANKAR & GEMMELL (1968) [621] explicitly demonstrated power-law properties for WTP aggregates. FORREST & WITTEN (1979) [366] recognised the power-law mass distribution of colloidal aggregates that is characteristic of fractal objects *, and estimated HAUSDORFF dimensions. In 1989 LI & GANCZARCZYK [658] formally identified water treatment aggregates as fractals [1018]. The particulate matter present in raw water is also often present as aggregates [429], and so may also be fractal-like. Observed fractal dimensions are not simple fractions, but rather “anomalous” irrational values [366]. It has already been mentioned that aggregates formed in real processes can exhibit edge effects, as they are not infinitely large [366, 666, 1112]. At the other extreme, when the aggregates are first formed, or at sufficiently small lengthscales, where discrete (countable) numbers of primary particles make up the object, fractal nature is not apparent [531, 666] (cf. the transition from the POROD region to the fractal region in scattering experiments, §R1▪5▪4▪2). Formally, the smallest component of the aggregate which should be used in scaling relations (like equation R1-18) is the ‘fractal generator’, which is similar with the larger aggregate [660]. By way of guidance, mass fractal scaling has been reported to become evident at lengthscales of approximately 6 d0 or greater [217]. (For a tenuous aggregate to endure on experimental timescales, d0 must be larger than the atomic lengthscale to avoid excessive susceptibility to thermal fluctuations [551] [cf. 697]. Gravity forces — and the corresponding reaction forces — are generally more important in limiting the size of real fractal aggregates, even for small ΔρS [697] [cf. 551].) SERRA & CASAMITJANA [920] noted that the apparent fractal dimension calculated for short ranges (d/d0 < 10) relates chiefly to early times when many primary particles, doublets and triplets would dominate the population, and these are not fractal objects. Moreover, at early times a different mechanism (particle–cluster aggregation, §R1▪5▪6▪3) that produces more compact clusters predominates. These limitations have been overlooked by a number of researchers, including OLES [799, 920] and S. TANG et alia [1005]. (The latter article [1005] provides an example of exactly what n o t to do: the ‘aggregate’ population comprises mostly singlets and doublets, and scattering analysis probed dimensions equal to and smaller than the size of the primary particles!)

*

Formally these aggregates are described as “ m u l t i f r a c t a l s ” [906] (cf. §R1▪4▪2). The term refers to the ability for the aggregate to manifest a s p e c t r u m of scaling behaviours [cf. 381] by s e l e c t i v e examination of its component parts, due to the existence of two separate scaling exponents that describe the structure and the growth probability [906]. To avoid confusion with the concept of multilevel structure (see §R1▪5▪7▪4), the term ‘multifractals’ will not be used in discussion of aggregates. R1▪5 : Aggregate structure and fractal dimension

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Further to this, it is important to recognise that colloidal aggregates are strictly s t a t i s t i c a l fractals [666]. That is, their fractal qualities only truly hold when considering the e n s e m b l e average, which is performed by averaging each aggregate over many orientations and by averaging over several aggregates containing the same number of particles [666, 967]. One of the main motivations for measuring Df is the idea that it is a single macroscopic parameter able to summarise the result of a huge number of microscopic effects in real systems (i.e. where numerous suspended and dissolved species have individual physicochemical properties and charges, and interact correspondingly) with implications for a further wide range of situations — e.g. aggregation rate (collision frequency), settling, permeability, shear sensitivity [730, 1018]. However, numerous statements in the literature indicate that caution is required, because Df does n o t provide a c o m p l e t e description and is not always reliable [e.g. 178, 413, 440, 730]. Complementary parameters include: aggregate “anisotropy” (essentially aspect ratio) [cf. 177, 410, 544, 581, 795, 991] [see also 838] or sphericity and roundness [e.g. 287, 355]; aggregate permeability [660]; aggregate size distribution [see e.g. 588]; fractal dimension of the aggregate’s ‘backbone’ (cf. §2▪1▪2, §S17▪1) [e.g. 551, 872, 967] [cf. 681]; and power-law scaling exponents based on topological distances (rather than ‘displacements’ in EUCLIDean space such as dagg, cf. equation R1-15) or random walks over the aggregate [see 735, 967] [cf. 695]. It is clear that Df does not describe a unique aggregate structure. Simulation algorithms to generate aggregates of t u n e a b l e Df have been published that rely on entirely different aggregation mechanisms (particle–cluster [see 730, 731] [cf. 472] and cluster–cluster [1025]); none generate a plane at Df = 2. A final key issue to be mentioned is the multilevel structure of many real aggregates (§R1▪5▪7▪4) [e.g. 355, 1055].

R1▪5▪2

Definitions of fractal dimension

Many alternative measures of ‘fractal dimension’ have been defined (aside from those mentioned here, see also SCHROEDER [906]). The first relevant quantification of fractal dimension was introduced by HAUSDORFF (1919) [455], and referred to as the HAUSDORFF (or HAUSDORFF–BESICOVITCH [726, 838, 966]) dimension. The HAUSDORFF dimension is defined like the box counting procedure (see p. 755), except generalised to potentially-overlapping (hyper)spheres — or (hyper)cubes, simplexes et cetera — rather than grid-based pixels [see 407, 455]. Thus it applies to a single object [cf. 1009, 1083]. Explicit reference to this measure was more common in earlier studies [cf. 366, 405, 407, 658, 906, 920, 1112, 1126], but is no longer common in studies of ‘natural’ fractal aggregates as in coagulation processes. The more commonly quoted [cf. 838, 944] ‘definition’ employed in recent (applied) work is [110, 217, 472, 658, 694, 899, 906, 913, 1048] [see also 966] [cf. 705]: magg ∝ dagg Df [R1-15] where magg is the aggregate mass, and dagg is a characteristic linear dimension of the 738



aggregate *. To apply equation R1-15 the correlation must be performed over a s e t of aggregates [cf. 1009, 1083] [see also 457]. Df in equation R1-15 is formally presented as the “mass fractal dimension” [899]. It is strictly a measure of the scaling of the structure, but is also interpreted as the degree of rugosity [217] or ramification [966] and an indicator of ‘solidity’ or ‘compactness’. The descriptor ‘mass’ is usually omitted, since “the bulk of the literature [...] is concerned with [...] monodisperse spherical particles” [217]. For such systems † mass, number and volume can be used practically interchangeably [e.g. 217, 531, 640, 841, 913, 915]. In view of the typical motivations to find Df, analyses to estimate Df, and interpretations of these estimates, it is actually more appropriate to talk about a ‘volume fractal dimension’, even though this term is rarely used [cf. 355, 1055]. Correspondingly it would be logical to employ mass-, volume- and number-weighted definitions of dagg for different purposes, but again this is rarely considered [cf. 215, 1009]. The mass fractal dimension is equivalent to the ‘correlation dimension’ (cf. §R1▪5▪4▪2, §R1▪5▪4▪4) for monodisperse systems [see 906] [cf. 730, 1083]. Although it is occasionally used interchangeably with the HAUSDORFF dimension [e.g. 405, 568, 658, 920, 1048, 1112] [cf. 966], the two are defined differently, and are only equivalent for e x a c t l y self-similar systems [730, 906]. The difference between these two common approaches is best illustrated with a series of simple examples. Table R1-12 presents nine aggregates of varying size and shape. Regular fractals are used for simplicity.

*

Theoretically, the r a d i u s o f g y r a t i o n is accepted as an ideal measure [e.g. 659, 913], and the (STOKESequivalent) hydrodynamic radius has been found to scale proportionally with this [217, 667, 705, 1047, 1048] [cf. 1068]. Many other measures have been employed in practice, including:

• • • •

the projected maximum length [217]; the geometric mean of the minor and major ‘axes’ of a two-dimensional projection [111, 568, 1112]; some more complicated ‘average’ of the two ‘axial’ dimensions [404]; various dimensions of the “close fitting rectangle” enclosing the projected image, including the larger sidelength [581, 962], the diagonal, and geometric and arithmetic averages of the sidelengths [1009];

• a dimension of the projection perpendicular to the flow field [997]; • 4 A / π , where A is area projected to a plane parallel [355, 1055] or perpendicular [217] to the flow;

• a median volume-average ‘size’ (d50) [111]; or • the collision radius (obtained from the smallest sphere that will fully encompass the aggregate) [217] [cf. 613]. See also SUTHERLAND [991]. Aside from the first two choices, these may not all scale proportionally with the radius of gyration [217]. The method of averaging is only likely to be important in the case of strong departures from sphericity [cf. 217]. †

It has been claimed that primary particle size polydispersity does not affect this equivalence [217], but both intuitive reasoning and the mathematical analysis in §R1▪5▪3 indicate that this cannot be true i n g e n e r a l . Equivalence is attainable only where all particle types are equally likely to be found a given distance from the aggregate’s centre. At the least, primary particle polydispersity introduces additional scatter into the data, requiring more or larger aggregates to obtain representative ensemble averages. Approximate equivalence has been demonstrated for large aggregates generated by idealised simulation of a few special cases of DLCA and transport-limited random ballistic aggregation [1009] [see also 214] and in an experimental DLCA study [215]. R1▪5 : Aggregate structure and fractal dimension

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Table R1-12: Schematic of the ‘fractal’ size correlations of several regular aggregates. j is the number of spheres (with d0 = 1), directly proportional to the mass. The aggregate diameter, dagg, has been taken as twice the radius of gyration* [see e.g. 396, 636, 944, 1009, 1025, 1083]. L is the length. The objects with L = 2 are (roughly) the fractal generators.

Shape

L=2 A

L=4 B

L=6 C

j ≈ 1.686 dagg1.021

Rods dagg ≈ 1.183 C

dagg ≈ 2.324 D

dagg ≈ 3.474 E

R2 ≈ 1.0000

j ≈ 1.722 dagg1.915

Tiles dagg ≈ 1.549 F

dagg ≈ 3.225 G

dagg ≈ 4.872 H

dagg ≈ 1.844 a

R2 ≈ 0.9999

j ≈ 1.422 dagg2.806

Cubes

Note

Correlation a

dagg ≈ 3.924

Limiting correlations for j → ∞ are j =

3 dagg; j =

dagg ≈ 5.950 3 2

R2 ≈ 0.9998

dagg2; and j = dagg3.

For each of the ‘rods’, taken i n d i v i d u a l l y , we can be confident that the HAUSDORFF dimension will be close to 1, approaching unity exactly as j → ∞. Similarly, for each of the ‘tiles’ it will be approximately 2, and for each ‘cube’ approximately 3. Besides this, for each type of shape the three relevant aggregates in the s e t have been correlated by equation R1-15, with the results shown in Table R1-12. The exponents are again close to the limiting values 1, 2 and 3, although there is some discrepancy due to greater deviations from the ‘ideal’ shapes at small j. The prefactors are not so meaningful: In order to obtain magg as in equation R1-15 the volume of the primary particles (here π/6) and their density must be used — but the density could be anything. (This reinforces the notion that ‘mass’ fractals are almost always ‘volume’ fractals in disguise.) The three correlations mentioned above are not the only ones possible. For example, it is theoretically possible that primary particles might aggregate first to linear tetramers, which orient to form ‘rafts’ (§R1▪2▪6▪3, §R1▪5▪5, §R1▪5▪7▪4, §S17▪1), which themselves aggregate in lamellar fashion. Thus, correlating aggregates B, D and H yields j ≈ 0.111 dagg4.244, with R2 ≈ 1.0000. The exponent now is quite unrelated to the fractal character of an individual *

740

Due to the small j it was necessary to perform the calculations rigorously by summing displaced moments of inertia (using the parallel axis theorem, for composite bodies) for uniformly dense spheres [see e.g. 396], rather than assuming all of the mass to be concentrated at the centres of the spheres. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


object in the set! Yet no mathematical fault has been made. Although only three objects were included in this correlation, when random fractal aggregates are considered a continuous spectrum can easily be generated [cf. 1025]. It is also possible to apply the concept of fractals to the s u r f a c e of an object, in which case the fractal dimension represents the degree of self-similarity (at arbitrary magnification) of the surface [899]. Similarly to equation R1-15, this can be expressed [899]: Sagg ∝ dagg Ds , [R1-16] where Sagg is the surface area, and 2 ≤ Ds ≤ 3 is the surface fractal dimension. The fractal dimension obtained analysing the p r o j e c t e d a r e a (‘silhouette’) of an aggregate also gives a two-dimensional fractal dimension, Df 2dim.; this will be [217, 546, 920, 997, 1009, 1112]: Df 2dim. ≈ min { Df, 2 } . [R1-17] Corrections may be applied to account for deviations of real aggregates from mathematically fractal properties [217, 1009]. In some systems the true Df may be significantly underestimated if equation R1-17 is applied in reverse [640, 1009]. Unreliable results will be obtained for oriented aggregates [906] [cf. 531]. Occasionally ‘one-dimensional’ fractal dimensions are measured, such as the exponents relating perimeter to aggregate size (‘diameter’) or projected area [531, 569, 913, 920, 944, 960, 962] [cf. 287, 355]. Unlike for Df, larger values of these parameters indicate greater rugosity [531, 640, 913, 920, 944, 960]. It is difficult — or impossible [640] — to relate these to the more widely used (mass) fractal dimension, Df [429]. They also hold less physical meaning for applications such as setting than Df and Df 2dim. [531]. The above relations serve as convenient de facto identifiers of fractal objects. (From a purely mathematical perspective the fundamental definition of a fractal object is problematic, and recognition of self-similarity properties may be intuitively more satisfactory — although non-scaling objects can also be fractals [694].)

R1▪5▪3

Theoretical properties of fractal objects

It is the nature of fractal objects that density will decrease as the diameter increases [217]. The overall buoyant density of an aggregate can be evaluated according to [110, 116, 217, 355, 1055] D −3  dagg  f  , [R1-18] Δ ρagg = Δ ρS k   d0  where k is a “structure prefactor”, d0 refers to the primary particle size, and the differences reference the liquid phase density. Provided that ρS and d0 are constant, equation R1-18 can be written [110, 111, 116] [cf. 112] *:

*

BACHE et alia [112] stated that equation R1-19 only holds at “high water content”. It is not clear whether this is intended to mean small Δρagg, small Df, or low system solidosity (i.e. sufficiently dilute for aggregates to be well separated, e.g. not in a gel). R1▪5 : Aggregate structure and fractal dimension

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D. I. VERRELLI

( )

Δ ρagg = k ∗ dagg

Df − 3

.

[R1-19]

Characterisation using this correlation is discussed in §R1▪5▪4▪3. The foregoing supposes that the solid phase is made up of primary particles of uniform size and density. Let us generalise a derivation published by TAMBO & WATANABE [997] based on their 1967 study. Consider a system composed of a liquid phase and two distinct types of solid, denoted A and B. We may write the volume of aggregate, solids, and liquid (respectively) as *: [R1-20a] Vagg = υagg dagg3 3 VS,A = jA υS,A d0,A [R1-20b] VS,B = jB υS,B d0,B3 [R1-20c] [R1-20d] VL = Vagg ‒ VS,A ‒ VS,B where the ‘volume-prefactors’ υi represent shape constants (π/6 for a sphere) and the ji are the number of primary particles of type i, with size d0,i, contained in the aggregate. Given consistent interpretations of the component densities, ρi, then by simple mass balance we obtain the equation ρagg υagg dagg3 = ρA jA υS,A d0,A3 + ρB jB υS,B d0,B3 + ρL (υagg dagg3 ‒ jA υS,A d0,A3 ‒ jB υS,B d0,B3) . [R1-21] The critical step is to a s s u m e that the ji can be expressed as a power-law function, namely

 dagg ji = αi  d  0 ,i which yields

βi

  ,  

[R1-22]

β −3

β −3

 υ   dagg  A  υS,B   dagg  B     ρ α , [R1-23] Δ ρagg = Δ ρS,A αA  S,A   + Δ S,B B  υagg  d0,A   υagg   d0,B          where the density differences are all defined with respect to the liquid phase density, ρL. It is then c o n v e n i e n t — but not essential — to treat all of the υi as equal (e.g. all for spheres †). Note that the derivation implies that the ratio of components A and B in the aggregates is n o t fixed. An equation containing two power terms is difficult to work with, and traditionally a single uniform solid particle phase has been assumed. We may then attempt to fit our data with average properties and parameters, viz. β−3  dagg   . [R1-24] Δ ρagg ≈ Δ ρS α   d0  Observe that β is the parameter commonly interpreted as the fractal dimension, Df (cf. equations R1-18 and R1-19). Although we are typically more interested in cases where

*

The choice of appropriately defined dagg to calculate Vagg is not straightforward. See footnote to equation R1-15 and comment following equation R1-27.

†

TAMBO & WATANABE [997] gave typical sphericities of WTP aggregates as ~0.8 [see also 913]. Greater anisotropies have been suggested for aggregates in general [410, 544, 991] and some WTP flocs [355]. This would (slightly) alter the absolute values of ρagg [442], but would not affect the calculated exponents, βi.

742



dagg [ d0, it turns out that α ~ 1 [997] *, consistent with the limit dagg = d0 †. (This does not generally apply to the component prefactors αA and αB.) This result is by no means general, as may be confirmed by considering a structure defined by particles on a w i d e l y - s p a c e d lattice with Df = 3, for which Δρagg / ΔρS, leading to α / 1. For the simplest fractals (cf. the cubes in Table R1-12) the limit of α as dagg → ∞ is easily seen to be given by the packing fraction [cf. 956]. BACHE [110] estimated α ~ O(106) for WTP aggregates with large dagg / d0, but this clearly cannot be valid across the full range of lengthscales — and perhaps not at all ‡ — and suggests serious experimental or analysis error leading to underestimation of Df (viz. 1.00 to 1.23). It is of interest to consider how the two solid components described would combine to affect the value of β (and, by implication, Df). The following limits apply:  d0 ,B as d → 0 0 ,A  as Δ ρS,B → 0  β → βA  Δ ρS,A . [R1-25] as αB → 0  αA  βB →0 as  βA These imply that the mass fractal dimension will tend to be dominated by particles that are larger, denser, and more numerous — and increasingly more numerous as dagg increases. Typically analyses in the literature have implicitly assumed βA = βB, obviating the need for the foregoing treatment. However natural fractal aggregates could be created with βA ≠ βB: an example is the (e.g. diffusion-limited) aggregation of large primary particles to a porous object followed by gradual addition of much smaller particles which slowly penetrate and bond (i.e. reaction-limited). HOSSAIN & BACHE [494] distinguished between solids consisting of precipitated coagulant and solids derived from the raw water itself. In the latter category were lumped dissolved materials (i.e. NOM) and true colloidal material (i.e. turbid elements) [494]. There is almost no end to the level of detail that could be included in this type of model, and the decision to consider NOM and turbidity together, for example, is not a necessary one.

*

TORRES, RUSSEL & SCHOWALTER [1047] used a slightly different, “ad hoc” function in place of equation R1-22: β

 dagg   +1 j = α ′    d0  and α′ ~ 0.6 for their system. DUCOSTE [330] suggests α ~ O(100) ~ Df / 3. †

SORENSEN & ROBERTS [956] made a more sophisticated analysis of the small-aggregate limit, concluding that (of the cases they studied), the most meaningful small-aggregate limit was of three primary particles arranged in a (short) ‘string’ or ‘rod’ [cf. 405, 991].

‡

It is exacerbated by replacing d0 with dclus [cf. 110], and it is difficult to conceive of a way that the prefactor could increase from a much, much smaller ‘initial’ value given the low (‘final’) Df estimates. R1▪5 : Aggregate structure and fractal dimension

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Another interesting derivation * (again extending TAMBO & WATANABE [997]) concerns the case of multilevel structure of aggregate morphology (§R1▪5▪7▪4). Suppose the primary particles form fractal clusters, assumed to have uniform size dclus [660], which in turn combine to form the larger aggregates. Then, with the same assumptions as in the foregoing derivation,

Δ ρagg

 dagg = α Δ ρclus   dclus

  

β−3

β−3 β −3   dclus  clus   dagg   ,    = α αclus Δ ρS     dclus   d0  = Δ ρS α∗ d0 3 − βclus dclus βclus − β dagg β − 3

[R1-26]

so the key influence on c o m p u t e d ‘fractal’ dimension in this case, if taken as equal to β, is simply the d i s t r i b u t i o n o f c l u s t e r s within the aggregate, n o t the distribution of primary particles within the clusters! GMACHOWSKI [407] independently derived a set of scaling relations for fractal aggregates of fractal ‘monomers’, including a discussion of the ‘effective’ fractal dimension. For example, he argues that at low solidosities (e.g. free settling), where the fluid predominantly flows a r o u n d the aggregate, the “hydrodynamic” fractal dimension of the a g g r e g a t e s dictates the resistance to settling; at high solidosities, where the fluid flow predominantly passes t h r o u g h the aggregates, the fractal dimension of the ‘ m o n o m e r s ’ dictates the settling (or permeability) [407]. By mass and volume balance the above equations can be rearranged to obtain expressions for the solidosity of the aggregate [cf. 217]: Δ ρagg V . [R1-27] φagg ≡ S = Vagg Δ ρS A key issue is the definition of dagg to calculate Vagg — cf. footnote following equation R1-15 [see also 913]. Supposing that double the radius of gyration is used [cf. 1083]: then for the aggregates in Table R1-12 φagg ~ 1.2 is obtained for the smallest, L = 2, clusters of any shape — which are rather compact; but as dagg → ∞ then φagg → 1 for cube-shaped aggregates, whereas φagg → 0 for rods and plates. The radius of gyration is an average over the entire substance of an object, so that it is equal to d0 / 5 for a solid sphere of diameter d0 [396]. More intuitive results are obtained by using an appropriate ‘envelope’ dimension (cf. the “external radius” of BUSHELL & AMAL [214]), although this may not scale with the radius of gyration (see footnote following equation R1-15). Now, although α is often taken as approximately unity [e.g. 997] [cf. 217], or implicitly assumed to be identical when comparing different systems, significant differences in α between systems would allow aggregates with β ≈ Df ~ 1.8 to be more compact than

*

744

A similar concept was independently illustrated in equations presented in BUSHELL et alia [217], referring to the work of MOUDGIL & VASUDEVAN (1989), except that they presumed a value of βclus = 3, which misses a key piece of information. Other researchers [355] have presumed that clusters have the same Df as the aggregate overall, which misses the point of multilevel structure. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


aggregates with β ≈ Df ~ 2.1 [cf. 441] or vice versa [405]. (Likewise for the prefactor k in equation R1-18.) For correlations based on the radius of gyration, reported values of the prefactor have ranged from 0.68 to 3.4 [217] [cf. 660] (generally the values below unity were associated with particle–cluster aggregation [956]). In one example, modelling showed that aggregates formed by diffusion-limited particle– cluster aggregation would be denser than those formed by cluster–cluster aggregation if they were of equal Df [956]. In another example, modelling showed that identical Df(t) profiles could be generated where in one case the aggregates were twice the size as the other [914] — this reinforces the dependence of ‘compactness’ not only upon Df, but also upon the relevant prefactor. Strictly speaking, comparisons of Df can only yield unequivocal conclusions regarding compactness if the aggregates are allowed to grow to (practically) infinite size [217] — impossible for real systems. It is also easy to show mathematically that a small aggregate of low fractal dimension may be (on average) more solid than a larger aggregate of higher fractal dimension. Writing Df 1 and (dagg/d0)1 for the first case, and Df 2 and (dagg/d0)2 for the second case, we have  dagg  Df 2 − Df 1    d0  2  dagg  3 − Df 2 = [R1-28] d0 1  dagg      d0  1 from equations R1-18 (or R1-24) and R1-27, provided that the structure prefactor, k (or α and the υi), is the same in both cases. Of course, the left hand side can be simplified if d0 is fixed. This is illustrated in Figure R1-10, where for compactness (dagg/d0) is written as ч. The interpretation of Figure R1-10 is as follows: suppose the first system comprises 100μm aggregates of 10nm primary particles (ч = 104) with Df = 1.75, then a second system of aggregates made up of the same primary particles would have the same o v e r a l l aggregate solidosity at Df = 1.85 if they were just a factor of 104 × 0.0870 ≈ 2 . 2 3 larger. Incorporation of varying k is not too much more difficult. The following can be derived:  dagg  Df 2 − Df 1 1   3 − Df 2 3 − D d d     f2  0  2  k2   agg  =  . [R1-29] k1  d0  1  dagg       d0  1 Using theoretical arguments GMACHOWSKI [405] indicated an i n c r e a s i n g trend of k with Df according to  α ≈ 0.40 Df ‒ 0.18, k∝ [R1-30] and this is included in Figure R1-10. Evidently the effect is very small: for the previous example one obtains (0.56/0.52)1/1.15 × 2.23 ≈ 2 . 3 8 . SORENSEN & ROBERTS [956] plotted prefactors for computer-generated aggregates (DLCA with 10 ≤ j ≤ 100) which suggested a d e c r e a s i n g trend of k with Df. The correlation  α ≈ –2.20 Df + 5.23 k∝ [R1-31]


745

D. I. VERRELLI

{ (d agg/d 0) for D f of x to be as porous } / ч 1.75

provides a reasonable fit to the data for 1.60 ( Df ( 1.95. (An ‘outlier’ at Df = 2.00 suggests that k may approach a constant limit at high Df.) This has a minor effect: for the previous example one obtains now (1.16/1.38)1/1.15 × 2.23 ≈ 1 . 9 2 .

1.E+3

1.E+2

(ч 2.10/ч 1.75) = ч 1.750.3889

(ч 1.95/ч 1.75) = ч 1.750.1905

x = 2.10

1.E+1

x = 1.95 x = 1.85

1.E+0 (ч 1.85/ч 1.75) = ч 1.750.0870 1.E-1 1.E+0

1.E+1

1.E+2

1.E+3

1.E+4

1.E+5

1.E+6

ч 1.75 ≡ (d agg/d 0) for D f of 1.75 Figure R1-10: Theoretical relationship between relative aggregate sizes, ч, to obtain the same solidosity with various combinations of fractal dimension, Df. The structure prefactor is assumed constant for the thicker, solid lines; for the thinner, dashed lines the correlation of GMACHOWSKI [405] is used; for the feint, dotted lines the correlation of SORENSEN & ROBERTS [956] is used.

It might be supposed that the gel point, φg, could be obtained by multiplying φagg by some p a c k i n g f r a c t i o n (say φg) [cf. 401] — with 0.5 being a reasonable first estimate [cf. 241, 386, 442]. (Application of percolation theory could yield a quite different treatment [see 841].) For the present work typically φg ~ 0.002, and so a reasonable first estimate of φagg is 10‒3.

746



1E+0

d 0 = 0.01μm Δρ S = 1500kg/m

β clus, β : d clus

3

1.5, 1.5, 1.5, 2.5, 2.5, 2.5,

Aggregate solidosity, φ agg [–]

1E-1

1E-2

2.5: 2.5: 2.5: 1.5: 1.5: 1.5:

0.01μm 0.5μm 10μm 0.01μm 0.5μm 10μm

1E-3

1E-4

1E-5

1E-6 10

100

1000

Aggregate diameter, d agg [μm] Figure R1-11: Theoretical relationship between aggregate solidosity, aggregate and cluster size, and aggregate and cluster fractal dimension (Df,i ~ βi). Note that taking dclus = d0 yields an aggregate characterised by a single fractal dimension only. Similarly, if dagg = dclus, then the ‘aggregate’ is made up of a single cluster only.

Using equation R1-26 to substitute for Δρagg, estimates of φagg for a range of exponent and size combinations can be obtained, as in Figure R1-11. From this figure the ‘low’ experimentally-observed values of φagg ~ 10‒3 may be due to: • relatively dense (i.e. high-Df) aggregates made up of primary particles only; or • loose, ‘wispy’ aggregates made up of very large, dense clusters of primary particles. The second case is effectively the same as the first case, given that the clusters would have to be so big that an aggregate could only contain a few of them. Note that Figure R1-11 indicates that larger clusters might increase or decrease the overall solidosity of the aggregate, depending upon how the clusters themselves bind to one another. This subtlety was not realised by SUTHERLAND [989].


747

D. I. VERRELLI

USHER and collaborators [1062] attempted to perform a similar analysis. Their work used the simplifying assumptions that no distinct clusters persist and a single fractal dimension describes the entire structure — reasonable for their small coagulated aggregates (dagg ~ 10 d0), but not necessarily for the larger flocs. By defining an ‘effective’ primary particle size they estimated e q u i l i b r i u m packing fractions, φg, of: 0.81 (“RLCA”); 1.15 (“DLCA”); and 7.8 (high-molecular-mass anionic polymer) [1062] *. The authors argued that the correlation between increasing φg and increasing dagg could be explained by enhanced ability for the tenuous extremities of the larger aggregates to i n t e r p e n e t r a t e [1062] (leading to φg > 1), although intrafloc compaction seems at least as plausible. (Interpenetration is predicted to be most significant for gelation (cf. percolation) at high solidosity, where the interpenetrating limbs form in situ [457, 590].) Further potential errors are due to the small sizes of the coagulated aggregates considering the primary particle polydispersity, and the assumption that the parameters in the scaling formulæ can be obtained by extrapolating back to a single (solid) primary particle (cf. the discussion following equation R1-24).

R1▪5▪4 R1▪5▪4▪1

Measurement of fractal dimension General

Fractal dimensions of WTP sludge aggregates are typically estimated from one of four methods [217]: 1. Analysing static scattering patterns of incident radiation. 2. Monitoring the terminal settling velocity and dimensions of a single aggregate. 3. (Magnified) image analysis. 4. Computerised modelling of the aggregation and disaggregation processes. The first three of these are treated in more detail in the following sub-sections. Several other approaches exist, and are also discussed briefly below.

Df can be estimated by exploiting instruments using the ‘electrozone’ principle (e.g. a Coulter Counter (Beckman Coulter, U.S.A.)), which only detect the solid phase, and building a relationship with the total aggregate volume through a second measurement using either

*

Without rigorous argument the e f f e c t i v e d0 in a polydisperse system was defined as (d0 ) 3 , D

f

(in

conventional notation [29]) [1062]. The derivation of BUSHELL [see 214, cf. 217] demonstrates that this definition i s appropriate for analyses of solidosity, where volume equivalence is most important [see also 215]. (Note that this disregards the location of the various sizes within an aggregate, unlike, say, the radius of gyration.) An alternative parameter is (d0 ) 4 , 3 , the volume-weighted diameter, which is a better (but not perfect) indicator of particle size measured by light scattering [613, 862, 915]: use of this parameter yields amended values of φg of 0.33, 0.47 and 3.2 (respectively). These amended estimates are still based on the simplistic assumption that Df = 2.0 for a l l of the aggregates [1062]: the fractal dimension of the “RLCA” case could be significantly higher, leading to greater φagg (especially considering the initial dominance of particle–particle and particle–cluster aggregation) and hence smaller φg; true DLCA aggregates and polymer flocs could have significantly lower Df, leading to smaller φagg and hence greater φg — note that the postulated corrections would tend to a m p l i f y the trend already present in the ‘amended’ φg values.

748



image analysis or a ‘light blocking’ particle counter [429] or through knowledge of the initial concentration [961]. Another method is the ‘ t w o - s l o p e s ’ technique, where fractal dimension is obtained from the ratio of exponents describing the cumulative aggregate size and volume distributions [143, 530, 531, 640, 1005] [cf. 440, 581]. A limitation of this approach is the uncertainty with which a given length can be correlated to a given volume [531], so that there is no straightforward means to confirm that the aggregate is a true fractal or to see trends of Df with intra-aggregate lengthscale. (This approach has the same weakness as direct application of equation R1-15, in that a hypothetical set of aggregates that undergo densification according to suitable dependence on dagg could produce a simple fractal dimension for the distribution that does not describe any of the individual aggregates.) A further concern is the ability to accurately measure the true volume of s o l i d matter in O(103) aggregates [cf. 531]. An inherent m e t h o d error of ±10% in Df was claimed [531]. Monitoring the time-evolution of aggregate size (distribution), such as by means of dynamic light scattering (e.g. using ‘photon correlation spectroscopy’ (PCS) [429] or ‘quasielastic light scattering’ (QELS) [667, 670]), can also permit estimation of Df if a valid aggregate growth model is known [217, 645, 953] [cf. 440, 706, 877]. A final technique, developed by GREGORY and co-workers, is based on analysis of the random fluctuations associated with turbidity measurement; however it relies on a number of assumptions and may not be suited to low fractal dimensions [429]. In all cases care must be taken lest the aggregates be damaged. One experimental comparison concluded that automated (flow through) sampling was less destructive than manual sampling [961]. Of course, in situ measurements are preferred wherever possible. Techniques have been suggested for ‘freezing’ the structure of a fractal aggregate to facilitate handling and inspection (e.g. polymer addition [677]; embedding in a resin or agar jelly [413]; freeze drying; freeze–fracture, or ‘freeze–etch’ [322]), but such processing might itself interfere with the structure [see also 278, 568, 989, 1009, 1112]. GLOVER et alia [404] provided an excellent summary of the respective advantages and disadvantages of settling and light scattering techniques. A key finding was that light scattering tends to be more suitable for small, open aggregates, while settling is more suitable for large or dense aggregates, and thus by this assessment may be considered “complementary” [404] [cf. 111, 1133]. Scattering is also better suited to aggregates with low refractive indices [217, 913]. Image analysis is appropriate for large, open aggregates of high visual contrast [217]. For WTP aggregates the sizes tend to be relatively large — of order 500μm or more for sweep or enhanced coagulation, or flocculation [116] — and so scattering analysis may not be suitable. In such cases scattering analysis can still be undertaken, but it will provide information about lengthscales much smaller than dagg; in contrast, settling experiments are expected to be most influenced by structure on lengthscales close to dagg — different results would thus be expected from each if the aggregates have multilevel fractal structure (§R1▪5▪7▪4) [1133]. An additional advantage of the settling analysis in the context of the present work, not reported, is the direct physical relevance to dewatering processes [e.g. 355], and especially to the gel point (cf. §R1▪5▪3).


749

D. I. VERRELLI

R1▪5▪4▪2

Scattering

Scattering patterns may be obtained using a variety of radiation sources, which are each associated with different wavelengths and hence probe domains of different sizes within the aggregate [217, 1047]. Small-angle neutron scattering (SANS) [217, 404], and small-angle xray scattering (SAXS) [103, 183, 184, 217, 1008] have been employed, but the most common radiation is visible light (SALS [e.g. 841, 913, 969] or SALLS [e.g. 569]) [see also 215, 706]. Laser light is a readily available source that conveniently probes the size ranges that are usually of interest, is accurate for dilute samples, and simply avoids the need for spatial ‘desmearing’ corrections associated with slit-collimated beams [706]. A typical light source is a helium–neon laser, with wavelength 633nm [215, 404, 666, 670, 705, 1004]. For comparison, SAXS and SANS techniques utilise wavelengths in the range 0.1 to 3nm, which probe structures from <1nm up to ~100nm — thus they are suited for sub-micron aggregates [103, 183, 706, 1004], and can only probe the shortest-range structure of WTP aggregates. Light scattering probes the particle structure by analysing the profile of scattered light intensity, I, as a function of the scattering angle, θ *, this angle in turn being associated with a wavenumber, q, through BRAGG’s law †: q = (4 π n / λ) sin(θ / 2) ≈ 2 / d , [R1-32] where n is the solvent refractive index, and λ is the wavelength of the incident radiation in vacuo [666]. The wavenumber, q, is the reciprocal of the linear dimension of the aggregate domains under examination, d / 2 [404, 666] ‡. q is also the m a g n i t u d e of the vector difference between scattered and incident light, called the “scattering vector” [841]. Of most interest in the context of aggregate structure are the lengthscales, d, considerably smaller than the aggregate size, dagg, but considerably larger than the primary particle size, d0 [404, 670]. (Larger domains are related to aggregate size; smaller domains are related to primary particle arrangement, of particular interest for crystalline materials.) In these intermediate size ranges it is found that for fractal aggregates there is a steady change in the correlation function (i.e. likelihood of finding primary particles separated by that distance within the aggregate), and this manifests itself as an exponential decay in scattered light intensity as smaller and smaller size domains are probed. The magnitude of this exponent is interpreted as the fractal dimension. In the RAYLEIGH–GANS–DEBYE limit (refraction and absorption negligible) scattering is represented by the formula [214, 1004, cf. 1082]:  P(q) S(q) . I(q) ∝ [R1-33a] The ( i n t e r p a r t i c l e ) structure factor, S(q), is the FOURIER transform of the density or pair autocorrelation function [544, 666, 730, 841, 1004]; thus S(q) relates to the a g g r e g a t e or network structure [214, 841]. § P(q) is the form factor of the p r i m a r y p a r t i c l e s [214, 544, 841, 1004].

*

Note that conventionally in XRD this angle is defined as 2θ (§4▪2▪1▪2(a)).

†

For small angles, θ, such as in SAXS, with constant n, it is possible to approximate the argument as simply θ / λ [103].

‡

Traditionally fractal analysis considers the r a d i i of the scattering objects, and defines the domain being probed at wavenumber q in a manner consistent with that, i.e. as d / 2 [e.g. 666]. Other definitions, differing only by a constant (viz. π) [e.g. 841, 899], are equally valid, but care must be taken to avoid confusion.

§

Density fluctuations can also be used to estimate material relaxation times [see 908].

750



Strictly, equations R1-32 and R1-33a are only exact for systems that are crystalline and monodisperse (respectively) [841]. Where this is a poor assumption, more complicated formulæ are required [see 453, 841]. The total scattering effect is made up of contributions from aggregates of different size ranges — i.e. it is a function of the cluster mass distribution [214, 457, 666, 667, 841]. In principle, at appropriate q, I(q) could be factorised  P(q) S0(q) Sagg(q) , I(q) ∝ [R1-33b] where S0 describes the arrangement of particles in an aggregate while Sagg describes the arrangement of aggregates in the system — although again this is only exact for ‘comparable’ (cf. monodisperse) primary particles and aggregates [457]. For infinite fractal objects [899] I (q) ∝ q Ds −2 Df .

[R1-34]

As the lengthscale approaches that of the primary particles (or below), Ds → 2 (see equation R1-16), and Df → 3 (equation R1-15), so [899] I (q) ∝ q −4 [R1-35] provided that they are smooth. The region where this holds is known as the POROD region [706, 899]. Rough primary particles can yield POROD region exponents between ‒3 and ‒4, or even less than ‒4 (referred to as ‘subfractal’) [899]. At lengths intermediate between the aggregate size and primary particle size, for mass fractals Df = Ds, and so [899] I (q) ∝ q − Df . [R1-36] The implication of the power-law dependency in this region is that the aggregate structure looks the same when viewed on any scale between d0 and dagg — hence the concept of ‘self similarity’ [906] or ‘scale invariance’ [670] (as per §R1▪5▪1). At lengths much larger than dagg the scattering is completely coherent, and so I(q) does not vary with q [666]. Some concerns in the experimental application of scattering techniques are the potential for either multiple scattering or shadowing to occur. Multiple scattering describes the situation where the concentration of (primary) particles is sufficiently high * that a significant proportion of the radiation is scattered (i.e. interacts with the particles) more than once before reaching the detector [404]. Research suggests that in fact multiple scattering need n o t affect the estimate of fractal dimension [217, 404, 666, 670, 1111]. Shadowing refers to systems containing high densities of particles, such that some of the (primary) particles are not exposed to the incident radiation, and so do not contribute to the scattering [404]. The consequences of shadowing have not been established [404]. A further concern is the application to r e a l s y s t e m s in which the primary particles are not identical (including coagulation for drinking water treatment [214]), and especially the case of size polydispersity. The effects of polydispersity are not well understood [404]. A particular complication is noted by BUSHELL et alia [217]:

*

A similar effect would be obtained by altering the pathlength of the incident radiation through the sample to the detector. However the pathlength is generally fixed. The high ‘concentration’ may be the bulk concentration of aggregates, or it may be a localised concentration referring to discrete clusters [666]. R1▪5 : Aggregate structure and fractal dimension

751

D. I. VERRELLI

[...] very fine particles may have different surface and electrochemical properties due to increased edges, corners and crystal imperfections [...] and this, along with the much higher specific surface area and differing relative strength of Brownian and fluid motion may mean that the aggregation behaviour of small and large particles will be different.

Aggregates of polydisperse primary particles may not exhibit fractal scaling, especially at short range, due e.g. to non-uniform distribution of the particle sizes throughout the aggregate [216]. However, at least in some cases the conventional analyses are able to describe data obtained from polydisperse systems [481, 1111]. In some systems Df has been shown not to be affected by size polydispersity [217] — for the aggregate as a whole, as well as for its constituent species — although certain characteristics (e.g. spatial distribution of mass) did change and were no longer truly fractal [214]. A further complication is the consideration of polydispersity in other primary particle properties, such as (mutual) reactivity [732, 736], aspect ratio, and roughness. Reactivity between and within particle classes has a larger effect in ‘erstwhile DLCA’ than ‘erstwhile RLCA’, as those non-interacting particle combinations act to shift the effective behaviour towards RLCA [732, 736]. ‘Asymmetric’ fractions of the particle classes slow the kinetics (although the optimum does not match simple stoichiometry) [732]; this is the main effect when a reaction-limited model is used [736]. Fractal character may be lost at the small and large aggregate lengthscales (or, equivalently, at short and long times) [732]. Further variations could be expected from working with continuous or semi-batch processes, rather than batch processes, or by considering unmixed or poorly mixed systems [cf. 655] with a large degree of interfacial disequilibrium. Aside from primary particle polydispersity, it should be recognised that each large aggregate will contain a different number of primary particles. When the aggregation proceeds by DLCA (§R1▪5▪6▪1), the scattering is likely to be dominated by the largest aggregates [666]. (At least in the GUINIER regime, at lengthscales larger than dagg, the scattering is weighted by the squared mass of the entities [215, 666, 913] [cf. 457, 841].) For RLCA (§R1▪5▪6▪1) the large clusters do not dominate the response, and in fact the large number of small aggregates formed in this mode of aggregation can dominate the scattering in some cases [666]. Moreover, the more polydisperse distribution of aggregate sizes generated by RLCA inhibits deconvolution of the structure parameter of the aggregates and their spatial arrangement — which is not a problem with direct imaging (§R1▪5▪4▪4) [440]. The size distribution of typical WTP aggregates may be sufficiently narrow to be neglected in fractal analysis [913, see also 960]. Additionally, given that real aggregates are of finite size, at larger lengthscales (above about dagg / 10 [666]) surface scattering effects become important [217]. To permit accurate extraction of Df from experimental data, a variety of ‘cutoff’ functions have therefore been proposed [366, 666]. A significant amount of research has been conducted into determining the ‘best’ cut-off function to use; a consensus is yet to be reached [cf. 217, 913]. Strong anisotropies in cluster shape may also prevent accurate analysis of scattering patterns [913]. As with settling, it is important to avoid damaging aggregates while loading and measuring samples [e.g. 913]. The precise thresholds will vary greatly from one system to the next, and the decision on what is acceptable may be somewhat subjective: one researcher [1004]

752



reported that stirring 2μm aggregates at 800rpm in a small sample chamber caused them no damage. Conversely, other research [355, 1055] deliberately allowed exposure of large flocs in a 450mL sample to stirring at 1000rpm (and passing through a “volumetric pump”); this was claimed to break the flocs down to sturdy constituent clusters.

R1▪5▪4▪3

Settling

Equation R1-19 has been used to estimate Df. Experimentally Δρagg may be estimated by correlation of observed free settling velocity and some average aggregate size given a particular flow regime. The settling rig should be designed to be free from vibration [1003] and avoid exposing the aggregate to shear that might destroy its structure [355]. It should minimise thermal convection gradients in the suspending fluid [1003] (which should be the same as the mother fluid the aggregate was sampled from). The settling column should also have a diameter much larger than the aggregate size, in order to avoid significant wall effects (at least 20mm for 500μm aggregates [404]). It is often a good assumption that motion is in the creeping flow regime (§2▪2) [111] [cf. 355]. Creeping flow requires Re < 0.1, which imposes limitations on the maximum values of dagg and the settling velocity for which this analysis is valid. Approximations (of decreasing accuracy) have been proposed to permit estimation for Re ( 1.0 [154], Re ( 10 [404] or Re ( 100 [530]. Combining equations R1-19 and 2-12b, aggregate terminal settling velocity (Δu∞) and size (dagg) are correlated by a power-law relationship, with exponent equal to Df ‒ 1 [217, 1133] to a first approximation. This approximation may result in overestimation for low fractal dimensions [217], or underestimation for Re > 1 (especially for low sphericities) [see 355, 997, 1055]. More accurate estimates require knowledge of the size-dependence of the aggregate permeability and shape factor (for drag correction), and likewise for the structure prefactor (k in equation R1-18) [217]. Orientation will also affect the result [217]. A serious limitation on the settling method is due to permeation of liquid through loose aggregates that occurs as they settle [cf. 215, 1054]. Work by VEERAPANENI & WIESNER [1068] suggests that for Df T 2.0 this effect will be negligible for dagg / d0 T 100; for Df ~ 1.7 the effect can only be neglected for the larger aggregates, with dagg / d0 T 1000 [cf. 404]. For a smaller, open aggregate with dagg / d0 = 100 and Df = 1.70, the drag force would be overestimated by ~14%, with я ~ 0.88 in equation 2-12b [1068] [cf. 404]. A number of permeability models * have been proposed. Popular choices include those of [217, 641, 660, 1068]: • KOZENY and CARMAN; • DARCY — suited for creeping flow with Df > 2;

*

Alternative terminology refers to ‘advection’ of fluid through flocs, and the ‘fluid collection efficiency’ (the proportion of fluid approaching a floc that passes through it) [1018]. R1▪5 : Aggregate structure and fractal dimension

753

D. I. VERRELLI

• BRINKMAN (1947) — assumes aggregates are uniformly porous spheres, suited for creeping flow with Df < 2 *; • HAPPEL (1958); and • KUSTERS (circa 1947) — assumes a uniformly porous shell around a solid core. In some cases permeability models may be extended from the creeping flow regime (Re / 1) to conditions of Re < 40 without excessive error [217]. Yet for fractal aggregates, where porosity is far from uniform, the simple models often underestimate the true permeability [140]. The more sophisticated choices recognise that permeability of the core will be lower than that of the periphery [e.g. 408]. An important refinement recognises that generally the largest pores will dictate the permeability † [660]. Based on the inherent self-similar scaling of fractal objects, the size of the largest pores will scale with the size of the aggregate itself [406] [cf. 660, 698], provided restructuring does not occur [217]. (This argument also discourages the use of uniform porosity particle or shell models [cf. 1068].) Permeability through these large pores would then be obtained from one of the above correlations [660]. Thus the permeability-based drag correction factor would be constant for a fixed Df [217, 660]. With this refinement the KOZENY–CARMAN model reportedly [660] performs poorly, while the BRINKMAN and HAPPEL models yielded reasonable predictions [641]. (Calculations based on uniform porosity lead to the same conclusion [1068].) Elongated particulates tend to adopt a ‘diagonal’ orientation in a compromise between minimising projected area (hence form drag) and friction drag; the relative importance of each component will depend upon the settling rate ‡. In transitional flow particulates settle with minimum projected area perpendicular to the flow [217]; in creeping flow there is no strong orientational preference, and asymmetric particles often spin or wobble [217]. Even if the structure prefactor and the correction factors associated with aggregate shape and permeability do not affect Df, they are still required to accurately estimate the aggregate solidosity [217]. Settling experiments are time consuming, and require the separate settling of many aggregates [217]. Particular care must be paid to temperature control [115, 1003]. Furthermore, the correlation between aggregate terminal velocity and dagg may be relatively weak [e.g. 1133]. Unfortunately, appropriate regression and statistical techniques (outlier analysis, robust regression, bootstrapping confidence intervals) are seldom applied [e.g. 1133], leading to occasional misestimation of fractal dimensions. Even where an attempt is made to estimate errors, these are often misleading. For example, FARGUES and TURCHIULI [355, 1055] found a power-law correlation between u and dagg with exponent ~0.798, from which they concluded that Df = 2.52±0.4 at the 0.05 level of

*

In fact, the BRINKMAN model tends to predict that advection can be neglected for Df > 2 [429]. However, this does not take into account the s i z e of the aggregate: a large aggregate of fractal dimension 2.1 may be more permeable than a small aggregate of fractal dimension 1.9.

†

Permeability is proportional to the s q u a r e of the pore size [217], and may be considered proportional to the square of the dense-cluster size [660].

‡

Hence errors are introduced depending upon whether aggregate size is estimated based on the laterallyprojected profile, rather than that projected in the flow direction (see footnote following equation R1-15).

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significance. Yet many other researchers would have interpreted the same correlation as implying the most likely value of Df to be ~2.2 (±uncertainty). The statistical error bounds did not encompass s y s t e m a t i c error. The study of LEE et alia [641] suggested parameter estimates could differ by two orders of magnitude, depending upon the permeability model chosen and the properties assumed for the primary particles.

R1▪5▪4▪4

Imaging

A major benefit of imaging over settling or scattering experiments is that detailed information about the aggregate morphology, or internal structure, may be obtained [217]. (This is similar to that obtained from computational modelling.) Fractal analysis of aggregates by imaging is generally carried out by projection into just two space dimensions. Conversions from the resulting Df 2dim. to ‘corresponding’ values of Df are thus often employed [e.g. 997, 1151], as per equation R1-17, as the latter is more physically relevant. There are a number of different image analysis procedures [217]: • Box counting — the image is discretised into bitmaps of varying resolution; then log( N ) lim Df 2dim. = l → 0 − , [R1-37] log( l) in which N is the number of pixels needed to ‘cover’ the object, and l is the pixel size [cf. 405, 407, 440, 838, 1083, 1126]. To avoid finite-size artefacts ideally d0 / l / dagg [cf. 659]. • Sand box — a reference pixel near the centre of the aggregate is chosen; then log( N ) Df 2dim. = , [R1-38] log( L) in which N is the number of aggregate pixels within the box of size L [cf. 366, 989, 1009, 1083]. To avoid finite-size artefacts ideally l & d0 / L / dagg [217, 1009]. Accuracy can be improved by averaging results obtained from several choices of reference pixel (or particle) [366, 1009, 1083] [cf. 735], and by averaging over several ‘comparable’ samples or aggregates [cf. 841]. (Averaging over all possible pixels or particles essentially yields the density autocorrelation function [217, 841].) • Confocal scanning laser microscopy (CSLM) — CSLM operates by restricting the microscope’s field of view such that effectively horizontal ‘slices’ of the object may be examined, which permits the acquisition of a three-dimensional image. • Physical sectioning (microtoming) — the object is set into a solid form and progressively shaved down; examining the top surface at each stage allows a threedimensional image to be constructed [e.g. 413, 1151]. The estimates of Df arising from these various techniques are “theoretically” all different; however, in practice they “amount to the same thing” [217]. The radius of gyration can be obtained if all of the primary particles comprising the aggregate can be identified; in such cases Df could be evaluated by equation R1-15 (p. 738) [440]. However, this is described as inherently weighting the peripheral parts of the aggregate more, so that it is especially sensitive to aggregate “anisotropy” [440].


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The fractal dimension can alternatively be estimated by directly evaluating the (two-point) density autocorrelation function [366, 726, 727, 728, 730, 1047, 1048, 1083, 1112] [see also 841], as is implicitly done in light scattering studies. The function should increase as a power function of lengthscale, with exponent Df [589, 726, 1047, 1048]. Imaging is also regularly used to provide a q u a l i t a t i v e assessment of compactness or porosity.

R1▪5▪5

Effect of aggregation mode

On sufficiently large lengthscales all kinetic aggregation systems yield fractal aggregates [899]. Much of the analysis of aggregate fractal dimension relies on results from computer simulation and mathematical modelling for interpretation of physical meaning. A useful warning is that [761]: In its original form the cluster–cluster model is a very rough simulation of physical reality.

There are numerous key modes and mechanisms of aggregation, which have significant effects on the fractal dimension of the final aggregate. Different models make assumptions on a variety of aspects of growth [e.g. 429, 691, 899], typically making the simplification that some l i m i t of behaviour applies [e.g. 706], as summarised in Table R1-13, and these yield different aggregate structures and different values of Df. It is thus very dangerous to attempt to “[ascribe] specific mechanisms [...] solely on the basis of power-law exponents” [838] [cf. 550]. Table R1-13: Limiting choices in formulating models of aggregation. Most common choices/assumptions are listed first. The column at far right gives the limiting assumption yielding the larger (apparent) value of Df.

Aspect Mechanism of motion and collision [211, 518, 530, 795, 921, 1070, 1071] a

Limiting assumptions • Aggregation due to BROWNian motion (perikinetic) • Imposed fluid mixing (orthokinetic) — note that the primary particles and smallest clusters are likely to always aggregate perikinetically • Differential settling [439, 518, 799, 921, 1018] *

n Flow regime [531]

*

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Orthokinetic kinetic coagulation may involve: o Laminar flow or mixing [85, 143] o Turbulent flow or mixing [467]

Most compact Orthokinetic (unless laminar, see below, or strongly attracting without restructuring [cf. 440, 872, 1048, 1071]) Turbulent

The fractal dimension of objects aggregated by differential settling is less well characterised. However, it is plausible for Df to be reduced compared to the (turbulent) orthokinetic case or perikinetic cases due to the greater tendency of the particles or clusters to adopt specific orientations in differential settling. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


n Cluster diffusivity [729, 761]

Perikinetic coagulation may occur in which: o Rotational diffusion of cluster is negligible o Translational diffusion of cluster is negligible (Similar conclusions could be drawn for other modes by generalising to rotational and translational m o t i o n [cf. 728].) Size-dependence of translational mobility affects structure through the size ratio (below) [178, 544, 545]. Cluster • Cluster polarisability is negligible polarisability • Cluster polarisability is significant — e.g. charge [104, 280, 542, differences are induced across the cluster by b, c, d neighbouring/approaching clusters 543, 761] Mass transport • Rapid, diffusion-limited (or convection-limited [440, and rate of 872]) growth reaction [531, • Slow, reaction-limited growth (as for strong interparticle repulsions [see 1070]) 899] • Ballistic growth (roughly intermediate to the above), in which particles/clusters approach each other along (random) linear trajectories The likelihood of reaction following an encounter is determined by inherent particle properties (especially at the surface), inherent fluid properties, and can also be affected by externally applied fields [709]. Accretion • Aggregate growth through combining of two (units that clusters (cluster–cluster) form bonds) • Aggregate growth one primary particle at a time [280, 899, 991, (particle–cluster) 1112] Cluster–cluster aggregation may be: n Size ratio of aggregating o Heterogeneous, i.e. between different-sized clusters clusters [178, 179, o Homogeneous, i.e. between same-size clusters only (hierarchical model [179, 544, 545, 546, 198, 405, 730, 734, 1025, 1048]) 441, 545, See discussion at p. 767. 706, 730, 734, 990, 991, 1025]

Reversibility [481, 531, 588, 613, 691, 730, 841, 899, 969, 1107]

• Kinetic growth (strong irreversible bonds form) • Near-equilibrium growth (processes are reversible, break-up is significant) — at long times this must apply to all systems


Rotational diffusion negligible

Negligible polarisability

Reaction-limited

Particle–cluster (unless highly polarised [542, 543] e) Heterogeneous [198, 405, 730, 734, 1025] [cf. 544] (unless as primary particles bidisperse [441]) or irrelevant [838, 991] [cf. 179, 544, 589, 761] Reversible (except single-particle disaggregation– reaggregation [176])

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Range of attractive forces [178, 541, 544, 841, 1091] Primary particle features

Primary particle size (compared to characteristic shear dimension)

Primary particle size polydispersity [214, 410, 860, 1091] 758

• Short-range (model requires surface contact) • Long-range (of order d0)

Systemdependent

• Smooth, hard, bare spheres — able to ‘roll around’ to a more compact position [85, 143, 481, 518, 845, 944, 989, 991, 1040, 1083] • Hard spheres with adsorbed species — bonding preferred on certain faces [989], sterically hindered from moving to more compact position after bonding [85] • Deformable spheres — bond may become more rigid with ageing, due to an increase in the contact area [814] or ‘sintering’ [261], reducing ability to roll about and restructure [cf. 386] f • Rough ‘clods’ or hard spheres with nanoscale roughness — may imply fractal surface structure [899], reduced ability to ‘roll around’ (as above) [814, 841, 860], or increased probability of bond formation [688, 709], or reduced (or enhanced) adhesive strength [81, 220, 438, 813] The same consequences may ensue from nonuniform surface charge distribution [709] as in ‘charge patch’ flocculation [326, 426, 1140] • Anisometric particles (e.g. aspect ratio significantly different from unity) — may not pack efficiently [211, 410]; may pack more efficiently, as in rafts [e.g. 280, 325, 388, 768, 1130, 1131] [see also 677, 1083] (For aspects that determine interparticle repulsion or attraction — or capture efficiency — such as surface charge [709, 1070] or any deviation from smooth, hard, bare spheres [e.g. 813] refer to ‘rate of reaction’ above.) • Small — negligible hydrodynamic resistance to collisions; inclined to densify by structural rearrangement • Large — significant hydrodynamic resistance to collisions; inclined to undergo breakage and regrowth

Smooth, hard, bare spheres (except in laminar or extensional flow [cf. 472])

• Nearly monodisperse • Bidisperse [215, 216, 441] [see also 262] • Significant polydispersity (arbitrary size distribution) [217, 453, 481, 489, 921]

L a r g e , if ‘formation’ dominant [cf. 427, 1070]; s m a l l , if ‘de-formation’ dominant [914] (Orthokinetic case only.) Systemdependent (often similar; may not be fractal at all scales)



Reactivity of • Nearly monodisperse primary • Significant polydispersity particle classes [732, 736]

Systemdependent (often similar; may not be fractal at all scales)

Notes: a It is assumed that the suspension is not concentrated. For concentrated suspensions (i.e. approaching the gel point) percolation * [243, 589, 681, 841, 966, 1151] and other models [705] (e.g. “polycondensation”, i.e. step growth polymerisation) have been considered, which yield greater fractal dimensions [590]. Large-scale structure in sedimenting systems may be affected by preferential horizontal alignment of clusters near the base [see 795]. b This is different to charge heterogeneity at cluster surfaces (e.g. due to adsorbed polymer): although this implies increased attraction, and hence less compact structures, in fact more compact structures are reported [1133], presumably due to restructuring effects. On the other hand, “anisotropic repulsive interactions” were also proposed as a mechanism yielding reduced fractal dimension [546]. c Dipole relaxation does not appear to significantly affect the structure [761] — see p. 772. d This may arise through, inter alia, magnetic and electrical effects. e Occurrence of both polarisation and particle–cluster aggregation together in real physical systems has not been identified [543]. f Other mechanisms unrelated to deformability could also lead to enhanced bond strength (particularly upon ageing — §S17▪1, p. 938), such as: solid bridging [cf. 616, 734]; adhesive bridges of natural organic matter (or other polymers) [762]; electrostatic interaction between differently-charged crystal faces [162]; and covalent or metallic bond formation [734], et cetera.

Many of the critical features and deviations from simplistic model behaviour were identified in the same two pioneering papers [viz. 589, 726] [cf. 544, 730] that introduced the modelling of perikinetic cluster–cluster aggregation: • E f f e c t o f c l u s t e r d i f f u s i v i t y . If the diffusivities are independent of mass, or decrease weakly or strongly with mass (the usual case), then individual particles and small ‘oligomers’ are rapidly consumed in the early stages, and conventional DLCA results [589]; if only the largest clusters have significant diffusivity, then WITTEN– SANDER particle–cluster aggregation results (in the limit of low initial concentration) [726]. [See also 545.] • I n i t i a l c o n c e n t r a t i o n [589, 726]. See above. • S t i c k i n g p r o b a b i l i t y . The fractal dimension was reported to be insensitive to sticking probability [726], delaying recognition of the importance of RLCA, as early studies did not consider sufficiently low sticking probabilities †. • L a t t i c e a r t e f a c t s . The researchers recognised the limitations of their early ‘lattice’ models, and were working on ‘off lattice’ models [726] — however later studies demonstrated that errors due to the lattice were small. • C l u s t e r s i z e d i s t r i b u t i o n [589]. This distribution is often ‘universal’ for a given model, with appropriate scaling. • T i m e d e p e n d e n c e [589]. Later work has enabled fractal dimension to be estimated from temporal profiles when an aggregation model is known or can be safely assumed.

*

While percolation is associated with aggregation processes, (cluster–cluster) aggregation in which no restructuring is permitted cannot yield true percolation, because “the irreversibility guarantees a memory of the regime [of low spatial coverage by the clusters] even when later on the clusters percolate” [589] [see also 705]. Other discrepancies between percolation analyses and observations of gelation have been reported [243, 590, 705].

†

Presumably a major contributor to this was the limited computational power available. R1▪5 : Aggregate structure and fractal dimension

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• R e s t r u c t u r i n g o r r e v e r s i b i l i t y . KOLB, BOTET & JULLIEN [589] predicted improved agreement with empirical data by incorporating restructuring into the model. • H y d r o d y n a m i c s . KOLB, BOTET & JULLIEN [589] also noted that in the experiment alluded to above the cluster and particle motion is determined by both “random” (i.e. BROWNian, perikinetic) and “hydrodynamic” (i.e. shear, orthokinetic) elements. Even before fractal analysis became de rigueur, MASON (1977) [709] indicated clearly the wide scope of behaviours encompassed within (orthokinetic) aggregation, realised according to variation of a multitude of parameters. It is unfortunate that these early insights and recognitions have sometimes been forgotten by later researchers. Difficulties associated with inferring a mode of aggregation based on estimates of Df were also recognised early on — e.g. KOLB & JULLIEN (1984) [591]: In experimental situations, the exact nature of the kinetic mechanism and the chemical bonding relevant for the aggregation are not known. [....] Nevertheless it is suggestive to compare [experimental evaluations of Df] with the models discussed here.

— but are also often ignored by current researchers. As Table R1-13 indicates, a huge number of aggregation scenarios can be classified based on combination of several limiting assumptions. This ultimately becomes infinite when intermediate cases [e.g. 795] are allowed. Table R1-14 illustrates a range of plausible scenarios for ‘simple’ cluster–cluster aggregation, highlighting the patchy research coverage and confusing labelling. Table R1-14: Plausible scenarios for ‘simple’ cluster–cluster aggregation based on transport mode and rate-limiting step. Outlines define strict range of label validity; shaded areas indicate ‘traditional’ areas of theoretical research focus. Labels are discussed in the text.

Transport mode BROWNian Shear • Laminar • Turbulent Ballistic • Random • Uniaxial • Unidirectional

Step controlling aggregation rate Transport Intermediate Reaction Jargon DLCA RLCA Perikinetic CLCA/

/Orthokinetic

SUTHERLAND/ /Ballistic

Orthokinetic “Ballistic” Differential settling a Sedimentation a

Note a It is helpful to draw a distinction between s e t t l i n g , which focuses on the f a l l of particulates, and s e d i m e n t a t i o n , which focuses on their d e p o s i t i o n at the bottom of the vessel [cf. 450, 945]. In the latter a connected (‘networked’) bed of particles is formed, rather than suspended aggregates.

The case of ballistic transport exemplifies the disjuncture: while both randomly-oriented and uniaxial ballistic growth strictly fall into this category, in the conventional jargon only the former case is implied by the term “ballistic”; furthermore, the research focus is narrowed to only the transport-limited case (also known as SUTHERLAND growth — see §R1▪5▪6▪1). Despite statements that reaction-limited aggregation removes the dependence upon particle trajectory (i.e. transport mode) [e.g. 544], in reality not all physically-accessible sites on a

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cluster will have equal probability of forming a bond, and the weighting must depend upon the transport mode.

R1▪5▪6 R1▪5▪6▪1

Details of aggregation mode mechanics Perikinetic and ballistic aggregation

The computer simulations and theoretical analyses most commonly employed model aggregation in a regime classed as p e r i k i n e t i c , meaning that the collisions between primary particles are due to BROWNian motion [505, 1070]. Perikinetic aggregation processes are considered to have t w o p h y s i c a l l i m i t s [1111] [cf. 1074], which apply ‘ u n i v e r s a l l y ’, “independent of the chemical details of the particular colloid system” [667] *. This universality extends to systems that interact through very different bonds — including metallic (e.g. gold), covalent (e.g. silica), and VAN DER WAALS (e.g. polystyrene) [667] bonds — provided that the energy barrier to bond formation can be sufficiently varied [cf. 1111]. Biological systems may be excluded from this class [640, cf. 667]. In the first limiting case a bond is formed whenever a collision between particles occurs — i.e. the collisions are ‘perfectly efficient’ [e.g. 80, 429, 530, 691, 1111]. This results in d i f f u s i o n - l i m i t e d cluster(–cluster) aggregation, or D L C A , for which Df ≈ 1.75 [100, 217, 404, 457, 706, 799, 1111, 1112] (or 1.78 [761], or 1.80 [734, 899, 956]) † given the usual assumptions indicated by Table R1-13 [cf. 730]. DLCA was traditionally called ‘fast aggregation’, and corresponds to aggregation energy barriers / kB T [666, 670, 1031, 1111]. The physical model of DLCA was developed in 1983 ‡ independently by MEAKIN [726] and KOLB, BOTET & JULLIEN [589]. In diffusion-limited growth most of the aggregate growth occurs at the ‘tips’ of the aggregate [899, 906, 990], which ‘screen’ the interior of the aggregate [591]. For DLCA the aggregate mass scales linearly with time [667], and so the aggregate size obeys power-law growth, with dagg ∝ t 1 / Df [481, 706]. In the second limiting case collisions only rarely result in formation of a bond, i.e. the collisions are much less than 100% efficient — in fact approaching 0% efficiency [e.g. 429, 530, 691, 1031, 1111]. This is known as r e a c t i o n - l i m i t e d cluster(–cluster) aggregation, or R L C A , with Df ≈ 2.09 [100, 198, 217, 404, 667, 706, 730, 734, 899]. RLCA was traditionally called ‘slow aggregation’, and corresponds to aggregation energy barriers of magnitude a few kB T [666, 670, 1031, 1111]. Physical models were first developed in 1984 by KOLB and JULLIEN [545, 591], who described them as “chemically limited”. Conventionally, in reaction-

*

The claim to universality is further supported by the notion of a trajectory dimension (§R1▪5▪6▪1(a)), whose two “physically realizable” limits correspond to the DLCA and RLCA aggregation limits [1111]. (This disregards space-filling trajectories, such as defined by the HILBERT curve [906].)

†

One reason for the spread of estimates is nicely illustrated by SORENSEN & ROBERTS [956]: the estimates are an e n s e m b l e a v e r a g e (§R1▪5▪1▪1), and values for i n d i v i d u a l simulated DLCA aggregates ranged between ~1.6 and 2.0 for 24 aggregates (no doubt a greater spread would be found for a larger sample size). [Cf. 706.]

‡

Earlier work by FINEGOLD (1976) did model DLCA, but was not quantified and did not discuss fractal properties [733]. R1▪5 : Aggregate structure and fractal dimension

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limited growth all available sites are considered equally probable targets for accretion [899]. The aggregate size grows exponentially, with dagg ∝ e Δ t (Δ is a constant) [481, 667, 706, 1111]. B a l l i s t i c cluster–cluster growth (with random trajectories) is named after SUTHERLAND [989, 991] [cf. 728, 732, 733], and has Df ≈ 1.95 [546, 730, 734, 899] [cf. 541]. Although SUTHERLAND growth still assumes that every bond forms instantaneously and irreversibly upon an encounter [989], as in DLCA, this case is sometimes described as ‘intermediate’ to DLCA and RLCA (cf. §R1▪5▪6▪1(a)). There is broad agreement in the literature on the RLCA and DLCA limits, on which most research has been carried out [cf. 404], and they are supported by most laboratory-based studies [404, 666]. Fractal dimensions associated with other scenarios are less well described. R1▪5▪6▪1(a)

Trajectories

In considering RLCA, DLCA and ballistic cluster–cluster aggregation it is helpful to refer to the f r a c t a l d i m e n s i o n of the particles’ and clusters’ t r a j e c t o r i e s , Df,traj. [727, 728, 730] [see also 591, 732, 1025]. In general the lower Df,traj., the more readily a cluster may be penetrated by a particle or a second cluster [727, 728, 730]. In the diffusion-limited process the particles and clusters undergo BROWNian motion (a ‘random walk’) with Df,traj. = 2; in the ballistic mode the trajectories are linear, and so Df,traj. = 1; in the reaction-limited case the e f f e c t i v e dimension of the trajectory is Df,traj. = 0 [545, 730, 732, 1025]. Intermediate values of Df,traj. are also feasible [727]. Note that a BROWNian trajectory can be modelled as effectively linear if the mean free path of the clusters is much greater than the largest cluster size [541] (i.e. high KNUDSEN number, as in a low-density fluid — normally a gas) [cf. 730]. It may seem surprising that RLCA has effectively Df,traj. = 0, given that the motion of the clusters prior to the f i r s t c o n t a c t is BROWNian — exactly as for DLCA. The difference is that in RLCA the first contact has negligible probability of resulting in a bond, so that the clusters then d i f f u s e l o c a l l y until a new contact occurs, and so on [cf. 591] until eventually a bond forms. It is conventionally inferred that all accessible sites on the clusters hence have equal probability of forming a bond [e.g. 544], and the bonding clusters have no ‘memory’ of previous contacts [cf. 589, 705], and it can be visualised as if the clusters were ‘appearing’ at various random p o i n t s around each other. A point has zero dimension (although a s e t of points does not [906]). When the probability of forming a bond is small, but not vanishingly so, then a transition of the aggregation mode from RLCA to DLCA occurs [591, 706]. In such cases the clusters are able only to explore a certain distance before bonding becomes highly likely, and so there is a limit to their interpenetration [591]. For small clusters the entire set of available bonding sites can be explored, but for very large clusters the clusters diffuse locally around the initial point of contact for only a relatively short distance, so that the interior particles are ‘screened’, and effective DLCA results [591]. In these models it is generally assumed that particle interactions do not significantly influence the trajectories of the particles and clusters until the separation is very small [cf. 178, 1091] — as typically expected in practice [968]. Long-range interparticle forces can 762



significantly alter the particle packing [1091] [cf. 178, 545, 838]. Long-range attractions were found to yield a l e s s c o m p a c t structure in the case of (diffusion-limited) unidirectional ballistic particle–cluster aggregation (i.e. sedimentation) [1091], which could be interpreted as a ‘hyper-diffusion-limited’ process. Yet in the random cluster–cluster counterpart they yielded a m o r e c o m p a c t structure (Df ≈ 2.06) than where short-range attractions are used (i.e. SUTHERLAND growth) — at least overall, for the larger lengthscales [178, 541] [cf. 728]. Moreover, if restructuring were allowed, then long-range attractions could potentially induce densification [cf. 1083]. Aside from long-range attractions, long-range r e p u l s i v e forces may lead to reduced Df (cf. increased Df due to a short-range energy barrier in RLCA), as “the end of a charged dendrite [...] presents less of an electrostatic potential barrier than the side” [513]. Furthermore, restructuring would tend to be discouraged. An alternative explanation can be made in terms of polarisation (§R1▪5▪6▪5) [542, 543]. R1▪5▪6▪1(b)

Underlying cause of reaction-limited aggregation

It has been established that RLCA occurs when the likelihood of bond formation upon particulate encounter is very small. The traditional view [cf. 280] has been that this could be explained in terms of conventional theories of colloid interaction, such as application of FUCHS’ [383] stability ratio [538, 924] on the basis of the DLVO [e.g. 304, 1074] model [cf. 877]. This model considers the likelihood of an encounter resulting in a collision — which is assumed to result in bond formation [383] — following from a summation of attractive VAN DER WAALS and repulsive electrostatic interactions between particles [e.g. 304, 1074]. Refinements have been introduced to more appropriately normalise the ratio [720] [cf. 489] and to take into account the (usually very small) possibility of spontaneous disaggregation [379, 538] [cf. 303, 804, 1073] [see also 701]. An important correction to the stability ratio, first suggested [804] by DERJAGUIN [302] (cf. BOOTH (1954) [1073]), accounts for additional hydrodynamic drag as particles approach [303, 489, 1131]. Rigorous [192, 442] and approximate [489] corrections have been presented; the correction f a c t o r is a function of separation only [220] — not the rate of approach (assuming “creeping flow” [442]). However, inclusion of this additional repulsion is reportedly insufficient to explain observed RLCA [see 877]. Short-range structural repulsion forces

Several other corrections that account for particle interaction terms missing from the simple DLVO model can be contemplated. An important example of these is a term to provide for the existence of short-range forces of repulsion [877]. Such forces are generally envisaged to arise due to the structuring of water in the immediate vicinity of the particle surface [e.g. 122, 538, 688, 1002, 1073] (but excluding water actually in contact with the surface [220]), and so are called ‘structural’, ‘solvation’, or ‘hydration’ forces [517, 877]. Observations indicate they may be significant for distances ( 5nm from the surface [113, 122, 517, 877] [cf. 220]. Theories for predicting these forces are not yet mature [877]. RUNKANA, SOMASUNDARAN & KAPUR [877] reported that incorporation of an exponential repulsive force term — attributed to water structuration or some other non-DLVO


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mechanism [cf. 220, 517] — with a (physically plausible) decay length of 0.6nm was able to provide agreement with experimental observations of RLCA growth kinetics. The foregoing discussion expressly excludes the consequences of more severe alteration of the interfaces, e.g. due to polymer adsorption. Importance of dynamic aspects of aggregation kinetics

It has been suggested [538] that the rate at which layers of structured solvent (and ions) surrounding each particle [see also 122, 688] can restructure is one of the fundamental mechanisms governing the dependence of aggregate structure (or Df) upon the aggregation rate. There is a competition between the timescale at which the ‘stagnant’ STERN layer can r e s t r u c t u r e — expected to be the rate-determining relaxation process — and the timescale of hydrodynamic particle i n t e r a c t i o n [498, 538, 686, 688]. The timescale of STERN layer relaxation is not well characterised in general, with 10‒7 to 10+5s (for surface charge adjustment) all considered f e a s i b l e [686, 804], but estimated as (10‒3s for metal oxide particles [538, cf. 688]. A simple means of estimating the interaction time is to calculate the time to contact for two spheres at an initial separation of 2 κ‒1 using Dt,eff in equation R1-39, and correcting [192, 442, 489] for hydrodynamic retardation [686, cf. 804]. (Note: this is n o t the time between encounters!) For low ionic strength (I ~ 0.0001M) and large particles (d T 1μm) an u p p e r l i m i t of order 10‒3s is obtained *. Smaller d, higher I [see also 498], or the influence of shear gradients (Pé [ 1) would all yield s h o r t e r interaction times (down to 10‒8s for d ~ 10nm and I ~ 0.1M), in which the STERN layer may not fully relax † [cf. 380]. In colloid science terms, the particles may have neither constant surface potential nor constant surface charge (density) [686, 688] [see also 537, 538, 636] [cf. 170, 804, 1074]. Fast coagulation tends to produce “loose and voluminous” aggregates containing a “large amount of trapped solvent” [538]. Conversely [538]: When the particles aggregate slowly, the aggregates are compact and frequently nonredispersible because there is enough time for desolvation and relaxation of the double layers to take place.

The kinetics of STERN layer relaxation may also be important in governing the transition from ‘flexible’ bonds that permit particles to restructure to rigid bonds upon (brief) ageing, or from weak bonds that permit disaggregation to ‘irreversible’ bonding [cf. 379, 380]. R1▪5▪6▪1(c)

Intermediate cases and transitions

Real aggregation may not match one of the limiting cases described [see e.g. 613, 706].

*

Two of the references [538, 686] contain misprints or numerical errors; values were recalculated from the (correct) formulæ. It is worth noting that the retardation is derived from approach along the line of centres [192, 442, 489], but this is not necessarily appropriate for chaotic motion [cf. 686, 688]. Furthermore, no account is made of the possibility of increased viscosity within a distance of κ‒1 from the particle surface [122] [cf. 538, 688, 1012].

†

It is interesting to speculate on the effect this would have on coagulation of polydisperse systems: the implication is that larger particles would relax more readily (more fully) upon interaction, and so would be preferentially coagulated [cf. 688].

764



HOEKSTRA, VREEKER & AGTEROF [481] presented a system in which initially aggregation apparently proceeded by RLCA, but at intermediate times went through a transition towards DLCA, which described the long-time behaviour. Transition from RLCA to DLCA can be explained in terms of a decrease in the aggregate diffusivity with increasing size [481]. Another hypothesis based on increased bond formation probabilities for larger aggregates due to an “increased contact area” [481] was also used to explain ‘induction’ or ‘incubation’ times prior to the establishment of significant aggregate growth [441], which would not necessarily correspond to an RLCA–DLCA transition. WEITZ et alia [1111] reported an apparent transition from RLCA to DLCA too, for a system with intermediate collision efficiency. Decreasing cluster (number) concentration was identified as a cause, along with the decrease in diffusivity [1111]. RLCA to DLCA transition was also reported in a system undergoing bridging flocculation [80]. A comparable transition is from perikinetic aggregation of the primary particles to orthokinetic aggregation of the clusters (or coagulation by differential settling) found at later times [530, 989] [cf. 299]. SMOLUCHOWSKI’s pioneering theoretical development of aggregation kinetics applied the concept of cluster–cluster aggregation, as this better reflected observations of physical behaviour [989]. Finally, another transition, this time for polystyrene aggregates at long times, was ascribed to “an increase in the energy barrier between particles [...] associated with partial coalescence on aggregation” [667, cf. 953]. If the probability of forming a bond upon collision is high, then small clusters will predominate the aggregation process due to their greater aggregate diffusivity; if the probability of bond formation is low, then collisions between larger clusters will dominate the aggregation process [441]. Despite the above reports, it has been questioned whether apparent RLCA–DLCA transitions might actually be manifestations of aggregate restructuring [877].

R1▪5▪6▪2

Reversibility and restructuring

The models typically assume aggregation is irreversible [e.g. 666]. Reversible aggregation is expected to give rise to denser aggregates (greater Df) [588, 691] — see §R1▪5▪6▪4(b), §R1▪5▪6▪6. Over time the transition from kinetic to near-equilibrium growth has been observed to result in smoothing of the surfaces of colloidal aggregates [899]. Simulations that allow for rearrangement of primary particles within an aggregate by ‘rotational diffusion’ (i.e. singly co-ordinated particles ‘rolling over’ one another until a second bond is formed) predict increases in Df from 1.8 to 2.18 (for DLCA) and from 2.09 to 2.25 (for RLCA) [730, 734] [see also 481]. This suggests the open DLCA structures are ‘more susceptible’ to rearrangement [e.g. 670, 706] [see also 523], however this is not universally applicable [cf. 481, 734]. Models of the restructuring of ballistically-formed aggregates predicted an overall increase in Df from ~1.9 to ~2.1; however, one restructuring stage (cluster-pair twisting according to the ballistic angle) was found to potentially yield a d e c r e a s e of about 0.1 units in Df [546].


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Even models which attempt to incorporate restructuring effects retain a number of key simplifications *, the most noteworthy being that aggregation occurs between r i g i d clusters that r a p i d l y restructure solely by spatial transformations around their f r e s h point(s) of contact, with the new bonds a g e i n g to form a new larger rigid cluster b e f o r e further cluster–cluster contact occurs [e.g. 733] [see also 544]. These assumptions will be more realistic at low particle concentrations [733]. Such processes will tend to produce compactification at small lengthscales, rather than at large lengthscales [cf. 838]. It is common for restructuring to be described as predominantly affecting only ‘part of’ the aggregate — either around the aggregate’s periphery [cf. 441], or on short lengthscales [467, 544, 733, 841, 944], or on long lengthscales [666, 670, 703, 706, 838, 913] — although more global restructuring effects are also possible [cf. 441]. (When restructuring occurs on small lengthscales the asymptotic Df may be unchanged [e.g. 944], but compactness increases, as per equation R1-26.) BOTET, JULLIEN & KOLB [178] presented a striking example of how an aggregate with a compact periphery but a quite open core could be obtained w i t h o u t restructuring, through a combination of long-range interparticle attraction and a ‘natural’ transition from heterogeneous cluster–cluster aggregation toward particle–cluster aggregation. These results reinforce the difficulties in attempting to infer characteristics of the aggregation process or the aggregates based on estimates of Df [440, 734]. Moreover, the fractal dimensions of many real aggregates cannot be explained by any simple aggregation model [546].

R1▪5▪6▪3

Particle–cluster aggregation

Most of the foregoing supposes that growth of the aggregate occurs (primarily) between clusters of primary particles (cluster–cluster aggregation). It is also possible for an aggregate to grow through the accretion of individual primary particles (particle–cluster aggregation). In particle–cluster aggregation eventually the primary particles will be depleted from the system and further aggregation must occur by cluster–cluster growth. The terms RLCA and DLCA refer exclusively, by convention, to cluster–cluster aggregate growth models; the corresponding particle–cluster terms are EDEN growth (Df = 3.00) and WITTEN–SANDER growth [1126] [cf. 366] (Df ≈ 2.50) [728] respectively [730, 899]. The ‘intermediate’ † case of ballistic, VOLD growth [514, 988, 1091, 1092] also has Df = 3.00 [728, 730, 899]. WITTEN–SANDER growth is an appropriate model for filtration processes [543] and a number of other processes, but not common aggregation [733].

*

Very simple models (e.g. cellular automata [164, 165]) can sometimes accurately predict very complex outcomes [see 1127].

†

Cf. §R1▪5▪6▪1(a). VOLD growth still assumes that every bond forms instantaneously and irreversibly upon an encounter [1091], as in WITTEN–SANDER growth.

766



The reason cluster–cluster aggregation yields less dense structures is that when clusters collide, they are likely to bond at only a few locations (perhaps one), at least initially — especially in the case of rigid bond formation and short-range attractions [1047]. Several other alternative growth mechanisms have been proposed. For example, the basic ‘EDEN growth’ model exists in several permutations, has been extended (e.g. poisoned EDEN growth, in which not all accessible sites are reactive [899] [cf. 183]), and has been generalised (e.g. ‘screened growth’, itself a special case of RIKVOLD growth [944], in which there is a continuous distribution of bonding probabilities at potential growth sites [731]) [730]. At short times normally only particle–particle interactions can occur [481, 691, 899], and at intermediate or long times it is often assumed that only cluster–cluster interactions are important. A situation where this is not true is where aggregates are either ‘seeded’ (for a batch process) or recirculated back (for a continuous process), such as in an upflow clarifier [429]. At long times there may be a shift back toward the accretion of smaller clusters or aggregate fragments. The underlying reason is that larger aggregates are more susceptible to breakup by shear, and so the combination of two very large clusters is not favoured, and will likely result in only ephemeral contact [405]. Rather, as dagg increases, the ratio dagg / dclus also increases (dclus refers here to the smaller accreting unit), leading to a shift from homogeneous cluster–cluster aggregation to heterogeneous cluster–cluster aggregation. As the extrapolated limit of such a shift would be particle–cluster (re)growth, it can be concluded that compactness and Df will tend to increase with this shift in behaviour [see also 405, 730] * [cf. 991]. The smaller clusters will be better able to penetrate large aggregates [198, 730]. Ultimately a dynamic balance of breakage and regrowth is expected, but gradual densification may persist for long times.

R1▪5▪6▪4

Orthokinetic aggregation

The complement of perikinetic aggregation is o r t h o k i n e t i c aggregation, in which primary particles collide under the influence of imposed flow fields (usually turbulent) of the fluid in which they are suspended [505, 518, 1070]. Orthokinetic aggregation is expected to dominate where the system is vigorously sheared (although this must be verified), however this mode can also dominate where little or no m e c h a n i c a l energy is added to the system. An example is where the particles are quite large (or the aggregates grow quite large), such that the diffusion rate is (or becomes) very small, while convective flow becomes more efficient; convection can arise from e.g. temperature gradients (i.e. conversion of t h e r m a l energy), which lead to density gradients that result in bulk flow according to the differences in gravitational p o t e n t i a l energy. Convection could even arise from the initial loading of the aggregation vessel and chemical addition. As with perikinetic aggregation, the orthokinetic aggregation rate may be limited by particle transport, or by ‘reaction’. Both varieties can yield different aggregate structures, and values

*

Incidentally, the decreasing fraction of clusters that are able to form a stable couple can be interpreted as a decreasing collision efficiency [405] (as in the transition from DLCA to RLCA), which is also known to increase Df (§R1▪5▪6▪1). The argument is not rigorous, however, as the compactness still increases within the RLCA regime [198, 734]. R1▪5 : Aggregate structure and fractal dimension

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of Df, compared to their perikinetic counterparts. Given that particle transport in the orthokinetic regime occurs predominantly by bulk fluid motion, the orthokinetic analogue of DLCA can be termed c o n v e c t i o n - l i m i t e d cluster(–cluster) aggregation ( C L C A ) [440, 872], although this term has not gained widespread use. It can be presumed that the aggregate structure and associated fractal dimension resulting from turbulent CLCA should be s i m i l a r to that for DLCA. This argument is based on the premise that trajectories of fluid elements in isotropic t u r b u l e n c e are similar to those under BROWNian motion [cf. 96, 656]. KOLMOGOROV’s model [593] and BROWNian motion are certainly formulated in a similar way [964]. (The manifestations of their respective trajectories appear more distinct, with turbulence seemingly emphasising complex distributions of spiral vortices and the like — see HUNT & VASSILICOS [509] and HINZE [476] — although for LEVICH [656] rotational motion was not an essential feature of turbulent flow [see also 110]. Local turbulence intermittency can probably be neglected in the first instance for aggregation, although it may not be negligible for breakup [cf. 123].) It is acknowledged that the eddies in this scheme are not truly independent of lengthscale — at very large lengthscales the physical container boundary eventually disrupts the uniformity [cf. 381], while at very small lengthscales (i.e. smaller than dKolmogorov) the eddies are practically ‘fully damped’ due to the increasing dependence upon viscosity [593, 650, 964]. (dKolmogorov is “in general” much larger than the molecular mean free path of the fluid [964] [see also 774] — or “always”, for real fluids [650].) Weak variation may also occur at intermediate lengthscales [123, 650]. Nevertheless turbulence can be taken as primarily a deterministically chaotic process [cf. 120, 650, 906], just as is BROWNian motion. The turbulent motion is s u p e r i m p o s e d on BROWNian motion (or vice versa) [613], so that at the smallest lengthscales the trajectory ought still to fluctuate accordingly [656]. If the particle (or cluster) size is no larger than dKolmogorov, then it ought to be subject to the motion of the eddies across the cascading lengthscales; the preceding argument no longer holds if the particle (or cluster) is much bigger than this. A mathematical treatment of the motion as a diffusion problem is presented by HINZE [476] based on the work of TCHEN and others. Naturally for CLCA under l a m i n a r flow conditions the aggregate structure and fractal dimension could deviate considerably from DLCA, perhaps being better approximated as a ballistic process [cf. 460]. (Laminar conditions may also be experienced in nominally turbulent flow at lengthscales less than dKolmogorov [587, 613, 763].) It has been proposed that in orthokinetic aggregation as the cluster size increases, the momentum transfer between clusters upon collision increases, leading to a reduced probability of bond formation [441]. (This opposes the trend for collisions between large clusters to be more successful in forming bonds where significant interparticle repulsion exists, due to their greater number of potential bond-forming sites [441].) At high shear rates this effect dominates the effect accruing from increased collision rates (as all particle sizes have similar mobility), and so h e t e r o g e n e o u s aggregation between a particle or small cluster and a large cluster is favoured [441]. (An alternative explanation relies on the “elastic floc” model of FIRTH & HUNTER (1976), which proposed that in a collision between two aggregates, a l l of the intra-aggregate bonds would be weakened [143].) 768



Heterogeneous aggregation is also favoured for perikinetic aggregation [441]. However, at lower shear rates orthokinetic aggregation predominantly occurs by h o m o g e n e o u s aggregation between large clusters (after an induction period) [441] [cf. 1048]. Homogeneous aggregation leads to increasing aggregate size polydispersity (as in RLCA), whereas heterogeneous aggregation results in a more monodisperse system (as in DLCA) [440, 441, 706] [cf. 457]. HAN & LAWLER [439] predicted that “water [...] pushed out of the way by the larger particle [would carry] smaller particles with it” (‘Queen Mary effect’ [531]), discouraging aggregation [cf. 427, 639]. However this conclusion was based on an analysis that treated the aggregates as coalesced spheres (Df = 3) [439], and is unlikely to apply to more permeable aggregates. Modelling and experimental results suggest that perikinetic and orthokinetic aggregation would yield identical aggregate structures for particles that form strong, rigid bonds (i.e. rearrangement of the structure is precluded) provided that both occur by heterogeneous aggregation [441]. R1▪5▪6▪4(a)

PÉCLET number and characteristic times

A good indication of the relative importance of BROWNian motion and shear-induced flow is provided by the translational P É C L E T n u m b e r (for an equivalent sphere) [481, 799, 920, 1047, 1071]: G d2 3 π η d3 G Pé = = , [R1-39] 4 Dt,eff 4 kB T in which Dt,eff is the effective BROWNian (or FICKian) translational diffusion coefficient. [See also 131.] The rotational PÉCLET number, Pérot, is identical (for a sphere), except that the coefficient of ¾ becomes a coefficient of ½ [709, 952] * [cf. 837]. In the context of p a r t i c u l a t e motion the PÉCLET numbers have also been called B R E N N E R n u m b e r s , with symbol Br [e.g. 709, 837]. Large values of Pé indicate shear dominance †, and low values indicate BROWNian motion dominance [481]; equivalently, Pé is the ratio of bulk or convective flow to flow by diffusion. More fundamentally, Pé is “the ratio of viscous energy dissipation due to translation and the thermal energy of an isolated sphere” [1071]. (Pé may also be interpreted as the ratio of total momentum transfer to molecular mass transfer, and is equal to the product of the REYNOLDS and PRANDTL numbers [655].) Note the strong (third-order) dependence on d. The value of d depends upon whether the focus is on primary particles, small clusters, or larger aggregates, and can change over time as clusters (and aggregates) grow in size. Under laminar

*

If a doublet is described in terms of d0, then compared to the constituent primary particles Pé increases by a factor of less than 1.5 (the precise value depends upon orientation) while Pérot increases by a factor of 3.74 [952]. Despite this similarity, under certain conditions BROWNian rotation may be important while BROWNian translation is not [see 1047].

†

It should be noted that some researchers have found that even “small amounts” of BROWNian motion could have “rather large effects” [1047]. This may be due to an increased likelihood of rearrangement in orthokinetic coagulation (due to rolling of particles over each other without bonding), implying significant reversibility, decreasing the effective coagulation rate [518]. In practice most researchers seem to accept values of Pé greater than 100 as ‘large’ [e.g. 80, 441, 920]. HOEKSTRA, VREEKER & AGTEROF [481] found shear effects were first apparent at Pé ~ 1 for their system [cf. 80]. R1▪5 : Aggregate structure and fractal dimension

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conditions * the characteristic velocity gradient, G, is practically the same as the shear strain rate, γ [cf. 228, 266, 427, 613, 799, 834, 968] (cf. §R1▪4▪1▪1 and §S26▪1▪2). At a characteristic velocity gradient of G = 10s‒1, the transition between perikinetic and orthokinetic coagulation occurs at d ~ 1μm in water [518]. Due to the third-order dependence of Pé upon d, orthokinetic coagulation would be expected to dominate for d T 5μm. For characteristic velocity gradients of 1 and 100s‒1 orthokinetic coagulation would be predicted to dominate for particulates with d greater than 10 and 2μm, respectively [518]. It should be noted that in water treatment G is seldom less than 10s‒1 in coagulation or flocculation processes — although spatial variation of ‘local’ G values may be significant (see §R1▪4▪3). In the context of coagulation, Pé may be seen as the ratio of characteristic times † for aggregation by BROWNian motion and shear effects, viz. [505, 1047] π t shear ∝ [R1-40] 4 φG and

t Brown =

3 π η d3 , 4 φ kB T

[R1-41]

where φ refers to the entire system (the overall rate increases in the same way as the particle concentration increases for both mechanisms [1018]). Both times may be divided by a factor corresponding to the bond-forming efficiency [505, 639]. These formulæ can be derived following the classical procedure of SMOLUCHOWSKI [see 505, 518]. For intermediate conditions it has been found that simple addition of the contributions to coagulation from each of the two mechanisms adequately describes observed behaviour [80, 639]. Analysis of the orthokinetic case shows that the coagulation rate varies according to the cube of the collision radius, the square of the number of particles, and directly with G [518]. This suggests optimal behaviour with [518]: • large aggregates — which take time to build up; • high numbers of particles — which decrease as coagulation proceeds; and • high shear rates — which lead ultimately to corresponding increases in the rate of aggregate rupture. In practice the best performance is obtained from ‘taper’ flocculation, where clusters are rapidly formed initially at high values of G, are aggregated further at moderate values of G, and finally form large ‘flocs’ at reduced values of G [518] (§S6▪1). The coagulation process is expected to scale according to the relevant characteristic time, at least in the earlier, growth stages, before break-up occurs [1047]. It can be seen that not only

*

Strictly for a two-dimensional flow field [264, 600].

†

It may be seen that the formulæ differ by a constant factor, due to differences in definition [cf. 428, 440, 441, 505, 518, 878, 953]. HANSEN & BERGSTRÖM [440] even replace the velocity gradient with the ‘actual’ bulk flow velocity.

770



is Df a characteristic of the structure, but — through its effect on d — it may also be seen as a key parameter of the dynamics of aggregation (and break-up *), as per equation R1-41 [799]. Rearranging the characteristic times it is possible to nondimensionalise the coagulation time so that the behaviour at various parameter values can be overlaid on a ‘master’ plot for a given regime (when the system is far from equilibrium) [799, 920, 921]. For example, equation R1-40 suggests [799, 1018]: t [R1-42] t∗ = φ G t ∝ t shear for orthokinetic coagulation. This is reminiscent of the ‘CAMP number’, G.t, and variants (§R1▪4▪1, §R1▪4▪5). According to GREGORY, coagulation due to BROWNian motion only would be too slow to produce aggregates of a useful size (say 1mm) [505], that can readily be dewatered. R1▪5▪6▪4(b)

Restructuring

Several workers have found that aggregate restructuring is more likely to occur for smaller primary particle sizes in both turbulent and laminar shear environments [914]. Aggregates made up of smaller particles tended to densify by structural rearrangement, while those made up of larger primary particles were more likely to undergo breakage (and re-growth) [914]. (Compact aggregates — with higher bond density — are more likely to undergo e r o s i o n in a shear field, whereas more open aggregates are more likely to undergo f r a c t u r e [1018].) It may be that the larger primary particles gave rise to larger aggregates which were closer to the characteristic shear dimension (e.g. dKolmogorov), and hence experienced greater (differential) shear forces [cf. 368]. Furthermore, any aggregates of similar size made up of smaller primary particles would have a much greater density of bonds, making them stronger and less susceptible to rupture. In fact, for sufficiently large primary particles the shear differential across just one particle diameter may be great enough to lead to rupture. Structural rearrangement has been reported to lead to denser aggregates than in a situation of dynamic balance between growth and fragmentation processes [588, 914].

R1▪5▪6▪5

Polarisability

The polarisability referred to in Table R1-13 may be relevant to the formation of aggregates in ferric sludges, where “magnetic dipolar interactions” have been reported [184, 1008]. The presence of complexing anions tends to decrease magnetic interactions [677] [cf. 568]. (While ferrimagnetic γ-Fe2O3 has been reported to comprise denser aggregates than non-magnetic αFe2O3 [401], the morphology of γ-Fe2O3 aggregates varies greatly with pH: viz. small clusters in acidic medium, small chains of circa 15 particles at slightly higher pH, and much longer strings of circa 50 particles or large compact aggregates around the p.z.c. [677] [cf. 538]. Superparamagnetic relaxation was identified for the shorter and longer chains and for small clusters, but not for the large aggregates [538] [cf. 324, 852].)

*

Analogously to the parallel modes of aggregation, b r e a k - u p may be caused by fluid stresses or by collisions between particles [799]. R1▪5 : Aggregate structure and fractal dimension

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As with all interparticle forces, the magnetic interactions are more likely to have a perceptible influence on structure if the dipole moment is significant compared to kB T — this is expected to occur only when the particles are sufficiently large *, and leads to increased formation of linear chains [568, 1019]. An experimental trend of decreasing Df with increasing saturation magnetisation (or magnetic moment [761]) of the primary particles has been suggested [568]. Ferrihydrite is classed as speromagnetic [279], and is paramagnetic or superparamagnetic at room temperature [520] [cf. 324, 397]. Given this status, the phenomenon of ‘superparamagnetic relaxation’ may also play a role. Superparamagnetic relaxation refers to the ability of the magnetisation to readily fluctuate between multiple axes (rather than being “pinned” on a single ‘easy magnetisation axis’) [324], enabling interaction † of magnetic moments when particles are close enough [538]. It arises when the magnetic anisotropy energy is ‘small’ — viz. on the level of thermal energy, i.e. kB T — which is favoured for small crystallites (in the range ~2 ‡ to 10nm) which comprise a single magnetic domain § [324, 538] [see also 397, 1019]. Goethite is classed as antiferromagnetic at room temperature [279], but might still be able to manifest superparamagnetic relaxation [cf. 324]. Simple modelling by MORS, BOTET & JULLIEN [761] indicates that near-instant relaxation of dipole moment following any (relative) cluster movement does not significantly affect Df. However THOMAS [1019] noted an increased energy barrier for reversal, i.e. enhanced irreversibility — which could affect Df through changes in bond rigidity, or restructuring, and collision efficiency. Polarisation was also suggested as an explanation for the low fractal dimensions sometimes reported for aluminium hydroxide aggregates [104, 542].

R1▪5▪6▪6

Flocculation

Much of the early work on fractal characteristics of aggregates was done by inducing aggregation either by reducing primary particle surface charge or increasing the ionic strength (screening the surface charge) [e.g. 666]. Another category of aggregation is b r i d g i n g f l o c c u l a t i o n , which refers to the action of polymers that adsorb to multiple primary particles and thus form ‘bridges’ between them. In one set of experiments aggregates of 0.4μm alumina formed by bridging flocculation had higher fractal dimensions (Df T 1.85) than those formed by DLCA (Df ≈ 1.75) [404].

*

A lower limit of ~10nm was observed for (ferromagnetic) cobalt spheres [1019]. Magnetic effects may eventually be suppressed as larger particles (say ~100nm) become multidomainic [568].

†

At long range these may take the form of magnetic dipolar interactions (of order kB T), and at short range “exchange” and “superexchange” can occur [538]. With favourable bonding, superexchange interactions can extend to long range [324].

‡

For smaller crystals the magnetic anisotropy energy becomes dominated by large contributions from atoms near or on the surface [324]. Superparamagnetism can also be discouraged by crystal defects that preponderate with increasingly finer particles, or by elevated temperature [324]. (Defects and nonmagnetic impurities are also common in “numerous natural materials mainly corresponding to iron oxides or hydroxides such as goethite, ferrihydrites, or protein cores” [324].)

§

In fact a single magnetic domain can be found in somewhat larger crystallites, below about 20 to 50nm [538]. 15nm is typical for iron minerals, but domains as large as 800nm exist for some unusual materials [324].

772



Under conditions of slow aggregation especially, which may be associated with the charge neutralisation regime, destabilisation of suspensions can occur through the tendency of particles to move into s e c o n d a r y m i n i m a of the potential energy; they will tend also to remain there, although often the energy required to move out of the secondary minimum is low (< kB T) *, and so the aggregation is “readily reversible” [280] [cf. 706]. In such cases aggregates often take on a linear configuration, which has been shown to be dynamically favoured. For example, formation of linear chains in a suspension of 1.2μm hæmatite particles was attributed to VAN DER WAALS forces, slightly enhanced by weak magnetic forces [280]. (Linear structures were also observed by VAN DER WOUDE, RIJNBOUT & DE BRUYN [1131] in their work on the slow destabilisation of goethite suspensions.) Such linear configurations are not necessarily supported by estimates of fractal dimension for real WTP sludges. However, consideration of calculated gel point values on the order of 0.5%V (typical), representing the minimum solidosities able to form a s p a c e - f i l l i n g † network for the given system, indicate that the sludge m u s t have a significantly linear character on the micron or sub-micron scale.

R1▪5▪6▪7

Differential settling

A final mechanism by which particles may collide is differential settling [439, 518, 530, 799, 921, 1018]. This has received the least coverage in the literature [cf. 530]. Differential settling involves the collision of fast-settling and slower-moving particles or clusters: this is often due to differences in size, but could also be due to different solid phase densities, or different aggregate densities (leading perhaps to different degrees of fluid permeation through the microstructure, and thus reduced drag). While BROWNian motion dominates the behaviour of small primary particles (say d < 1μm), and shear becomes important as aggregate size exceeds 1μm (see §R1▪5▪6▪4(a)), differential settling is only significant for large aggregates: say d > 40μm [921]. In fact, the initial small-scale aggregation may produce a wide range of aggregate sizes — especially for perikinetic aggregation — which could subsequently lead to significant differential settling [518].

R1▪5▪7

Specific results

A huge range of values of Df for WTP aggregates has been reported: early (1989–1992) estimates ranged “between 1.0 and 3.0”, according to LEE et alii [644]. Many of the lowest estimates have come from the group of BACHE employing settling tests. These estimates are certainly not all correct; in many cases the discrepancies arising between methods (cf. §R1▪5▪4) are as large or larger than the structure-dependent differences investigated [see e.g. 1083]. Nevertheless it is reasonable to infer qualitative trends from data obtained in a single given study.

*

POON & HAW [841] suggest that reversibility will be significant whenever the strength of attraction (cf. barrier height) is (4 kB T.

†

In fact, the gel point represents the lowest solidosity at which a network forms that is able to t r a n s m i t a p p l i e d s t r e s s e s . For the purposes of the point at hand, the difference in definition can be ignored. R1▪5 : Aggregate structure and fractal dimension

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R1▪5▪7▪1

Aluminium

TAMBO & WATANABE [997] followed the settling of a range of aggregates formed by laboratory coagulation of kaolinite clay suspensions. For equation R1-19 they obtained exponents, m, spanning a wide range from 0.7 to 1.7, implying fractal dimensions 2.3 T Df T 1.3 [997]. The trends they observed may be summarised: • increasing the Al dose led to an increase in m from about 1.0 to 1.4 (2.0 T Df T 1.6) at “neutral” pH; • decreasing the pH from 8.0 to 6.5 led to an increase in m from about 0.7 to 1.2 (2.3 T Df T 1.8) at low Al doses, but had little effect at higher Al doses; • changing the nature of the Al from alum to PACl had no significant effect on m; • changing the coagulant type showed relatively low values of m “at the optimum coagulation conditions” — for both Fe and Mg m ≈ 1.1 (Df ≈ 1.9); • increasing “natural” colour and decreasing turbidity in the raw water gave increased values of m — for Al m ≈ 1.3 (Df ≈ 1.7), for Fe m ≈ 1.4 (Df ≈ 1.6), and for Mg m ≈ 1.5 (Df ≈ 1.5) — however the doses were also typically higher than for the clay cases; • adjusting the alkalinity had no significant effect on m; • increasing the agitation intensity had no significant effect on m; (although the proportion of inherently denser small aggregates did increase); and • addition of flocculants in typically low doses had no significant effect on m; (although the floc strength was improved, so the proportion of larger aggregates did increase). For a sequence of increasing alum doses, the increasing values of m mean that the curves of Δρagg(dagg) appear to converge or coincide at small values of Δρagg [997], suggesting the smallest aggregates are essentially indistinguishable. Further extrapolation of the curves to very low sizes yields unphysical estimates of ρagg — larger than the (average) component solid phase density, ρS — and so the exponent was proposed to change at a transition diameter of 4 to 20μm. Implications for the present work accrue by consideration of the range of treatment conditions in each case. The present work dealt primarily with low-turbidity raw waters, with moderately low coloration and relatively high coagulant doses: from the above this would lead to a relatively large value of m, and little dependence on pH; extrapolation suggests m T 1.5 for most combinations studied in the present work, implying Df ( 1.5. KIM et alia [569] found that Df was greater for aggregates formed by sweep coagulation of highly coloured raw water with alum (~2.2) than by charge neutralisation (~1.9). However these results are not entirely conclusive given the unusual size distributions of the ‘aggregates’ — nearly identical to the raw water for charge neutralisation, and bimodal for the sweep coagulation [569]. Other studies showed that dense aggregates of aluminium hydroxides (Df ~ 2.3) precipitated in the presence of organic acids were “built by uncondensed monomers” [707, 708], which suggests consideration of a formation process analogous to particle–cluster aggregation (§R1▪5▪6▪3). AXELOS et alia [103] studied the precipitates formed by partial neutralisation of aluminium chloride (AlCl3·6H2O) with sodium hydroxide (NaOH). At a hydrolysis ratio,

774



[OH‒]added/[Al] *, of 2.5, primary particles of 1.8nm were found in isolation (25%) and aggregated as ramified chains of up to 40nm size [103]. It was inferred that the primary particles were tridecameric aluminium [103]. The aggregates were found to have Df = 1.42 [103]. Such a low fractal dimension is somewhat surprising in view of the “violent agitation” to which they were exposed during the synthesis [181], although the macroscopic turbulence may well be irrelevant at such small lengthscales. At a hydrolysis ratio of 3.0, denser aggregates formed, also up to 40nm in size, with Df = 1.92 [103]. The internal structure was described as a ‘mosaic’, with Al13 polycations no longer identifiable [103]. In each case the aggregates were modelled as branched structures oriented in a plane, i.e. effectively confined to two EUCLIDean dimensions [103]. Although these model structures predicted concordant density autocorrelation functions, it is likely that the ‘solution’ is not unique: i.e. a multitude of structures may produce consistent density autocorrelation functions. Indeed, a later publication [104] suggested, more reasonably, that the low fractal dimensions were due to cluster polarisation, resulting in t i p - t o - t i p collisions and bond formation being favoured. This confirmed the apparent fractal dimension at a hydrolysis ratio of 2.5, namely Df = 1.45, although the scattering pattern did not appear purely fractal — possibly due to the small aggregate size [104]. But moreover it demonstrated the great structural difference upon increasing [OH‒]added/[Al] by only 0.1 unit to 2.6, where “precipitation starts to occur” and Df = 1.86 [104]. This suggests that 2.6 constitutes a ‘threshold’ for rapid aluminium precipitation, similar to the “flocculation threshold” described for iron(III) (§R1▪2▪6▪3(a)). Additionally, it was determined that ordinary cluster–cluster aggregation (DLCA) provided a good model for [OH‒]added/[Al] = 2.6 [104]. AXELOS, TCHOUBAR & JULLIEN [104] also proposed a reason why different mechanisms might prevail: at the lower hydrolysis ratio the positive charge on each Al13 polycation unit is greater, leading to a strong p o l a r i s a t i o n of the surrounding water molecules. FARGUES and TURCHIULI [355, 1055] estimated Df ~ 2.5 from settling tests at 1 < Re < 50 for WTP flocs generated from either alum or ferric chloride plus a large dose of anionic polymer. Examination of the floc growth kinetics indicates that the structure probed was determined by the polymer [see 355, 1055], explaining the lack of difference for the two coagulants. Various relativities were ascribed to the ‘alum’ and ‘ferric’ flocs, but aside from the polymer dominance, the coagulant doses were very different, and the method of dose determination (turbidity after 10min settling) may not be appropriate, considering the low initial turbidity [see 355, 1055]. PAPAVASILOPOULOS & BACHE [816] claim that the flocs they studied — pure aluminium hydroxide flocs, as well as flocs from humic suspensions treated with aluminium sulfate — had fractal dimensions of approximately 1, “representing solids joined in a chain form,” irrespective of dose. They also assert that the fractal dimension of (aluminium-based) flocs is insensitive to their constitution [816].

*

The article implies that a species of formula Al(OH)2.5 forms [103], however this is n o t an appropriate interpretation of the hydrolysis ratio or of the experimental procedure. R1▪5 : Aggregate structure and fractal dimension

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BACHE et alia [116] stated that the exponent in equation R1-19 “generally” varies between 1.8 and 2.0 * for aggregates derived from coloured waters coagulated with alum, giving 1.0 ≤ Df ≤ 1.2. Interestingly, an exponent of magnitude ~2 causes cancellation of dagg in the evaluation of the STOKES terminal settling velocity; at a given coagulation condition there is a distribution of aggregate sizes, but they may all settle at similar rates [111]. Low fractal dimensions such as this describe a “‘necklace’ structure” [116]. These aggregates are characterised as weak, with low settling velocity, and high water content [116] — in comparison, say, to mineral industry flocs. More particularly, the sludge formed by the collection of aggregates tends to have a very low gel point, which could be explained physically by the existence of long chains of primary particles [235]. A simple illustration of how this might occur in two dimensions is given in Figure R1-12.

A:

B:

C:

D:

Figure R1-12: Possible structures to illustrate low-solidosity networks in two dimensions. In the first instance, small clusters of particles (A: φ2D ≈ 32%) aggregate to form larger clusters (B: φ2D ≈ 18%), which in turn combine to form a low-density network (C: φ2D ≈ 4.3%). This seems more physically realistic than the corresponding simple ‘string’ network shown in D (φ2D ≈ 4.3%). Note that the proportional increase in the number of such clusters (hence particles) required to span a three-dimensional space is smaller than the proportional increase in the amount of empty space, leading to lower values of φ ≡ φ3D for ‘equivalent’ structures.

Later studies on nine alum WTP sludges by BACHE and colleagues produced estimates of Df from 1.00 to 1.23 [110]. There was no significant effect of polymer dosing [110]. A ferric WTP sludge they tested fell in the same range, with Df = 1.06 [110].

*

776

Analysis of exponents published by BACHE & HOSSAIN in an earlier paper [111] shows that if the exponent in equation R1-19 is taken as Df ‒ 3 (as written), then the 20th and 80th percentiles of the fractal dimensions observed do correspond to about 1.0 and 1.2. This leaves 20% of observations at somewhat higher values of Df, up to about 1.3. Of more concern, in the lowest 20% of observations 0.4 ( Df ( 1.0, which clearly is not physical. It can only be presumed that a computational or statistical error has led to these unphysical estimates. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


ZHAO [1146] estimated a similar Df (1.06) for an alum sludge obtained from a WTP treating coloured, low-turbidity water. Upon conditioning with anionic polyelectrolyte Df increased consistently to 1.7±0.1 independent of dosage, while the floc size increased with dose [1146].

R1▪5▪7▪2

Iron

LAGVANKAR & GEMMELL [621] reported power-law correlations between projected area and dagg for turbidity-free ferric WTP aggregates grown with G = 11s‒1. Analysing their data [see 621] using equations R1-17 and R1-19 yields Df increasing from about 2.3 for 0.5mm aggregates up to 2.8 or more for 3mm aggregates. Breakage due to shear will be very important for such large aggregates, setting up a dynamic equilibrium between breakage and regrowth which tends to increase Df [e.g. 913] [cf. 962]. Experimental results of AMAL, RAPER, WAITE and co-workers showed Df = 2.3 for rapid aggregation and Df = 2.8 for slow aggregation of ~50nm isodimensional hæmatite particles [280]. TCHOUBAR, BOTTERO et alia [1008] studied the precipitation of ferrihydrite from ferric chloride at hydrolysis ratios up to about 3, which is above the rapid precipitation threshold. In this case the precipitate size increased from about 12nm to 0.2μm as [OH‒]added/[Fe] increased from 1.0 or 1.5 up to 2.7 [1008]. It was suggested that the precipitates found for [OH‒]added/[Fe] of 2.0 to 2.5 at 400s may be clusters made up of primary particles as small as ~1.6nm, having Df ~ 1.7 [1008]. The constant size of the primary particles — equated to “polycations” in the paper — was attributed to the strong inner-sphere complexation of chloride ions with ferric ions, such that the olation and oxolation reactions necessary to increase the polycation size are limited [184]. Precipitates produced at the lowest hydrolysis ratios, [OH‒]added/[Fe] = 1.0, did not show clear fractal properties at 400s [1008]. It was suggested that these precipitates may be linear clusters of ~1.6nm primary particles at 400s, compacting slightly to “slightly branched” structures at 3600s comprising perhaps as few as 8 primary particles [1008], implying very low ‘apparent’ Df values. At larger hydrolysis ratios (2.0 and 2.5), an apparent Df of 1.74 was estimated [1008]. At the largest hydrolysis ratio, the apparent Df increased further up to 2 [1008]. It was expected that increasing [OH‒]added/[Fe] would lead to more primary particles being precipitated, but with reduced surface charge and (hence) reduced electrostatic repulsion [1008]. Interestingly, the cluster size was found to decrease over time [1008]. The same workers, BOTTERO, TCHOUBAR et alia [184], also studied the hydrolysis and precipitation of ferrihydrite from ferric nitrate solution at various hydrolysis ratios. Similar results were found as for ferric chloride, except that the size of precipitate clusters was found to depend upon the hydrolysis ratio [184]. As for the ferric chloride hydrolysis, the cluster size was found to decrease over time [184]. As ‘equilibrium’ was attained, relatively stable aggregates could be characterised. At the lowest hydrolysis ratios (1.5 and 2.0) the primary particles within the aggregates seemed to be arranged in linear configurations (at the local scale) [184]. As the hydrolysis ratio was increased (2.2 to 2.5), more branched or “semilinear” structures were inferred [184]. R1▪5 : Aggregate structure and fractal dimension

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However only the aggregates produced at the highest hydrolysis ratio (2.8) demonstrated fractal properties, for which Df was estimated to be 1.75 [184]. As the hydrolysis ratio increased from 1.5 to 2.5 the size of the clusters increased due to an increase in the number of constituent particles (from ~5 to ~9 *) along with an increase in the diameter of those primary particles (from 1.4 to ~2.7nm) [184, cf. 573]. The primary particles, equated in the paper to “polycations”, seemed to approach a constant size for hydrolysis ratios above 2.0, indicative of a constant stoichiometry [184]. It was argued that nitrate ions are not tightly bound to ferric ions, and so they can readily be exchanged for OH‒ or O‒ ions, leading to larger polycations [184]. The presence of NOM was found to significantly increase the fractal dimension of aggregates formed from ferric chloride [1082]. In conditions typical of conventional water treatment, Df was estimated at 2.4 (pH 5.5) and 2.3 (pH 7.5) for a turbid, low-TOC river water, and 2.9 (pH 5.5) and ~2.1 (pH 7.5) for a non-turbid lake water of moderate TOC [1082]. The decrease in Df at higher pH was attributed to adoption of less dense conformations by the NOM due to increased electrostatic repulsion arising from enhanced deprotonation [1082]. Alternative studies on ferrihydrite coagulated at pH 7.8 by LO & WAITE [679] suggested aggregates of about 60μm size became significantly more compact over time (apparent Df increasing from ~1.5 to ~2.6) and in response to mixing (from ~2.0 to ~2.6) [679]. Addition of salt to the system prior to coagulation led to small decreases, about 0.1, in the apparent fractal dimension [679] — higher salt concentrations somewhat decrease interparticle repulsion, promoting a diffusion-limited mechanism. The range of apparent fractal dimensions spanned is unusually large, and suggests that the lower values may not correspond to fully-developed fractal structures. All of the values of Df estimated may also have been subject to systematic error introduced through the choice of fitting technique — an alternative technique did not indicate any change in fractal dimension with time [679]! Furthermore, dagg was large compared to the wavelength of light (633nm) and primary particles (101 to 102nm), and it could not be stated with certainty that the assumptions implicit in the use of RAYLEIGH–GANS–DEBYE scattering analysis hold true [cf. 217, 1003]. It may also be noted that LO & WAITE [679] used a buffer to maintain constant pH, which avoids ‘interfacial disequilibrium’ effects [146] that may be significant in industrially relevant systems [300]. The use of slowly-dissolving lime (Ca(OH)2) as alkali in contrast to readily-available sodium hydroxide was found to yield denser aggregates in one study of ferric chloride precipitation [388]. It may also reduce the number of nucleation sites, encouraging the formation of larger particulates [388]. Likewise, even strong bases such as sodium hydroxide may be added gradually, or stepwise, in order to reduce the number of nuclei as well as the rate of deposition of precipitate on those nuclei [388] by reducing the magnitude of interfacial disequilibrium [see 146, 148].

*

778

The low numbers of constituent particles may be the main reason fractal geometry could not be identified. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


Similarly, strategic blending of a recycled portion of sludge may favourably alter the temporal pH profile [388]. Recycling of sludge has another effect, in that it provides ‘preformed’ nuclei for further precipitation, which may also yield larger particulates [388]. It remains to be confirmed whether a slow precipitation rate caused by the c o a g u l a n t , rather than the a l k a l i , would yield similar results — if so, then magnesium would seem to be favoured over aluminium or iron. Akaganéite formed upon neutralisation of ferric chloride was found to contain intracrystal channels equivalent to micropores of 0.5 to 0.6nm in size, making up a very high percentage of the crystallite (for comparison, the crystallites are of order 1.5nm in size); larger interaggregate pores are also formed [182]. For hydrolysis ratios above 1.5, the polycations aggregated to form larger clusters; these were highly linear for hydrolysis ratios up to 2.2, but became branched at higher proportions of added alkali [182].

R1▪5▪7▪3

Other

Silica solutions are now known to yield chain-like ‘polymers’, which can be distinguished from colloidal silica aggregates by static light scattering experiments [899]. While both systems exhibit similar fractal dimension (~2.0 to 2.1, respectively) at large lengthscales, at small lengthscales eventually the colloidal particle size dictates that scattering occurs in the POROD regime, whereas the neutralised solution shows fractal behaviour down to <1nm [899]. (It could be said that even the colloidal aggregates are ‘polymeric’ in one sense, if the primary particles are seen as analogous to monomers [899].) Aggregates of 22nm and of 7nm silica spheres formed under rapid (diffusion-limited) coagulation conditions have been found to ‘spontaneously’ restructure in some cases, with Df increasing from 1.75 to 2.08, the higher value being identical to that observed for aggregates formed under slow (reaction-limited) coagulation [100]. At neutral pH compact aggregates were formed immediately at high silica concentrations, loose aggregates persisted at low silica concentrations, and aggregate restructuring was observed for intermediate silica concentrations [100]. This was described as a “somewhat surprising” result [100]. Variation was also observed with respect to pH at fixed silica concentration [100]. AUBERT & CANNELL [100] attributed this restructuring to r e v e r s i b l e bond formation in the initial rapid diffusion-limited aggregation. However the dense aggregates were “quite stable, and [...] not affected even by ultrasonic agitation” [100]. It could not be confirmed whether bond formation in initial reaction-limited growth or following restructuring was reversible [100], as the measurements could not distinguish between a dynamic equilibrium and a static equilibrium. ILER and others have suggested that “a bond which persists long enough becomes fully irreversible” [100] (see also §S17▪1, p. 938). The restructuring was deduced from changes in static light scattering experiments, which yield information on ensemble average properties of the suspension (§R1▪5▪4▪2). The largest aggregates have the greatest influence on measured scattering properties, and if restructuring also involves a “sufficiently radical” change in the aggregate size distribution, then interpretation of the data “would necessarily be more complicated” [100]. (It may be noted that later publications citing AUBERT & CANNELL [100] have not been concerned by the possibility of a radical size distribution change.)


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MARTIN et alia [706] strongly criticised the claim of “spontaneous” restructuring in the above work, and performed more controlled experiments with ~22nm silica spheres to show that the structural changes should be attributed primarily to s h e a r . Df for DLCA aggregates was increased from ~1.8 to ~1.9 upon swirling, and to ~2.1 upon vigorous shaking [706]. Observations also indicated coagulation occurred in a secondary minimum of the interparticle potential, so that massive decreases in aggregate size were realised upon reduction of the ionic strength [706].

R1▪5▪7▪4

Levels of aggregate structure

The structure of flocs is difficult to observe in practice, as “the dehydration process normally needed for sample preparation seriously damages the flocs” [278]. Problems are also encountered with atomic force microscopy (AFM), as the floc readily deforms under interaction with the cantilever tip, and may be even be fractured [278]. Reproducibility was improved by operating in a continuous-flow mode, and minimising damage to the flocs due to exposure to shear after formation [278]. Observations made on the formation of flocs from gradually neutralised ferric sulfate showed the following progression [278]: 1. Formation of a “fluffy” substance formed, with no identifiable particles. 2. Transformation to a “granular” precipitate, with particles of 0.5 to 1μm. 3. Closer packing of the particles, and “strings” between the larger aggregates. It was proposed that the ‘strings’ were “more likely [...] caused by stress on the [aggregate,] causing it to be partly pulled apart” * [278]. Formation of strings was observed under a number of conditions, with differing timescales of formation (perhaps faster at pH 9 than at pH 6 to 7) [278]. In one case (pH 9) spherical aggregates of order 2μm size were observed that were in turn composed of globular, string-connected clusters 30 to 50nm in size; these clusters were themselves observed to be made up from “interconnected string-like entities” built out or 3 to 5nm diameter particles [278]. It was suggested that the 3 to 5nm particles may consist of around 5 to 9 Fe12 species, the diameter of which has been predicted to be approximately 1.6nm [278]. In another case (pH 6), the clusters were measured to be 60 to 90nm in size. These observations show many orders of structure (from top down): 1. sludge / flocs 2. ~2μm spherical aggregates 3. 30 to 90nm globular, string-connected clusters 4. 3 to 5nm diameter particles 5. 1.6nm Fe12 units (reported as 1.5nm Fe24 polycationic units when from FeCl3 [182]) (According to TCHOUBAR, BOTTERO et alia [1008], even the 1.6nm units “could be aggregates of small particles”. In the presence of NOM, 0.4nm polycations, probably trimers, predominated [1082] †.)

*

Rather than being a phenomenon that promotes the packing process.

†

These were associated with very low fractal dimensions (~1.1), indicating either that the units formed a linear structure, or that they were isolated (i.e. did not aggregate) [1082].

780



DOUSMA & DE BRUYN (1978) [325] reported similar observations on the species produced by ageing ferric nitrate solutions ([Fe] ~ 0.06M) at low to moderate hydrolysis ratios (0.4 ( [OH‒]added/[Fe] ≤ 2.5) and low pH (1.5 < pH < 2.5): 1. aggregates of the secondary particles a. low ionic strength (I ( 0.4M): single chains of ~10 spheroidal particles (‘necklace’) ~0.5μm long b. high ionic strength (I > 1M) and “high” hydrolysis ratio: ‘isotropic’ aggregation [RLCA] resulting in a polydisperse mixture of roughly fractal aggregates 2. spheroidal particles about 20 to 50nm in diameter (‘beads’, ‘clusters’) 3. platelets or rafts of closely-packed rods, these rafts aligned “in the direction of the chain length” (perpendicular to the chain axis, from the published figure) 4. rods of primary particles 5. polymeric species of diameter ~2 to 4nm with each made up of the smaller component. Later observations by VAN DER WOUDE, DE BRUYN and colleagues [1130, 1131] ageing ferric nitrate solutions ([Fe] ~ 0.06M) at low to moderate hydrolysis ratios ‒ (0.3 ( [OH ]uptake/[Fe] ≤ 2.4) and low pH (1.9 < pH < 2.6) reproduce these results quite closely: 1. aggregates of the secondary particles a. low ionic strength (I ( 0.4M): single chains of ~10 spheroidal particles (‘necklace’) ~0.5μm long b. high ionic strength (I > 1M) and “high” hydrolysis ratio: ‘isotropic’ aggregation [RLCA] resulting in a polydisperse mixture of roughly fractal aggregates 2. spheroidal particles about 20 to 50nm in diameter (‘beads’, ‘clusters’) 3. rafts of closely-packed rods, these rafts aligned perpendicular to the chain axis (long rafts approximate “strings” due to the moderate aspect ratio of the rods) 4. elongated “secondary particles”, with aspect ratio ~2 to 10 and diamond-shaped cross-section, made up of sub-units 5. elongated goethite “sub-units”, either acicular/ellipsoidal/rod-shaped with ~3nm diameter or lath-shaped (thin, elongated plates) with ~3 to 4nm thickness, formed a. by oriented growth — i.e. preferential deposition of dissolved species onto the sub-units — at the lowest hydrolysis ratios (cf. ionic strength) b. by oriented coagulation — i.e. by regular “stacking and cementing” of the aged primary particles — at the higher hydrolysis ratios (cf. ionic strength) 6. spheroidal polymeric primary particles (nominally amorphous) of diameter ~3nm with each made up of the smaller component. MURPHY, POSNER & QUIRK [768] recorded similar observations upon ageing ferric chloride * solutions at moderate hydrolysis ratio (~2) and ferric concentration: 1. Raft-like arrays of rods or twinned rods. 2. Rods

*

They found similar results for ferric nitrate and ferric perchlorate solutions [see 769, 770]. R1▪5 : Aggregate structure and fractal dimension

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Lower concentration ([Fe] ≈ 0.02M and I / 1M): 2nm-diameter rods of 4 to 10 spheres; upon ageing a portion formed twinned rods (two spheres across) with the constituent 2nm spheres still distinguishable. b. Higher concentration ([Fe] T 0.1M or [Cl‒] T 1M): short 2nm-diameter rods of 2 to 5 spheres; these aged to yield thicker, longer rods (~20nm length, 3nm diameter) of “ c o a l e s c e d ” spheres — apparently by deposition of small ‘dissolved’ ferric species. Higher concentrations yielded faster ageing. 3. Discrete spheres 1.5 to 3nm in diameter. The precipitate was stated to be akaganéite [768]. a.

These levels of structure can each be associated with different fractal dimensions (or densities) [e.g. 845]. This m u l t i l e v e l character of floc morphology is widely known [e.g. 112, 217, 355, 368, 369, 407, 413, 621, 742, 845, 1055, 1069, 1092, 1133]; objects with such structure have descriptively been termed “fractals of fractals” [1133]. Typically the smallest units are the densest [112, 467] and have the smallest pores [413]. They are also expected to be least susceptible to shear [413]. The nomenclature of BOTTERO & LARTIGES [cited by 355, 1055], which is consistent with the conventions used to describe modes of aggregation (§R1▪2▪1), is preferred to that of MICHAELS & BOLGER [742] (and followers [e.g. 368, 369, 1069]). The term ‘ f l o c s ’ refers to the l a r g e s t -scale structures, which are often the most ‘open’, i.e. porous and lacunar, consistent with the connotation of f l o c c u l e n c y , and the physical formation of these structures by adding polymeric flocculants to existing aggregates. For a general four-level scheme, the next-largest structures should be called ‘ a g g r e g a t e s ’ , and then ‘ c l u s t e r s ’ , and finally (primary) ‘ p a r t i c l e s ’ . Of course, additional terms must be introduced as needed (e.g. ‘clods’, ‘units’). Agitation experienced by the forming flocs is likely to be the most important influence on the structure above about 0.1μm, encouraging the formation of an amorphous phase [278]. It was reported that increasing the pH (from 5 to 7 to 9) resulted in formation of larger aggregates composed of more closely packed particles [278] — despite the care taken with the microscopy work in that study, it is possible that those findings were affected by the sample preparation process. Still, the results are consistent with those of BOTTERO et alii (1991), who found an i n c r e a s e in Df with increasing pH [278]. The formation of larger aggregates may be linked also to the decrease in solubility associated with the pH increase imposed. BOTTERO and co-workers [183] investigated the microstructure of aggregates formed by coagulation of 40nm silica suspensions and organic solutions * with aluminium hydrolysis species formed by partial neutralisation of aluminium chloride (AlCl3·6H2O) with sodium hydroxide (NaOH). The mixtures were stirred for 2min at G = 450s‒1 and allowed to settle [183]. These observations show many orders of structure, which vary depending on the coagulation conditions (from top down) [183]:

*

782

Molar ratios of organic species to aluminium of 0.5 and 1.0 were used [183]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


1. 2.

3.

4.

sludge: 20 to 600μm aggregates clusters a. S i l i c a : >100nm clusters with Df ≈ 1.75 to 2.20; denser aggregates were obtained when the aluminium hydrolysis was higher (counter-intuitive, as these units were roughly linear), or for coagulation at pH 4.5 rather than 7.5. At pH 7.5 the hydrolysis and aggregation rates were promoted. As the size of the Al13 clusters is much larger than the silica particles, the fractal dimension approximates that of pure Al13 aggregates. b. O r g a n i c s : >10nm clusters * with Df ≈ 2.30 to 2.92 at pH 7.0; denser aggregates were obtained when the proportion of organics was increased (2.42 to 2.92, compared to 2.30 to 2.60). The type of organic species was also important, with more strongly chelating or bridging species (e.g. oxalate (ethanedioate, ‒O‒CO‒CO‒O‒)) leading to more compact structures. units a. S i l i c a : units made up of isolated 1.4nm polycation (Al13) species at low hydrolysis ratios ([OH‒]added/[Al] = 2.0), implying Df ~ 3; or multiple polycation species forming linear combinations at intermediate hydrolysis ratios ([OH‒]added/[Al] = 2.5), with Df ≈ 1.43, and more compact aggregates for higher hydrolysis ratios (essentially complete hydrolysis, pH > 6) with Df ≈ 1.85. (The Al30 polycation has a length of order 2nm [231].) b. O r g a n i c s : short linear units (2 to 5 members) comprising primarily chelated or bridged Al monomers (70 to 97%) and oligomers (0 to 30%), plus a small amount of Al13 (0 to 10%), with Df ~ 1. 0.6nm sub-units formed of “small, loose” hydroxo species oligomers (‒Al‒OH‒Al‒), typically dimers or trimers, or the equivalent with organic ligands (‒L‒OH‒L‒), depending upon the fluid composition. (The Al ‘monomer’ size is of order 0.38nm. Al6(OH)126+ has been said to be about 0.66nm in size [1100].)

Multilevel characteristics complicate the analysis of aggregate structure. Most models assume that an aggregate has a single fractal dimension; some authors go further and suggest or imply that an aggregate’s structure can be described by a single fractal dimension. Such assertions are incorrect, as e.g. the co-ordination number has been seen to vary independently of Df in both modelling and experiment [151, 217, 733]. In particular, researchers who construct models using centrosymmetric interactions postulate the existence of thick chains of multiply-connected particles [844], the analogue of a truss structure, which do have the requisite angular rigidity [347]. These may form through restructuring [733]. The practically measured fractal dimension is often dominated by the long- to mediumrange structure [546]. Hence it is possible for an aggregate with a rather open structure, and low effective Df, to have high co-ordination number [e.g. 347] due to local compactification ensuing from certain restructuring processes [733]. In such cases the ‘restructured’ aggregate is visually near-indistinguishable from unadjusted aggregates on macroscopic scales except

*

HSU & BATES (1964) [500] observed roughly isodimensional particles of size 5 to 25nm in electron microscopy of amorphous aluminium precipitates. R1▪5 : Aggregate structure and fractal dimension

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for an overall decrease in ‘size’, the appearance of more loops in the structure at intermediate lengthscales, and a slight thickening of the ‘skeleton’ (i.e. particle chains) [733].

R1▪5▪7▪5

Shear

Shear may affect the structure of aggregates in different ways depending on whether the aggregates are exposed to the shear field while they are forming, or only after they are fully formed [481]. It has been suggested that aggregates formed under quiescent conditions and subsequently sheared may be less affected by shear, as restructuring (especially on small lengthscales) would require the break-up of many interparticle bonds [481]. Both experimental and computer simulation studies indicate that shear restructuring of aggregates grown perikinetically occurs rather on longer lengthscales [703]. Classic experimental work by LIN, KLEIN, LINDSAY, WEITZ, BALL & MEAKIN [666] investigated the effect of exposing aggregates of 7.5nm gold particles formed under DLCA conditions to shear. (DLCA formation conditions were chosen for the lower degree of polydispersity and lower Df, implying greater susceptibility to shear rupture [666].) The aggregates were of approximate size 0.5μm [666]. The suspension of aggregates was forced through a short, narrow tube exposing the aggregates to a maximum (time-average) shear of ≤58Pa for a period of <0.5s [666]. Taking the tube diameter to be 0.5mm implies that the mean suspension velocity was 3.6m/s [1110] (tube length < 1.8m), Re ≤ 1.8×103 (laminar), G ≤ 4.1×104s‒1 [cf. 670], and the hypothetical KOLMOGOROV turbulence microscale would be dKolmogorov ≥ 1.5μm, far larger than dagg. Scattering experiments showed that as the shear stress was increased, the loose fractal structure of the aggregate was disturbed at steadily decreasing lengthscales [666]. For the system studied, the original fractal structure (Df ~ 1.84) always persisted at lengthscales less than about 0.10μm (regardless of aggregate size) [666, see also 670]. However, at the larger lengthscales the structure seemed to contract to a denser form, manifest in an increased ‘apparent’ fractal dimension * (up to 2.6 for the smaller aggregates, up to 2.8 or more for the larger aggregates) [666]. The denser form, comprising a greater density of interparticle bonds, has a stronger structure, which is able to withstand the imposed stresses (also slightly reduced due to the more compact size) [666]. Break-up of the aggregates was not identified in this experiment [666, see also 838]. In summary [666]: Whereas the [aggregates] are restructured at large length scales, they are found to maintain their original fractal correlations at small lengths.

Earlier work by OLES [799] on aggregation of 2.2μm, neutrally buoyant polystyrene spheres at high dilution (φ ~ 10‒6) showed the same trend. The shear rates investigated, 2.8 to 17.2s‒1, corresponded approximately to an unsteady, transitional flow regime, however this was claimed to nevertheless still give behaviour typical of the laminar case [799]. At the smaller

*

784

The slope of the scattering intensity function I(q) on logarithmic co-ordinates has “no special meaning”, and need not even be constant over the lengthscales affected by shear, and so it is not a true fractal dimension [666], but only suggestive of a more (or less) compact structure. (In fact, the physical basis lies in the proportionality between the amount of solid material in a volume defined by a characteristic length probed by a given wavelength of radiation and the resultant scattering intensity [906].) Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


lengthscales the apparent fractal dimension was lower (2.1) than at longer lengthscales (2.5) [799]. It was hypothesised that although the coagulation would be reaction-limited, fluid shear accelerated the restructuring rate leading to Df ≈ 2.1, perhaps by particles ‘rolling’ over one another [799]. At larger sizes it was suggested that aggregates would ‘densify’ through the preferential breakage of relatively weak parts of the aggregate, which would generally correspond to the more open, porous parts, where the density of interparticle bonds is lower [799]. These results should not be interpreted as true fractal dimensions, as the largest clusters were less than 50μm in size (d/d0 < 25) [799]. HERMAWAN et alia [467] found a superficially opposite trend in 30μm aggregates of 22 to 28nm silica particles coagulated at pH 8 with magnesium chloride (MgCl2). At short range (d < 100μm) the structure was found to be extremely compact, with Df ≈ 2.7, attributed to spontaneous restructuring due to silica’s unique surface chemistry [467]. At long ranges (d > 100μm) the structure was far more open, with Df ≈ 1.7, characteristic of DLCA [467]. These different porosities at different lengthscales were confirmed by TEM imaging [467]. These results were obtained by only ‘briefly’ stirring the samples to obtain initial mixing [467]. When the systems were sheared at 50s‒1 for 1h using a 3-blade fluid foil Lightnin A310 impeller (giving turbulent flow with Re ~ 7530, dKolmogorov ~ 140μm), the long-range structure appeared unaffected, while the short-range structure seemed to become even more compact, with Df ≈ 2.9 [467]. The long-range structure probably formed by perikinetic aggregation in the period a f t e r m i x i n g c e a s e d (final measurements made 90min after mixing ceased [467]). Hence the results still allow a correlation between high Df and intense shear. It is not clear how much of the structure would develop during ‘brief’ stirring. These results are somewhat counter-intuitive, as ordinarily shear would be expected to have the greatest effect on larger lengthscales. HERMAWAN et alia [467] suggested that the shortrange restructuring enhancement due to shear may be caused indirectly through an improvement of the kinetics of some surface chemical reaction(s). Batch settling and centrifugation tests on the aggregate suspensions showed that the more compact aggregates also tended to form a more compact sediment [467]. The differences between ‘sheared’ and ‘unsheared’ samples were most significant for settling under gravity only; at the higher centrifugation rate (453g m/s2) the differences were insignificant, suggesting that the microstructure had been disrupted [467]. As the differences in microstructure were observed at the smallest lengthscales, while structure is expected to collapse first at large lengthscales [467], it seems that the low-speed centrifugation rate (50g m/s2) disrupted only the long-range structure, which was the same in both cases. TORRES, RUSSEL & SCHOWALTER [1047] performed experiments on small aggregates of 0.1μm polystyrene spheres. The experimental conditions were expressly chosen in order to allow only the formation of rigid interparticle bonds * under the exclusive influence of a linear, laminar shear field in (diffusion-limited) rapid coagulation conditions at high dilution (φ = 10‒6); results were compared with equivalent perikinetic conditions [1047]. Shear rates

*

Rigid bonds are expected for coagulation in the primary minimum of a DLVO-type interparticle potential; bonds formed through ‘flocculation’ in a secondary minimum would allow rotation [1047]. R1▪5 : Aggregate structure and fractal dimension

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up to 1590s‒1 were imposed for up to 30min, and the aggregate sizes were small: of order only 1μm (10 d0) [1047]. Although the imposed shear affected the aggregate growth dynamics, they observed no significant differences in the final aggregate structures obtained, with data for all cases implying Df ≈ 1.8 [1047]. Break-up was claimed to occur in the absence of restructuring for the above system [1047]. In all cases the REYNOLDS number was below a “conservative” estimate of the critical value for turbulent flow, 1500 [1047]. If we consider the hypothetical situation where this extreme of mixing was (just) turbulent, then interpreting the reported shear rate as G would yield a hypothetical KOLMOGOROV turbulence microscale of dKolmogorov ≈ 42μm, far larger than dagg. Subsequent simple modelling for e x t e n s i o n a l flow fields produced aggregates with similar characteristics, including Df and asymmetry [1048]. SERRA & CASAMITJANA [920] investigated the aggregation of 2μm polystyrene particles at low concentration (φ = 5×10‒5) in a COUETTE shear device operating in the laminar flow regime, but with TAYLOR vortices * present. Aggregates of up to 100μm in size were formed, and their structure was found not to be affected by G in this regime [920]. At short range an apparent fractal dimension of about 1.8 was calculated, and curve fitting suggested a larger fractal dimension (Df ~ 2.2±0.2, albeit with extremely heteroscedastic data) at longer range [920]. ALI & ZOLLARS (1987) [85] investigated orthokinetic coagulation of 384nm polystyrene spheres in a high-shear COUETTE device. At shear rates of 21000s‒1 and 29000s‒1 the flow field was laminar, but with TAYLOR vortices. The key finding was that the clusters tend to orient along the streamlines, which promotes more linear structures [85]. In laminar flow the particles tend to approach each other from a few directions only, constrained by the fluid flow, unlike the random approach of BROWNian (and turbulent) motion [85]. Under the conditions described, ALI & ZOLLARS [85] also observed planar aggregate growth, occurring exclusively along a shear plane. The particles could be strongly stabilised against coagulation by chemically-attached ionic groups, and adsorbed species provided weaker stabilisation [85]. Such surface groups would also hinder the coagulated particles from rolling into tighter configurations (as to relieve hydrodynamic stress) [85]. LE BERRE, CHAUVETEAU & PEFFERKORN [143] aggregated 1.09μm polystyrene spheres in a COUETTE device with G = 14s‒1. Under these orthokinetic conditions aggregation was found to increase with increasing particle concentration, however break-up also increased with increasing particle concentration [143]. The slower aggregate growth at high concentrations was more pronounced under reaction-limited conditions, and the authors attributed this to a time-dependent ageing effect of the interparticle bonds [143]. Thus, newly-formed interaggregate bonds are relatively weak (especially in the RLCA case) and may quickly break, whereas aged bonds will only rupture infrequently [143]. The mechanism behind the ageing was proposed to be a gradual decrease of the interparticle gap after collision and initial bond formation: restructuring (by ‘rolling’) and rupture would be easier in the earlier stages [143].

*

786

This is a steady flow regime — unlike turbulent flow — with the vortices being macroscopic features, unlike the microscopic eddies of turbulent flow [169]. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


There was no observed effect of particle concentration under perikinetic conditions [143]. Rather low fractal dimensions were estimated, in the range 1.4 (DLCA) to 1.8 (RLCA) [143] — a plausible explanation is that the flow field caused preferential orientation of the aggregates [143] * (the dimensions of their device indicate that the flow regime was laminar, with no TAYLOR vortices). The authors introduced an explanation based on a rotation mechanism [143]. LE BERRE, CHAUVETEAU & PEFFERKORN [143] postulated that under low shear aggregates would simply be rotated, while high shear would cause break-up and fusion of the fragments into more compact structures [143]. If the shear field encourages certain orientations of the aggregates, then new particles or clusters are more likely to attach at the ‘more exposed’ or ‘more available’ points of the aggregate [143]. In such a case the tips of the aggregate would effectively be more “reactive”, and the sides less so [143]. MEAKIN [729] compared the effects of translational and rotational diffusion, showing that in the limit of rotational dominance a linear aggregate would result with Df ≈ 1.0 † [143]. HOEKSTRA, VREEKER & AGTEROF [481] aggregated polydisperse (40 to 100nm) nickel hydroxycarbonate crystals, either under quiescent conditions or in a shear field produced by a COUETTE device, up to final aggregate sizes of 1 to 20μm. In the absence of shear, typical DLCA (Df = 1.7) and RLCA (Df = 2.0) behaviour was obtained [481]. In the rapidly reacting systems Df increased from 1.7 to 2.2 under turbulent conditions (stable between G = 200 and 400s‒1) [481]. In slowly reacting systems Df increased from 2.0 to 2.2 under laminar conditions (with TAYLOR vortices, G = 7s‒1), and up to 2.7 under turbulent conditions (G = 200s‒1) [481]. The KOLMOGOROV turbulence microscale was no less than dKolmogorov ≈ 50μm, somewhat larger than dagg. The densification mechanism was attributed to a combination of rotational diffusion of primary particles within the aggregate and “elastic deformation or breakup of the clusters with the weaker parts being disrupted” [481]. It was found that weakly-bonding systems (corresponding to RLCA) are more susceptible to shear [481], as intuitively makes sense. HANSEN et alii [441] coagulated 3.4μm polystyrene particles under quiescent conditions and in a COUETTE shear device with a very low shear rate (G = 3.5s‒1, laminar flow, Pé ~ 480). The categorisation as laminar flow is a simplification, as streamlines were observed to be perturbed around large clusters, so that particles or small clusters following those streamlines would not collide as otherwise expected [441]. Attrition was observed as a result of collisions between clusters — When the two large clusters met they rolled edge to edge and entanglements occasionally ripped off or transferred among the clusters.

— but never ‘spontaneously’ due to hydrodynamic stresses [441]. concordant with the description of THOMAS, JUDD & FAWCETT [1018]:

This observation is

As particles collide, the fluid in the diminishing space between them is squeezed out. This motion of the fluid causes the particles to rotate relative to one another [...].

(Yet the possibility of ‘spontaneous’ attrition in the case of very weak interparticle attraction remains [1069].)

*

Modelling of polarisable aggregates by JULLIEN [542], which found Df = 1.42, supports this contention [143].

†

This value was obtained from a model of processes in two-dimensional space, but is expected to apply also to three-dimensional space [143]. R1▪5 : Aggregate structure and fractal dimension

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At high electrolyte concentrations, where the particles are strongly aggregating, fractal dimension was constant; at lower electrolyte concentrations, where significant repulsive interparticle forces remained, the measured Df increased to a value ultimately greater than for the strongly coagulating system [441]. The low measured Df was attributed to the initial population of ‘oligomers’ formed under perikinetic conditions prior to shearing, and provides circumstantial support for the susceptibility of weakly bonded aggregates to densification in a shear field [441]. Conversely, it appears that aggregates in strongly coagulating systems do not densify [441]. Further evidence to support densification came from directly imaging the clusters, which showed that the primary particles were especially densely packed in the periphery of clusters formed in dilute electrolyte, typical of localised structural rearrangement [441]. Furthermore, analysis of the density autocorrelation function indicated that these clusters underwent continuous densification with time at even the smallest lengthscales [441]. This is contrary to some other studies, which reported densification only on large lengthscales. In some experiments an excess * of 0.39μm polystyrene particles was added (Pé ~ 0.7) [441]. While the small particles did not themselves aggregate, they were able to aggregate with the larger particles, and form ‘bridges’ between them [441]. However, such bridges (large– small–large) are not individually likely to withstand the imposed stresses, and so aggregation of clusters at multiple connection points is favoured, which in turn suggests heterogeneous aggregation, as “the probability of finding multiple favourable connection points [between like-sized clusters] simultaneously is low” [441]. (This is the reverse of the trend for aggregation between large clusters to be promoted in the case of weakly aggregating systems [441].) The measured Df for the bidisperse system was slightly lower than for the monodisperse system [441]. A possible explanation for this observation is that aggregates formed in the bidisperse systems have fewer degrees of freedom to rearrange “due to the presence of small particles incorporated in the joints between large particles” [441]. Further, it is speculated that the presence of smaller particles may “reduce the bonding probability of cluster collisions” [441] — this might be expected to lead to more dense aggregates by analogy to the RLCA case, except that the effect for the bidisperse system was found to be greater for small clusters than for large clusters [441]. SPICER et alia [961] studied the effect of different shear schedules upon 0.87μm monodisperse polystyrene spheres in a stirred 2.8L baffled tank and coagulated with aluminium sulfate. For turbulent orthokinetic aggregation it was reported that the larger aggregates were more compact than the smaller aggregates, and had higher fractal dimensions (2.1 versus 2.5), because the larger aggregates were more susceptible to shear-induced restructuring [961]. Exposing aggregates to a high shear rate spike (up to G = 500s‒1) resulted in slight decreases in dagg but increases in Df after steady-state was reattained (at G = 50s‒1) [961]. On the other hand, exposing the aggregates to high shear with a gradual, ‘tapered’ decrease back to the original intensity resulted in considerable decreases in dagg with slight increase in Df and aggregate density when equilibrium was re-established [961]. There was little difference between 300 and 500s‒1, although these were much more effective than a spike of 100s‒1 [961]. This is not entirely surprising, as shear rupture is associated with

*

788

An excess by number, but not by volume. Appendix R1 : Conditions Affecting the Nature of the Sludge Material Formed


the KOLMOGOROV lengthscale, which (roughly) varies with G‒1/2 (equation R1-7b). Thus, for G = 50, 100, 300 and 500s‒1, dKolmogorov ~ 141, 100, 58, and 45μm respectively. The stable aggregate sizes reported by SPICER et alia [961] correlate fairly well with dKolmogorov . Rupture of bonds between the particles and the precipitated aluminium species was described as irreversible [961], as it is statistically (entropically) highly unfavourable for the bonds to reform (to the same extent). It was speculated that this would result in a decrease in collision (bond-forming) efficiency [961], which is known to lead to the formation of denser aggregates (e.g. §R1▪5▪6▪1). (Capture e f f i c i e n c y is predicted to slowly decrease asymptotically to zero as G becomes very large — although the f r e q u e n c y of encounters would increase, so that the capture rate still increases with G [1070] (ignoring any subsequent rupture). Within a narrow range of suspension conditions the capture efficiency has been predicted to increase with increasing G at moderate shear rates [1070]. ) An interesting result was the dip and subsequent increase in aggregate density after the high-shear spike, attributed to (first) the reformation of larger aggregates and (then) the restructuring of those aggregates [961]. SELOMULYA et alia [913] aggregated 0.38μm monodisperse polystyrene particles using KNO3 under various shear conditions (16s‒1 ≤ G ≤ 100s‒1) in a stirred tank fitted with an axial mixer (Lightnin A310). As aggregation proceeded the aggregate size increased [913]. At low shear rates this growth gradually slowed, and a steady-state size was obtained [913]. At higher shear rates the aggregate size peaked and then asymptotically decreased to the steady-state value [913]. This decrease coincided with a decrease in (average) aggregate mass, indicating that some erosion or fragmentation must have occurred [cf. 913]. Consistent estimates of Df ~ 1.7 were obtained initially for all shear rates, but at lengthscales greater than ~2μm the apparent value rose to ~2.1 and eventually became non-fractal (no power-law correlation) as G was increased [913]. These changes were attributed to restructuring, for which the kinetics were apparently faster than for breakup [913]. SPICER, KELLER & PRATSINIS [962], coagulating 0.87μm polystyrene particles with Al2(SO4)3, made the same observations for axial-flow agitators, but not for radial-flow impellers (as used in the present work) [913]. They [962] argued that the peak in size could be caused by shorter circulation times in the former case, implying more frequent exposure to the highshear impeller zone [913]. Unfortunately their fractal analysis was ambiguous [913]. Interestingly, although several researchers have interpreted increases in (apparent) fractal dimension at larger values of dagg as evidence that shear has effected densification on larger lengthscales (vide supra), MEAKIN [729] presented an analysis which indicated that at least a small degree of increase in the apparent value of Df can be expected as dagg (or rather, the mass) increases, as an artefact of the calculation procedure (and the finite aggregate size). An early investigation by SONNTAG & RUSSEL [953] found very large changes in Df for a system of 0.14μm monodisperse polystyrene spheres aggregated in a quiescent state, and subsequently sheared in a COUETTE device. In order to isolate the effect of hydrodynamic shear gradients, the shear rate was repeatedly ‘spiked’ up to 6000s‒1 for short times, which was expected to minimise rupture due to particle collisions [953]. Although it was claimed that this yielded a purely laminar flow regime [953], comparison with a later paper by RUSSEL and co-workers [1047] indicates that turbulent flow would have been attained. Light


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scattering indicated that Df increased from 2.2 to a high value of 2.48 in response to the shearing [953]. (Df for the unsheared aggregates had itself apparently increased from a low initial value of 1.6, ascribed to ‘spontaneous’ structural rearrangement [953] — although another ‘ageing’ mechanism may have been involved [cf. 667].) The magnitude of these changes is surprisingly high in contrast to comparable studies.

790


R2.

BEHAVIOUR OF SLUDGE-LIKE MATTER

The focus of the present work has been on dewatering imposed on WTP sludges. Conventional work in this area encompasses an array of theories that were developed over time, running from DARCY’s law, describing permeation through a fixed medium, to the recent models of LANDMAN, WHITE and colleagues, describing more sophisticated industrial dewatering unit operations that include settling or thickening, centrifugation, and filtration. These were the subject of detailed discussion in Chapter 2. Yet it is wrong to think that sludge will only dewater in response to some external (‘exogenous’) driver. Endogenous dewatering does occur in some systems, and is called ‘synæresis’. It is also dangerous to ignore parallel developments in associated fields of endeavour. The discipline of soil mechanics has contributed numerous theoretical and empirical models to describe the behaviour of soils in deformation, consolidation, and creep. Macrorheological models also capture interesting aspects of behaviour related to such aspects as consolidation, stick–slip motion, and stress distribution and evolution.

R2▪1 R2▪1▪1

Endogenous synæresis General

Synæresis has been described as the expulsion of liquid due to contraction of the gel in which it was being held [314, 1087]. Synæresis may occur due to the application of an external pressure [cf. 680, 853, 1045], but the phenomenon of more interest here is e n d o g e n o u s s y n æ r e s i s [314, 1087]. Endogenous synæresis — called simply “ s y n æ r e s i s ” in the present work — may be defined as the (“spontaneous” [305, 901]) “contraction of the gel under the absence of external forces, such as gravity” [1087] [314] and in the absence of evaporation [305, 901]. For certain systems it is known as the reverse of swelling [1087], i.e. de-swelling. Proposed mechanisms include condensation reactions [cf. 901], surface energy effects [cf. 901], hydrophobic attractions, VAN DER WAALS forces (e.g. promoting sintering [261], §9▪1▪1▪1(b)), and electrostatic attractions [305]. It has been suggested that entropic effects or non-equilibrium thermodynamic effects may hinder synæresis [461]. Occurrence of significant settling may mask minor synæresis effects [cf. 1030], or disrupt the slow approach and fusing of primary constituents (just as BROWNian motion can disrupt settling of very small particles). Physical constraints may prevent synæresis occurring altogether. Synæresis is inclined to occur isotropically, however it is often physically constrained in certain directions [261, 305, 680, 1107]. For example, a gel sitting at the bottom of a sealed cylinder can only expel liquid through the upper (gel–liquid) interface *: the material at the base is more physically constrained, and so in synæresis typically greater solidosity is *

In principle liquid could be expelled through the lower surface, but this would require detachment of the gel from the vessel and support of the weight of the entire superposed gel by the expelled liquid (which might perhaps slowly drain via the sides). Expulsion at the sides is disregarded here. R2▪1 : Endogenous synæresis

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observed moving u p the bed [1030, 1107] (rather than down the bed, as in gravity settling). Material deep within the bed feels an isotropic force from neighbouring particles [1107], and cannot synærese as long as its contraction is resisted by the walls *. Physical perturbation of the gels can remove or reduce these constraints, promoting synæresis [261]. For example, gentle spinning of round sample cells detached a polystyrene gel from the wall without breaking it, permitting synæresis of the bulk to take place [261]. Where the constraints persist, ‘localised’ synæresis may take place: this may manifest as uniform one-dimensional shrinkage [305, 680], or as the inhomogeneous formation of macroscopic regions of higher and lower solidosities [261]. A number of publications suggest that an ‘induction’ period (cf. §9▪1) precedes synæresis [261, 305, 901]. This could be a result of ongoing chemical processes [261] or development of the balance between (gradients of) stress in the solid network and pressure in the liquid phase [901]. Alternatively, physical perturbations may initiate a synæresis-like phenomenon [851]. Increases in the endogenous synæresis pressure have been associated with increases in the ratio of loss and storage moduli (G′′ / G′ ≡ tan δ) [1087], corresponding to a transition from more solid-like (elastic) to more liquid-like (viscous) rheological behaviour [636, 779]. This transition has not been observed in all synæresing systems [1058], although this can also be a consequence of the limitations of rheological measurement.

R2▪1▪2 R2▪1▪2▪1

Particulate networks Theory

A number of researchers have proposed models to characterise and predict shrinkage due to synæresis. Models employed in different fields often differ greatly, and no single theory has yet become established and generally accepted. For modelling respectively the original compression, the swelling, and the re-compression of soils KEEDWELL [559] presents equations of the following form: m

 1 dp  dh  , = − Ξ   dt  p dt 

p > pc and

dp >0 dt

[R2-1]

p < pc and

dp <0 dt

[R2-2]

m

 1 dp  dh  , = + f redn Ξ   dt  p dt  m

 1 dp  dp dh  , >0 [R2-3] p < pc and = − Ξ   dt dt  pc dt  in which h is the height, Ξ > 0 is constant for a given system, m is a material parameter (here 0 < m < 1), p is the mean effective pressure, pc is the “preconsolidation” value of p, and fredn is a reduction factor to account for the irreversibility or hysteresis of compression [559]. The preconsolidation pressure is equivalent to the maximum pressure at which the sample was

*

792

Then the only way for the gel to synærese more uniformly along the column is if the synæresis forces are strong enough to overcome both adhesion at the wall (energy required to create new surface) and ensure cohesion against gravity. Appendix R2 : Behaviour of Sludge-like Matter


equilibrated, and represents the stress history of the sample. For viscous “Zone 1” ‘cohesionless’ soils (e.g. sands) taken as having direct mineral–mineral contact m = 0, while m = 1 corresponds to thixotropic “Zone 2” ‘cohesive’ soils (e.g. clays) where it is assumed that there is contact between the mineral and a surrounding layer of water only [559]. KEEDWELL [559] presents a useful discussion of the mechanisms prevailing in sequence: • Compression of fresh sample — As the [...] pressure is increased, [...] the size and stiffness of the contact zones will increase. This is accompanied by sliding at some contacts while others act as hinges [...].

• Swelling of compressed sample — When the applied pressure is decreased, [...] the soil will start to swell [...]. However, because of the hinge and slider mechanism the contact zones do not diminish in size on unloading as much as they previously increased. Consequently, during [swelling] the contact zones are relatively stiffer than they were during consolidation [...].

• Re-compression of swollen sample — On reloading deformation is partly controlled by contact zones which differ in size from those applicable when the soil had no stress history. However, once a stress level is reached which is greater than the previous maximum, [...] the size and stiffness of the typical contact zone are mainly influenced by current stress level [rather than stress history].

A number of studies [152, 314, 901, 1030] featured the appealing use of DARCY’s law (§2▪3▪1) to model resistance to liquid expulsion. BIOT [152] treated the solid network as an ideally e l a s t i c structure (see §R2▪3▪1), and developed equations showing that one-dimensional consolidation of a sample constrained laterally and draining at one face will proceed initially with the square root of t1/2 (cf. §R2▪2▪2▪2). VAN DIJK, WALSTRA & SCHECK [314] derived equations modelling one-dimensional synæresis on the basis of a d i f f u s i o n equation in non-standard form, in which the motion of the solid is implicit. The ideal solution again predicts that the initial consolidation rate is proportional to t1/2 [314]. It was suggested that the exponent would increase to 1 if gravitational consolidation dominated (cf. §2▪4▪5▪3(a)), and furthermore would be increased if permeability improved over time [314]. Experimental results on milk gels have variously shown exponents that increase from 0.5, initially, up to 0.78 [314] or decrease from 1.0 (i.e. linear), initially, down to 0.7 [680]. It was suggested that a viscoelastic model may better match the empirical results [680]. An alternative ad hoc one-dimensional theory was developed by TIJSKENS & DE BAERDEMAEKER [1030]. SCHERER [e.g. 901] has developed a theory for synæresis that considers the solid phase as a v i s c o e l a s t i c network (e.g. modelled as MAXWELL elements * — see §R2▪3▪1) that induces a pressure gradient in the liquid phase which drives liquid expulsion and permits gel shrinkage. As well as three-dimensional synæresis [901], constrained, one-dimensional systems should be able to be modelled using the same approach.

*

VAN VLIET et alia [1087] modelled the solid network as a set of parallel MAXWELL elements of varying specification, representing various protein–protein bonds. R2▪1 : Endogenous synæresis

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FEDA [361] indicates that swelling can be modelled using the usual partial differential equation of TERZAGHI [1013] for hydraulic diffusion (e.g. so-called primary consolidation): equation R2-7.

R2▪1▪2▪2

Observation — milk gels

Milk gels (e.g. junket) are considered to be viscoelastic particulate gels made up of primary particles (or micelles [680]) of diameter 20 to 300nm, with the largest particles containing thousands of protein molecules [1087]. Milk gels may be formed either by appropriately reducing either the electrostatic or steric stabilisation [680, 1087]. The particles tend to aggregate into a structure composed of ‘nodes’ of many primary particles clumped together, connected by ‘strands’ one to four particles thick and 10 particles long, with pores up to 10μm in diameter [1087] [cf. 1030]. Synæresis will be “greatly enhanced” if strands are broken [1087]. One may consider that if bonds are not broken, the deformation and ensuing synæresis must rely on the flexibility or ‘elasticity’ of the bonds. Breakage of the bonds allows plastic deformation of the network, allowing much larger ‘strains’ to occur, with consequential expulsion of pore liquid. Local breaking of strands was “confirmed” by an observed increase in the permeability of milk gels with time, attributed to increasing pore sizes [1087]. As with all viscoelastic materials, the “fracture stress” of milk gels decreases as the strain rate is reduced; equivalently, the gel will fracture more rapidly as the (constant) applied stress is increased [1087]. This dependency is stronger for paracaseinate gels than for acid casein gels [1087]. There are two ‘internal’ factors that may contribute to breakage of strands, and these may operate synergistically [1087]: • spontaneous breakage due to bond relaxation, and • breakage due to an internal network stress being developed. Furthermore, synæresis is enhanced by externally-imposed mechanical stresses [680]. See also §S17▪1. BROWNian motion or transient deformation of the strands into less thermodynamicallyfavoured conformations or positions may enable new bonds to form between exposed surfaces [cf. 680], giving rise to a stress in the strands, and hence an endogenous synæresis pressure in the system [1087]. This model of ongoing aggregation can be used to explain breakage due to an internal stress that exceeds the gel’s “fracture stress” [1087], analogous to the balance between pS and py in LANDMAN–WHITE theory. Breakage may still occur when the internal stress remains below the fracture stress, and depends upon the distribution function of relaxation times of the bonds to be broken. The relaxation time, trelax, may be defined as the “average time during which a bond exists due to Brownian motion”, so that the probability of a bond breaking within time trelax is identically equal to ½ [1087]. Where there is a distribution of relaxation times, the longer times will control the rate of yielding; the rate increases as trelax decreases [1087]. By supposing that around 80 bonds would have to be broken essentially simultaneously for the “thin part” of a strand to fail, VAN VLIET et alia [1087] found that the probability of 794

Appendix R2 : Behaviour of Sludge-like Matter


‘permanent’ strand breakage within a given time would be vanishingly small in most cases where there is no tensile stress. When a tensile stress is imposed, the formation of new bonds is no longer random, and the likelihood of the just-broken bond being reformed is much reduced [1087]. If the relaxation time is sufficiently small, then it is possible for the stresses in the strands to be relaxed so quickly that the continuous liquid phase will experience negligible compressive stress [1087]. Sufficiently large relaxation times can also prevent synæresis, where in such a case the rate of yielding may be negligible. VAN VLIET and co-workers [1087] found (initial) endogenous synæresis pressures ranging from / 1Pa for acid casein gels, to 0.3Pa for paracaseinate gels at 25°C, to 1.0Pa for paracaseinate gels at 35°C [cf. 314]. Other workers calculated larger pressures up to 3.5Pa [680]. Increases in the endogenous synæresis pressure corresponded to increases in tan δ, increases in the “permeability coefficient” (with KD ~ 10‒13m2 [cf. 314]), increases in the rate of yielding, and increases in the extent of synæresis observed [1087]. For comparison, measured fracture stresses varied from around 120 or 200Pa with a 10s exposure for paracaseinate or acid casein gels (respectively) down to around 10 or 90Pa with a 1000s exposure [1087]. In milk gels greater initial r e l a t i v e shrinkage rate was observed for thinner slabs [680, 1058]. Thinner slabs have a shorter average drainage pathway. Wall effects (physical constraints) are also expected to be important (more significant for thinner slabs) [1030]. Greater final shrinkage was observed at lower pH, where both permeability and strength were larger [680, 1058]. The larger strength is presumably related to the reduced interparticle repulsion [cf. 1087], which suggests stronger bonding: although stronger bonds may be expected to be better able to withstand a given synæresis pressure, the synæresis pressure itself may increase in response to the increased interparticle attraction. Many of the gel properties and gelation conditions are interrelated [cf. 1058], and so it is difficult (or impossible) to assess the individual importance of each variable. Interestingly, as synæresis proceeds and overall porosity decreases, milk gel permeability has been found to increase [1030]. This implies the formation of larger ‘channels’ * [cf. 314, 1030].

R2▪1▪2▪3

Observation — clayey soils

A distinction is made between the behaviour of three prominent categories of clay minerals [559, 771, 850] [cf. 82, 1014]: • kaolin, including kaolinite and halloysite; • smectite , including montmorillonite; and • illite. All three are made up of alternating sheets of gibbsite and silica [559]. Water is unable to enter between the sheets of gibbsite and silica to expand the unit cells in kaolinite [771]. Separation of successive layers by a single molecular layer of water is possible in halloysite [771]. Entry of water into montmorillonite is facilitated by the weak bonds and excellent cleavage between oxygen atoms of adjacent layers, and can cause significant expansion [559, 771]; multiple molecular layers of water are possible [82]. Illite is similar to montmorillonite, except that some of the Si species are replaced by Al, with the charge balanced by non-

*

Simple models predict decreasing permeability with time [901]. R2▪1 : Endogenous synæresis

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D. I. VERRELLI

exchangeable potassium ions, K+, between layers — illite has a swelling behaviour intermediate to the kaolin and smectite groups [82, 559, 771, 1014]. Swelling pressures up to ~3MPa have been observed, defined as the pressure required to prevent volume expansion of a soil in contact with water (e.g. as measured with an œdometer [11, 37, 267, 850, 912, 946, 975, 976, 1007, 1014] [cf. 598, 1012]) [771, 1014]. R2▪1▪2▪3(a)

Subaerial soils

Clayey * (or ‘argillaceous’) soils, in particular those of the smectite group, commonly experience swelling in the environment due to the changing availability of water [771]. At one limit, cracking may occur due to subaerial desiccation [305, 851]. R2▪1▪2▪3(b)

Subaqueous soils

Synæresis in subaqueous environments is associated with fine-grained soils with high clay contents, especially smectite [305, 851]. Synæresis does not occur in all such soils, and depends on a number of other factors — e.g. organic matter is expected to discourage synæresis [305, 851], cementation resists the moderate synæresis pressures [305]. Cracking occurs due to lateral confinement [305] and the existence of local stresses [851]. It may also be considered that the cracking occurs as expulsion of the liquid occurs faster than the maximum rate of transport through the porous media. Often material from surrounding laminæ enters (or is “injected”) into the cavities so formed [851]. While adjustment of the diffuse layer of ions surrounding soil particles due to rising salinity would increase interparticle repulsion and is commonly advanced as the cause of soil synæresis [305], it is not universally accepted [851]. It is clear that the mechanism cannot be simple consolidation due to self-weight, as the observed volume reductions would then only occur at depths of order 102m, whereas the phenomena occur at a range of depths from order 101m to approximately 103m [851]. In one typical model gelation of clay particles occurs through attractive interparticle forces, and these forces continue to act after the initial formation of a network [305]. That is, the forces act to bring particles into closer contact, which has the effect of increasing the network yield stress [305]. The result is then dependent upon a number of conditions [305]: • High compressibility †, high permeability, low gel viscosity (e.g. at shallow depth) o Large gravitational stresses (i.e. from self-weight) — gravitational strains will overwhelm synæresis strains, so cracks will not appear, although network contraction will occur. • Low compressibility, low permeability, high gel viscosity (e.g. at increasing depth) — network will attempt to shrink in three dimensions; lateral constraints will dictate the formation of large ‘faults’, or slip faces. *

The word “clay” is ambiguous, and has multiple meanings [82, 267]. In the geotechnical engineering sense, a ‘clay’ refers to “a material composed of a mass of small mineral particles which, in association with certain quantities of water, exhibits the property of plasticity” [771]. Note that such behaviour is also a function of water (and air) content [771]. More formally, in soil mechanics, “ c l a y f r a c t i o n ” refers to the mass fraction of particles smaller than 2μm s i z e [267, 1014] [cf. 1012], while “ c l a y c o n t e n t ” refers to the mass fraction of clay m i n e r a l s (of any size) [305].

†

Used here in the sense of ‘ability to be f u r t h e r compacted’.

796



• Low permeability, low gel viscosity — large variation in synæresis-induced strain rate will lead to localised cracking. This is also promoted by increased distance to a drainage boundary, i.e. with increasing depth. Networks comprising coarse-grained mineral particles can be considered less compressible and more permeable, and so synæresis cracks do not appear in these materials [305].

R2▪1▪2▪4

Observation — polystyrene

Polystyrene particles of 21nm diameter were observed to undergo a process of gradual synæresis [261]. As “disordered” systems far from equilibrium, these networks tend to exhibit large relaxation times, and sintering of the primary particles proceeds slowly [261]. (Thermally-induced formation may be ruled out, as the well-known random properties of this mode should yield exponential decay of the scattering structure factor [261] [cf. 263]. Diffusion and drift were also ruled out [261] [cf. 263]. See §9▪3▪2▪5.) The samples were observed to develop inhomogeneities on relatively large lengthscales, which could be seen unaided after prolonged ageing [261] [cf. 263]. This suggests that physical constraints — namely adhesion to the walls of the container — prevented the network from shrinking uniformly. Rather, boundaries such as between previously unconnected clusters are likely to constitute weak points that are unable to withstand the stresses due to synæresis, and so the material on either side contracts locally, away from the conceptual boundary, creating a real void and weakening the network [261]. As synæresis progresses, the network shrinks further, and with the formation of more bonds, the strength increases considerably [261]. The weakening described above may lead to (sudden) macroscopic collapse under gravity due to self-weight [261].

R2▪1▪2▪5

Observation — silica

Using 88nm silica spheres sterically stabilised by a 12nm-thick layer of polystyrene WEEKS, VAN DUIJNEVELDT & VINCENT [1107] conducted consolidation experiments in cyclohexane. At lower temperatures or higher concentration — where gels were “stronger” — they observed [1107]: The gel compacts mainly under the influence of inter-particle attractions, which favour a final state which is more concentrated than the initial suspensions. Gravity plays a minor role.

This is equivalent to synæresis. Numerous other observations of synæresis in silica gels and titania gels have been made [see e.g. 901].

R2▪1▪3 R2▪1▪3▪1

Flexible macromolecular networks Theory

FLORY (1953) [365] derives equations describing the thermodynamics of swelling in polymeric gels. Treating these as (elastic) solutions, he casts the derivation in terms of the difference between the chemical potential of the continuous (‘interstitial’) liquid phase and R2▪1 : Endogenous synæresis

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D. I. VERRELLI

that of the pure liquid (e.g. external to the gel) [365]. Naturally the former quantity depends upon the degree of swelling [365]. The difference in chemical potential may alternatively be interpreted as a pressure acting on the network, π = πnon-ionic, as an osmotic pressure [365]. When the network is made up of polyelectrolytes, an additional complication is introduced to the theory, as electrostatic repulsions between polymer chains tend to expand the network (although these will be screened by mobile ions in solution) [365]. The concentration of mobile ions in the liquid phase will always be greater in the network than outside it, because of the attraction of the charged sites on the polyelectrolytes, leading to a higher osmotic pressure inside the gel [365]. This osmotic pressure driving liquid i n t o the network from the bulk may be equated to an expansive force [365]. This may be expressed [365]: πionic = R T [Cpolyelectrolytes ‒ (Cmobile ions in bulk ‒ Cmobile ions inside gel)] , [R2-4] in which C represents some (appropriately weighted) charge concentration. Given that πnon-ionic drives liquid o u t of the network when positive, equilibrium requires π = πnon-ionic ‒ πionic = 0. FLORY [365] provides a brief discussion of the two limiting cases in which the bulk electrolyte concentration is alternatively very small or very large in comparison to the (weighted) concentration of polymer charges in the network. For some polymer networks the effect of ionic interactions allows volumetric swelling ratios greater than 500 [365]. Unfortunately the above theory describes directly only the e q u i l i b r i u m situation, and does not directly describe the k i n e t i c s . Nonetheless it may be instructive to investigate the order of magnitude of the osmotic pressures described and to compare these with the network or particle pressures commonly encountered here in filtration and batch settling. Furthermore, the rates ordinarily depend upon the extent of deviation from equilibrium.

R2▪1▪3▪2

Observation

Very high osmotic pressures can be obtained in polymer ‘solutions’ *, in excess of 10MPa [745]. Synæresis is known to occur in gel systems such as κ-Carrageenan gels [332]. Addition of potassium ions (K+) has been reported to increase the rigidity and brittleness of the gel, thereby enhancing synæresis [332]. Careful experiments carried out by DUNSTAN and coworkers [332] confirmed that addition of K+ yielded a more rigid structure, but this was found to be “less likely to undergo a structural reorganisation of the aggregates within the gel network, hence reducing the degree of syneresis” [332]. Synæresis also occurs in agar jellies [1045].

*

798

Made up of poly(oxyethylene) of molecular mass 17200g/mol [745], suggesting a nominal size of ~5nm [248, 861]. Appendix R2 : Behaviour of Sludge-like Matter


R2▪1▪4

Microgels

Microgels can be described as soft particles where each particle is made up of entangled and partially cross-linked polymer strands [999]. The particles are thus somewhat flexible, and can swell and de-swell according to solution conditions; as they swell they become more porous and ‘impregnated’ with the solvent phase [999]. A typical example of such a microgel is ‘polyNIPAM’ (poly(N-(1-methylethyl)-2propenamide)) particles.

R2▪1▪4▪1

Theory

Microgel swelling and de-swelling can be caused by differences in osmotic pressure. At equilibrium the difference between these two osmotic pressures is balanced by the elastic pressure exerted by the polymeric network, πelastic, viz. πelastic = πoutside ‒ πinside , [R2-5] where πinside and πoutside are the osmotic pressures within the microgel and in the bulk solution, respectively [998]. πelastic is in turn determined by structural factors and the degree of swelling [998]. The osmotic pressure difference can be decomposed into non-ionic and ionic components to aid calculation [998], viz. πelastic = πnon-ionic ‒ πionic. [R2-6]

R2▪2

Geomechanics and creep

Useful analogies may be drawn between the behaviour of WTP sludges undergoing dewatering and similar phenomena observed or modelled in other materials. In this section observations and theories developed for (clay) soils are presented. TERZAGHI [1012] recognised the value of analogies between soils and sludges in 1925, and indeed set this as a motivation for his theory of consolidation (§R2▪2▪2▪1(a)). The following section presents more general, conceptual models.

R2▪2▪1

Phases of consolidation

Consolidation of clay soils is conventionally seen as occurring in three phases [771, 912, 946] [cf. 1012]: • i m m e d i a t e c o m p r e s s i o n , due to elastic deformation. This is associated with particle deformation and displacement w i t h i n potential wells [1007] *. • p r i m a r y c o n s o l i d a t i o n , due to expulsion of liquid, with the result that particle separation decreases and new particle–particle contacts are formed; hydrodynamic resistance dominates the response to the applied load. This can be thought of as interaggregate rearrangement. • s e c o n d a r y c o n s o l i d a t i o n , where the particle–particle contacts in the network can resist the majority of the applied pressure, and the excess pressure of the fluid *

For natural samples trapped air could contribute [912, 946]. In the context of metal creep, at high stresses generation of an initial p l a s t i c deformation is also possible [187] — this should be interpreted to mean that there is some plastic deformation that occurs on the same timescale as the ‘instantaneous’ elastic strain. R2▪2 : Geomechanics and creep

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D. I. VERRELLI

approaches zero. MURTHY [771] attributes this ‘creep’-like phenomenon to “a delayed progressive slippage of grain upon grain”; CRAIG refers to the disturbance of structural bonding of aggregates or the ‘creeping’ of particles within them [237] — i.e. intra-aggregate rearrangement. TERZAGHI suggested an additional mechanism, viz. shearing caused by gradual lateral displacement [126].

R2▪2▪2 R2▪2▪2▪1 R2▪2▪2▪1(a)

Primary consolidation TERZAGHI diffusion equation Basic equation

Primary consolidation of soil is conventionally modelled by TERZAGHI’s partial differential ‘hydraulic diffusion’ equation [1014] [cf. 1011, 1012, 1013], which is written: ∂ 2 p ∂p , [R2-7] cv c 2 = ∂z ∂t in which cv c is the ‘coefficient of consolidation’ and p is the excess pore-water pressure defined p ≡ p ‒ ρL g (h ‒ z) = P ‒ ρL g h, with h the liquid surface level [see also 361, 771, 946] [cf. 168]. For consolidating clays cv c is typically of order 10‒7m2/s [361]. (TERZAGHI [1013] assumes the identical form of equation applies to swelling, with cv s in place of cv c [cf. 1014].) TERZAGHI [1013] explicitly acknowledged a large number of common assumptions involved in theories of soil consolidation, which he used [cf. 37, 297, 1007]: • the voids are completely full of fluid (two-phase assumption); • both phases are incompressible; • DARCY’s law (§2▪3▪1) is strictly valid *; • KD / ηL † does not vary spatially; and • the permeability of the sample controls the rate (i.e. other resistances are negligible). He also uses the following assumptions [1013]: • the sample is laterally confined; • all horizontal derivatives are zero (i.e. one-dimensional model [361]); • the ‘coefficient of compressibility’, av c, is constant (see Table 2-2); and [361]: • strains are small; • the soil ‘skeleton’ deformation is “linear and time-independent”— a first-order ‘correction’ was proposed by SCOTT (1963); • a unique relation exists between volume change (or axial strain) and effective stress (e.g. constant œdometric (i.e. constrained) modulus of compression), thus no secondary consolidation — as at small strains; and [152]: • the material is (macroscopically) isotropic; and

*

TERZAGHI’s [1013] intention was to refer to DARCY’s original formulation (§2▪3▪1): along with the following point, this would additionally require spatially invariant ρL g.

†

This follows from the mathematics, although TERZAGHI [1013, 1014] rather stated that the “coefficient of permeability” (KD 1856) needed to be constant.

800



• deformation is reversible (no hysteresis); and [1014] • dewatering due to creep is insignificant compared to that due to ‘primary consolidation’, so av c = ‒av c σ. TAYLOR [1007] identified the assumption of constant av c as the most restrictive and least justified. For sufficiently large t equation R2-7 gives simple e x p o n e n t i a l decay of strain, ε, to a finite value, εpc∞, (equilibrium strain if secondary consolidation did not occur) [361, 946, 1007, 1013, 1014] [cf. 698, 1012]. Many extensions and amendments to this theory have been proposed [e.g. 126, 152, 297, 724] [see also 698, 931, 975, 1013]. SHIRATO et alii [931] criticise application of the “crude” TERZAGHI approach in the present day due to the theory’s assumption of a constant cv c — they state that cv c may increase by around two orders of magnitude from its initial value [cf. sample data in 37]. Correlations to describe this have been proposed [e.g. 78]. MESROI & CHOI (1985) found that a unique relationship existed between the solidosity at the end of primary consolidation, φpc∞, and the applied (effective) stress, and therefore φpc∞ is independent of the thickness of sample (or maximum drainage path length, hdrain) [361]. Other workers have proposed alternative hypotheses, in which the behaviour is not independent of the sample thickness, and this too is supported by some experimental data [361]. R2▪2▪2▪1(b)

Relation to DARCY’s law and LANDMAN–WHITE theory

In soil mechanics permeability is commonly measured using a ‘coefficient of permeability’ which is just KD 1856 [e.g. 771, 912, 946, 1007, 1013, 1014] [cf. 1011, 1012]. This is also called the ‘hydraulic conductivity’ when the permeating fluid is water [771, 1014], and is equal to ρL g KD / ηL for spatially invariant ρL g (see §2▪3▪1). Derivations given in the literature [e.g. 267, 771, 912, 946, 975, 976, 1007, 1013, 1014] [cf. 320, 361, 1011, 1012] indicate that cv c takes the general form KD KD c~v c = , [R2-8] ~ ~ =η φ ηL m av c vc L ~ ~ and φ in which ~ cv c , m vary from source to source (see also Table 2-2). vc TERZAGHI’s original (1923) derivation [1011] a p p e a r s on first inspection to define * KD c v c = . ηL av c

*

[R2-9a]

The original formulæ presumably omit ρL (because it has magnitude ~1 for water in the centimetre-gramsecond system of units) and g (historically often implied by context only [e.g. 1013]). R2▪2 : Geomechanics and creep

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D. I. VERRELLI

In this case his derivation contains an e r r o r in equation 3 (page 129), omitting a factor of φ, and so it is n o t correct to substitute cv c for cv c in equation R2-7. Rather, cv c = cv c / φ. The working in the original paper is not straightforward. A clearer presentation of essentially the same material appears in TERZAGHI’s 1925 textbook [1012]. This confirms that the intended definition is modified by ‘correction’ of the permeability to yield [1011, 1012] [see also 570, 1007]: K φ c v• c = D . [R2-9b] ηL av c (This “original definition” was reported in 1941 to have been s u p e r s e d e d circa 1935 — by equation R2-9f — although usage persisted for some time after [570, cited in 1007], cf. below.) Clearly this ‘correction’ c o m p o u n d s t h e e r r o r already identified: DARCY’s law should not have been treated in the same way as the mass balance calculation. Moreover, i m p l e m e n t a t i o n of the ‘corrections’ was i n c o n s i s t e n t , viz. [1011, 1012] K φ c v••c = D 0 [R2-9c] ηL a v c or

c v••c• =

K D φ∞ . ηL a v c

[R2-9d]

The latter was justified with the claim that the ‘average φ’ is close to φ∞ [1012]. TERZAGHI’s 1943 textbook derivation [1013] sets KD KD c ∗v c = = . ∗ ηL mv c ηL φ0 av c

[R2-9e]

This derivation is also i n e r r o r . The error enters in §99 on page 270. The first inconsistency is that the ‘modified porosity’, defined as VL / V0, that was introduced in §98 is written now as the true porosity (VL / V) without any conversion factor. Once this is corrected, his equation [4] should be φ φ ∂(VL / V0 ) ∂p ∂v dz = − dz = − mv c dz, [R2-10] φ0 ∂z φ0 ∂t ∂t and the correction factor carries through to equation R2-7. substitute

cv∗ c

for cv c in equation R2-7. Rather, cv c =

φ0 φ

c∗v c

Thus it is n o t correct to

.

Finally, the most recent textbook derivation by TERZAGHI, PECK & MESRI (1996) [1014] gives KD KD cv c = = . [R2-9f] ηL mv c ηL φ av c Although this i s the c o r r e c t term to substitute into equation R2-7, it is worth mentioning that the derivation itself contains an error, with the statement on page 227 that φ0 dV is timeinvariant: if the volume of solids in the differential element is supposed to be constant *, then dV can vary with time, and so it is φ dV that is constant [e.g. 912, 1007, 1011, 1012].

*

802

If the volume (i.e. thickness) of the differential element were forced to be constant, then solid material would have to enter or leave to compensate for the nett loss or gain of liquid. Appendix R2 : Behaviour of Sludge-like Matter


Many other textbooks [e.g. 771, 912, 946, 1007] [cf. 320] — but not all [e.g. 296, 850] *† — seem to use the correct definition of cv c. In principle this also relies on defining mv c ≡ φ av c [e.g. 320, 912, 1014], given the universal use of equation R2-8. Yet a significant number of sources still use m∗v c ≡ φ0 av c [e.g. 267, 975, 1013], even (some of the time) those who have correctly defined cv c [e.g. 771, 946, 1014] — i.e. there is a lot of ~ as m∗ , and later m , SMITH [946] inconsistency in the literature. After initially writing m v c vc vc finally suggests using mv c ≡ φ av c , in which φ is an average (implicitly the harmonic mean). The inconsistencies no doubt arise because of the fact (or assumption) that φ0 / φ ~ 1 for typical clay experiments (or analyses) [cf. 1014]. Now that the correct definition of cv c has been confirmed, it is straightforward to relate this to LANDMAN–WHITE dewatering parameters by substituting for av c and KD. For samples undergoing compression ‒σaxial = pS ≈ py (§2▪4▪5▪1(c)). Hence applying the chain rule to the derivative form of av c (Table 2-2) yields av c ≈ (1 / φ2) dφ/dpy — i n p r a c t i c e this will n o t generally be constant, of course, but rather decreases because py is unbounded while φ → φcp [e.g. 771, 946, 1011] ‡. The relation between KD and R was given in equation 2-121. After simplifying and using the definition of the solids diffusivity (equation 2-63), it is found that: cv c ≈ D . [R2-11] (Despite this strict mathematical equality, typically cv c and D are obtained by different experimental procedures and used in different ways.) This is different from the relationship claimed by STICKLAND et alii [975] [cited by 604, 605, 976]. φ c ∗v c = D. [R2-12] φ0 Unfortunately STICKLAND and colleagues [604, 605, 975, 976] did not notice the error in TERZAGHI’s derivation [1013] outlined above, and so did not realise that the correct application of their relationship is φ0 ∗ ∂ 2 p ∂p . [R2-13] cv c 2 = φ ∂z ∂t  D

Aside from the mathematical errors associated with its derivation, use of c∗v c is discouraged by the explicit dependence upon φ0, which implies that it is not a state (material) property — given that D and φ are. The nature of the errors of derivation makes them difficult to perceive. It is hoped that the foregoing exposition will help to avoid similar confusion over these parameters in future. This is important because of “the” TERZAGHI theory’s enduring status as the default model for soil consolidation [e.g. 126, 946] [cf. 354].

*

DAS’s [296] error enters in equating VS with φ0 V, when actually φ0 V = (V / V0) VS.

†

POWRIE’s [850] error enters in equating a small change in layer thickness, δh, with δσ δz mv where

∗

∗

mv = d(Δh/h0)/dσ, rather than with δσ δz mv where mv = (1 / h) d(Δh)/dσ. ‡

The fact that KD also decreases means that cv c remains more-nearly constant [126, 946] (equation R2-9f). R2▪2 : Geomechanics and creep

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D. I. VERRELLI

Surprisingly, extensive searching of literature databases did not turn up any previous publication dealing with these matters *. Indeed, even (some) articles that did deal with the topic of “errors” perpetuated the strictly incorrect usage of mv∗ c in equation R2-8 [e.g. 78] or an inconsistent definition of strain [e.g. 297].

R2▪2▪2▪2

Empirical correlations

Primary consolidation is often described by [297, 559, 771, 946, 1007, 1014] Δh / φ0 h0 = Δ(1 / φ) ≈ ‒ Cc log10(Δp / p0), Δp > p0 , [R2-14] where Δp is the axially applied stress and p0 is the vertical stress to which the sample had been equilibrated prior to testing †. Notice that Δh is unbounded [297]. Assumption of constant Cc is not always reasonable [1014]. Cf. equation R2-22. Using typical values (φ0 ≈ 0.48, Cc ≈ 0.4) [771], it was found that this model is fitted quite well by a simple power-law relation between Δp and φ, and even better by a modified power-law equation typically used in dewatering analysis (viz. equation 2-49) ‡ [628] or a cubic. That is, the same behaviour can be described by several functional forms with similar accuracy. TAYLOR (1942) [cf. 1007] initiated an alternative convention which supposes that the initial primary consolidation proceeds according to the square-root of time [11, 37, 361, 912, 946, 975, 976], i.e. Δh ∝ ‒ t1/2 . [R2-15] (This correlation can be obtained as an approximate limiting solution of equation R2-7 with appropriate conditions, apparently determined by TERZAGHI & FRÖHLICH (1936) [see 1013] [cf. 1014] [see also 125, 724, 1007].)

R2▪2▪3

Creep, or secondary consolidation

MURTHY [771] explains that secondary compression effects dominate the overall consolidation behaviour when “the rate of plastic deformations of the individual soil particles or of their slippage on each other is slower than the rate of decreasing volume of voids between the particles”, which is somewhat vague. Creep, or secondary consolidation, is also described as commencing when the pore liquid pressure gradient in the sample goes to zero [361, 559] — in fact if this were i d e n t i c a l l y the case, there could be no flow and hence no consolidation [cf. 724, 1014]. The creep mechanism exist if this condition is not met [361], and indeed presumably co-exists with the primary consolidation (i.e. ‘yield stress’) mechanism from the beginning [126, 1014]. It might be helpful to suppose that, whereas in primary consolidation viscous drainage is rate-

*

FILLUNGER (1936) made a number of specific and general criticisms of the “soil mechanics” discipline practised by TERZAGHI [see 168].

†

If the sample had previously been exposed to a stress greater than p0, or if the material ‘naturally’ formed a yield stress greater than p0, then a second term must be added to equation R2-14 due to the differences in response for recompression, as distinct from (virgin) compression [1014].

‡

Although it could not be confirmed whether the gel point predicted had physical meaning.

804



limiting, in secondary consolidation it is the network failure itself that is rate-limiting, in which case ∇P ≈ 0. Classification of consolidation into primary and secondary stages is rather subjective [see 126] [946]. Secondary consolidation is generally of less interest to civil engineers than primary consolidation, because for many sites the duration of primary consolidation is long compared to the design life of the construction, so “secondary settlement is an insignificant component of the total settlement” [1014] [cf. 850].

R2▪2▪3▪1

Phases of creep

Figure R2-1 illustrates the nominal phases of the secondary consolidation process, i.e. ‘creep’ [361]: • p r i m a r y c r e e p , where the rate of creep, ε , is decreasing;

• s e c o n d a r y c r e e p , where the rate is constant and minimum (“usually” a singular point); and • t e r t i a r y c r e e p , where the rate is increasing. The onset of creep failure is characterised by the prevailing of tertiary creep, and so a period of constant creep rate (i.e. secondary creep) may be considered ‘incipient’ failure. FABENY & CURTIN [352] observe that composite materials often exhibit “substantial” primary creep deformation and stress relaxation over timescales relevant to the application life. Others have found the same for particulate systems [e.g. 452]. Strain, ε total creep–failure time

ε min

time to failure (primary creep)

remaining creep– failure time

0 Time, t

0

Figure R2-1: Illustration of typical creep progression, showing key parameters that describe creep failure life [361].

R2▪2▪3▪2

Primary creep

KEEDWELL [559] presents an equation to describe uniaxial creep deformation of soils, i.e. the rate of strain under constant stress: R2▪2 : Geomechanics and creep

805

D. I. VERRELLI

t dε = ε1   dt  t1 

−m

, t > t1 ,

[R2-16a]

in which ε is the strain (ε = Δh/h0  ε = h / h0 ), t the time, and m a material parameter; t1 is the time at which the stress becomes constant and creep (i.e. secondary consolidation) commences, at which point the axial strain rate is ε1 and the strain is ε1 . Although not stated, it should be presumed that the sample is laterally constrained. An equation equivalent to this empirical power-law type relation between strain rate and time is also presented by FEDA [361]. This relation has been found to provide a good fit to the creep of polymers in simple compression, torsion and tension; application to soils was proposed by GOLDSTEIN & BABITSKAYA (1959) and SINGH & MITCHELL (1968) [361]. To ensure the strain rate is bounded as t → 0, equation R2-16a may be adjusted to [361]

t  dε = ε1  + 1 dt  t1 

−m

, t > t1 .

[R2-16b]

For viscous materials m = 0, and for thixotropic materials m > 0 [559]. For soils m = 0 corresponds to “Zone 1” ‘cohesionless’ soils (e.g. sands) whose properties depend on direct mineral–mineral contact, while m = 1 corresponds to “Zone 2” ‘cohesive’ soils (e.g. clays) where water interposed between particles controls the behaviour [559]. Alternatively, it may be recognised that soils for which m = 0 to m ≈ 0.5 tend to consist of spherical, granular, or ‘blocky’ particles (e.g. sands), while soils for which m ≈ 1 tend to comprise ‘platy’ particles (e.g. clays) [361, 559]. For plastic m varies between 0.09 and 0.21, it is 0.22 for wood, and 0.2 to 0.45 for different metals (typically 0.3) [361]. BAŽANT, OZAYDIN & KRIZEK (1975) found that m for kaolin was independent of flocculation but increased as the solids concentration increased, and was larger for isotropic consolidation than for anisotropic consolidation [361]. The material parameter m may be related to the exponent in ABEL’s creep kernel (see equation R2-40), n, by n = 1 ‒ m [361]. According to CONRAD, two processes operate during creep — one increases the resistance to flow (recovery), the other decreases it (strain-softening) [361]. When they are in balance, a constant rate of creep (“secondary creep”) occurs, which is obtained for m = 0 [361]. For many soils secondary creep is not significant — in particular those with brittle (irreversible, cementation, diagenetic *) bonding and a ‘hard’ structure (e.g. dense sand); it is more typical of materials with ‘soft’ structures and without brittle bonds [361]. By integrating equation R2-16a and setting m = 1 the creep strain can be obtained as a function of time [559], viz. t ε = ε1 t1 ln   + ε1 , t > t1 [R2-17a]  t1 

= ε1 t1 ln (t ) + constant .

This result is consistent with the creep analyses of SINGH & MITCHELL (1968) [559].

*

806

I.e. solution–re-precipitation. Appendix R2 : Behaviour of Sludge-like Matter

[R2-17b]


An approximately equivalent equation with a modification in the style of equation R2-16b (say, set t1 = 1d) is presented in AS 1012.16–16 [6] for application to concrete: ε + ε = Ψ ln (t + 1) + t → 0 , [R2-18] σ σ where Ψ is the “creep rate”, t is the time [d], σ is the applied (compressive) stress and ε t →0 + is the (elastic) strain assumed to exist “immediately” upon loading. According to the standard, although the logarithmic expression is not necessarily exact, for concrete it is sufficiently accurate for t up to about 365d, i.e. one year. The presentation of this equation illustrates the assumption that, for concrete loaded at <40% of its compressive strength, creep is proportional to stress [3]. If m ≠ 1, then equation R2-16a integrates to the general equation: 1− m  ε1 t1  t    ε= − 1 + ε1 , t > t1 1 − m  t1   

ε t  t  = 1 1   1 − m  t1 

[R2-19a]

1− m

+ constant .

[R2-19b]

For completeness, integration of equation R2-16b yields:  t + t1   + ε1 , ε = ε1 t1 ln  for m = 1 ; [R2-20]   2 t1  1− m   ε1 t1  t  + 1 ε= − 21 − m  + ε1 , for m ≠ 1 . [R2-21] 1 − m  t1     (The dependence proposed by BARDEN [126] also takes the form of a modified power law with positive, fractional exponent.)

Figure R2-2 illustrates the influence of m upon the strain behaviour.

R2▪2 : Geomechanics and creep

807

D. I. VERRELLI

0

Additional strain, ε – ε 1 [–]

-1 -2 -3 -4 -5

m m m m m

-6

= –0.5 = 0.0 = 0.5 = 1.0 = 1.5

-7 0

1

2

3

4

5

6

7

8

9

10

Dimensionless time, t / t 1 [–]

Figure R2-2: Strain behaviour as a function of material parameter m, the exponent in equation R2-16a for the arbitrary specification ε1 =1/t1 . Alternative profiles for the solution to equation

R2-16b are shown by the lighter, red curves. The thicker curves are for the typical limits on m.

MURTHY [771] adds that: It is often assumed that secondary compression proceeds linearly with the logarithm of time. However, a satisfactory treatment of this phenomenon has not been formulated for computing settlement under this category.

The rate of secondary consolidation can be expressed by [771, 1014] Δ(1 / φ) = ‒ Cα log10(t / t1), t > t1 , [R2-22] where Cα is the ‘secondary compression index’ (a nominally constant material property). FEDA [361] presents an equivalent equation in terms of the (axial) strain, ε *. A value of Cα above 0.016 is considered to yield high secondary consolidation, while a value below 0.004 would give little secondary consolidation [771]. Although it has a similar form to equation R2-14, the equation here describes kinetics while the earlier one describes equilibrium. Logarithmic creep is also observed for some metals or alloys [187]. FEDA [361] notes that secondary consolidation sometimes follows a non-logarithmic decay (or, equivalently, has a non-constant value of the ‘secondary compression index’ Cα, defined in equation R2-22), such as a ‘semilogarithmically bilinear’ or h y p e r b o l i c c r e e p relation attributed to cataclastic deformation, i.e.

*

808

Note that Δ(1 / φ) = Δε / φ0, given that the volume of solids is fixed. Appendix R2 : Behaviour of Sludge-like Matter


ε = ε 0 (1 − ε / ε∞ )2 =

[R2-23]

1 ε 0 (1 / ε 0 + t / ε∞ )2

which integrates to t ε= . 1 / ε 0 + t / ε∞

[R2-24]

For material behaving in such a manner, the number of bonds grows at an increasing rate with strain, more rapidly than for materials undergoing logarithmic secondary consolidation [361] (the rate of increase of B is still expected to decrease with time as the strain rate also decreases — cf. §R2▪2▪3▪4). TERZAGHI, PECK & MESRI [1014] also warn that “in general Cα [...] does not remain constant with time”. Yet it has been found empirically that for geotechnical materials the ratio Cα / Cc (cf. equation R2-14) i s constant, taking values between 0.01 and 0.07, with 0.04 being typical for inorganic clays and silts [771, 1014].

R2▪2▪3▪2(a)

Primary creep in settling

Given that axial strain is defined as ε = Δh / h0, and the change in reciprocal solidosity can be expressed as Δ(1 / φ) = Δh / φ0 h0 [771], equations R2-17 and R2-22 are each equivalent to t h = h t1 ln   + h t , t > t1 . [R2-25] 1 t1  t1  and the coefficient of the logarithmic term is equal to ‒ Cα φ0 h0 / ln(10). One standard method [see 11, 37] likewise indicates that h decreases l o g a r i t h m i c a l l y in t at long times (after primary consolidation). Notice that this is u n b o u n d e d in h as t → ∞. Thus, the simplest identification of primary creep in settling is to plot h(t) on log–linear coordinates to see whether a straight line is obtained. To validate the finding, regression can be performed on the relevant end part of the h(t) curve. Yet other forms of creep are possible. Equation R2-24, for example, implies 1 1 1 = + , t > t0 .  Δh th Δ h∞

[R2-26]

t0

R2▪2▪3▪2(b)

Primary creep in filtration

While it is possible still to follow the same approach as for settling, the experimental filtration device allows additional information on the rate of filtration to conveniently be captured, principally dt/d(V 2), in which V is the specific filtrate volume, ΔV / A. This is often plotted as its reciprocal, d(V 2)/dt, as a function of t. It has been noticed that some very-long-time compression runs (such as some multiplepressure permeability runs that go into compression *) exhibit a tendency to follow an a p p r o x i m a t e l y linear relationship in the slope

*

Or where in any case the stoppage criterion is quite tight. R2▪2 : Geomechanics and creep

809

D. I. VERRELLI

dt = a t + b , t > t1 [R2-27a] dV 2 beyond a certain point in time, t1, where a and b are constants. This can be inverted dV 2 1 , t > t1 [R2-27b] = dt at +b and integrated from some creep commencement condition V1 at time t1 to give  1  1  at +b   ln  + V1 , t > t1 , V =  [R2-28a]     V +V1  a  a t1 + b  or  1 1  ln a∗ t + b∗ + V1 , t > t1 , V =  [R2-28b]  V V + 1a  where a∗ and b∗ are conveniently defined constants with values determined by a, b, and t1. Recognising that for these filtration runs empirically it is typically found that, for t > t1, d(V 2)/dt will be approaching zero fairly quickly, as a first approximation (V + V1) may be taken as a p p r o x i m a t e l y constant. Thus equation R2-28b may be seen as having a similar form to the equations obtained from equations R2-16a and R2-16b, and it is clear that the decreasing strain rate qualifies this behaviour as primary creep. We have dV d V dV 2  1  1  , t > t1 , [R2-29] = ⋅ ≈   dt dV 2 dt  V + V1  a t + b where again V and V1 are taken as a p p r o x i m a t e l y equal. Practically it can be difficult to obtain accurate dynamic filtration data at long times due to the increasingly long intervals between linear encoder points, but especially due to minor thermal expansion and contraction effects in the rig (and sample) in response to ambient temperature changes.

(

)

In contrast, LANDMAN & WHITE predicted that for cases in which the filtration time was long compared to the time for cake formation, to a first approximation during the consolidation phase the compression behaviour would approach simple e x p o n e n t i a l d e c a y , following equation 2-125b. Differentiating equation 2-125b gives ∗  e −t  ∗ E −V d V 2 dV 2 dV , = ⋅ = 2V 3 = 2 E3 − e − t ⋅  [R2-30]  E2  dt dV dt E2   where t∗ ≡ (t ‒ E1) / E2, which is clearly a very different form to the relations described previously, although it still expresses a type of primary creep.

(

)

The most important practical difference between equations R2-28b and 2-125b is that the former is u n b o u n d e d in V as t → ∞, while the latter approaches an equilibrium V∞. This matter is investigated further in §9▪3▪2▪3.

R2▪2▪3▪3

Secondary and tertiary creep, and failure

The dependence of the long-time strength, σfailure, upon time was found by REGEL', SLUCKER & TOMASHEVSKIY (1972) to follow the form [361]

810



 A −α σ  [R2-31] tfailure = tv exp 0 d failure  , σfailure [ 0 , kB T   where tv ≈ 10‒13s is the mean period of thermal vibration of atoms in solids, A0 is the activation energy * of the unloaded sample, αd is a structural parameter indicating the number of bonds (or intensity of bonding) †, kB is the BOLTZMANN constant, and T is the absolute temperature. This implies that a time-dependent accumulation of structural defects occurs that is t h e r m a l l y a c t i v a t e d [361]. Rearrangement and grouping yields 1 σfailure = [(A0 + k B T ln tv ) − ln tfailure ] , σfailure [ 0 . [R2-32] αd A0 can be expected to increase as the strain rate decreases, approximately following [361] A0 ≈ R T ln( 2.1 × 1010 T ) − ln γ . [R2-33]

(

)

The activation energy, A0, for soils has also been observed to decrease slightly (of order 10%) after subjecting the sample to pre-shearing [361]. Regardless of the above, it remains the case that the total creep–failure time increases as the (minimum, or constant) creep rate decreases [361]. For clays the correlation of SAITO & UEZAWA (1961) is typically used [361] [R2-34a] log10 tfail ≈ ‒0.92 log10 ε min ‒ 1.33 ± 0.59 , where tfail is the total creep–failure time in minutes and ε min is the minimum creep rate in 1/min. The minimum creep rate arises, it would seem, from the original strain response occurring very rapidly, then approaching almost a constant (equilibrium) strain, whereupon the material ‘fails’ and therefore the strain rate is able to increase [see 361]. The strain prior to attainment of the minimum creep rate is called ‘primary creep’, and is said to usually be short relative to the total creep time up until failure [361]. This is shown in Figure R2-1. Only logarithmic creep requires that the physical process is isomorphous [361]. Note that physical isomorphism does not control primary or tertiary creep exactly, as structural perturbations mean that they are not physically homogenous (each being combinations, in different proportions, of strain-hardening and strain-softening) [361]. Physically isomorphic deformation may be expected from soft to medium (‘wet’) clays and loose (to medium) sands [361]. While this work does not concern itself directly with the properties of clay, equation R2-34a has a number of general properties of interest. In particular, it has been found to be independent of shear history and stress level, so that it applies equally to undisturbed and (say) remoulded clay [361]; the long-term strength is similarly unaffected [361]. Equation R2-34a is sometimes quoted in the form [361]: 0.92 log10(tfail ε min ) = ‒1.33 ± 0.59 , [R2-34b]

*

The activation energy is defined as the energy barrier separating two stable states corresponding to some displacement [361].

†

Apparent constancy of αd (regularly observed) indicates “mutual compensation of strain-hardening and strain-softening or, better, physical isomorphism in one creep axis” [361]. R2▪2 : Geomechanics and creep

811

D. I. VERRELLI

in which the exponent on the left hand side is occasionally taken as unity. When the exponent is n o t taken as unity, the equation describes p a r a b o l i c c r e e p [361]. Creep rupture life is longer for ductile materials (e.g. metals) and shorter for brittle materials (e.g. rocks) [361]. One would intuitively expect WTP sludges to fall between these extremes. For tertiary creep, the strain–softening effect of distortional creep prevails [361]. The increasing magnitude of strain rate may be modelled by the relation of SAITO c c +ε / c = e , [R2-35] ε = tfail − t tfail where the second equality follows from t ε = c ln fail , tfail − t

[R2-36]

and c is a constant. Comparison with equations R2-43 and R2-44 reinforces the idea that the key difference in the relations for primary and tertiary creep is one of sign. The creep is again logarithmic and thermally-activated [361]. ABEL’s creep kernel (equation R2-40) with n ≠ 1 may be used to derive alternative formulations. FEDA [361] demonstrates that secondary creep, with constant strain rate, cannot exist for a long period of time except for NEWTONian fluids that “have entered into a state of no hardening/softening effects”. However a “quasi-secondary” creep may be observed from the superposition of primary and tertiary creep effects [361].

R2▪2▪3▪4

Micromechanics

An alternative approach is to apply the statistical micromechanics theory developed by EYRING and co-workers, which describes a wide range of situations in which matter undergoes time-dependent rearrangement [361]. FEDA [361] states that creep of soils “complies” with the definition of “thermally activated processes”. Analysis using this approach shows the following [361]. • The activation energy for soils ranges from about 84 to 126kJ/mol unless the solid content is so low that a continuous particulate network is not formed, in which case it approaches the value for water, about 17kJ/mol; • Creep deformation is not controlled by the viscous flow of water. • As the proportion of water is decreased, more interparticle bonds form, and this correlates directly with macroscopic strength. Some problems with the application of this approach to particle-based systems are that particles cannot thermally vibrate in the way postulated, and the number of bonds postulated exceeds the number of interparticle contacts observed [361]. The statistical mechanical approach outlined above yields the following generic equation for creep in soils [361]:     k T −A /R T  − σ  λ     exp  ε ≈ −  B e 0 [R2-37]  2 k T  , h B  P B          C1 C2   in which 812



ε kB T hP A0

is the strain rate [1/s], is the BOLTZMANN constant, 1.381×10‒23 J/K [752], is the absolute temperature [K], is the PLANCK constant, 6.626×10‒34 J.s [752], is the activation energy [J/mol], R is the molar gas constant, 8.314 J/mol.K [752], λ is the separation between flow units (i.e. discrete/independent particles) [m], ‒σ is the (effective) applied compressive stress [Pa], and B is the number of bonds per m2 [1/m2]. C1 and C2 are compact constants for a given material at a specified temperature. The derivation of equation R2-37 assumes that the stress is distributed uniformly over the ‘flow units’ (or discrete particles), that the number of flow units is equal to the number of bonds, and that the exponent is larger than unity (which is mostly the case for creep in soils *) [361]. If the exponent is smaller than unity (as for molecular flow, or NEWTONian flow), then the correct expression is rather [361]  λ −A /R T  σ  . [R2-38] ε ≈  e 0 B P h    C3

This equation exhibits the same proportionality as an ideally viscous system (see §R2▪3). When the strain is not small, λ will also vary significantly. FEDA’s [361] analysis demonstrated that creep follows a logarithmic profile — as above — if exclusively s t r a i n - h a r d e n i n g occurs; the density of bonds in the sample increases hyperbolically with the axial strain, ε, viz. (by comparison of equations R2-37 and R2-41) σ B ∝ C2 , [R2-39] ε − ε0 in which C2 is constant — i.e. the number of bonds increases very rapidly at first, and slows to asymptote to some larger value. In the same way, logarithmic creep requires that in s t r e s s - h a r d e n i n g the number of bonds increases linearly with the stress [361]. The r a t e of strain-hardening is enhanced by increasing the applied stress [361]. It has been shown that this result of rate–process theory (as in equation R2-37) corresponds to secondary creep, and so its application to describe deformation involving structural hardening or softening is “at least questionable” [361]. Related models (BAILEY–OROWAN) are used to describe the primary and secondary creep behaviour of metals [187]: Creep [is] the result of competition between recovery and work-hardening processes. [In recovery] a material [...] regains its ability to undergo additional deformation. [...] Workhardening [makes] a material increasingly [...] difficult to deform as it is strained.

A general equation describing creep uses ABEL’s creep kernel in an integral [361]:

*

Probably also a reasonable assumption for many other materials: e.g. for particles of order 1μm size

−

 O(10 −6 ) σ  λ  O(10 0 )   = O(10 3 ) , ≈  12 0 23 2 − B  2 k B T  O(10 )  O(10 ) O(10 ) O(10 ) 

given a rather small compressive stress of order 1Pa. R2▪2 : Geomechanics and creep

813

D. I. VERRELLI

t

ε = ε0 +

 a (t − α )

−n

σ(α) .dα ,

[R2-40]

t0 = 0

where ε is the strain, a is a material parameter, α may be taken as a dummy integration variable (supposed to be the time at which the load is applied), and σ is the stress [cf. 1097]. n is another material parameter — often 0 < n ≤ 1 — which is commonly taken as equal to unity, giving BOLTZMANN’s kernel and the logarithmic consolidation relation [361] discussed further below. While n typically decreases with increasing stress and temperature, n = 1 is a good fit for most low-temperature creep observations in soils [361]. Suppose that the strain rate magnitude is d e c r e a s i n g — implying primary creep — according to ε = ε0 e(ε − ε0 ) / b , [R2-41] with a and b = ‒ ε0 t1 both constant, then integration with t0 = 0 yields ε   [R2-42] ε = ε0 − b ln 1 − 0 t  , b   [361], similar to equation R2-20. This implies that logarithmic creep is a t h e r m a l l y - a c t i v a t e d process in which the activation energy increases linearly with deformation, i.e. s t r a i n - h a r d e n i n g dominates behaviour [361]. The slowing in the rate of structural deformation, or ‘hardening’ is at least partly attributable to the progressive exhaustion of structurally-weak regions [361]. These kernels are good models of the behaviour of laterally confined samples undergoing primary creep (the first phase of secondary consolidation). Supposing that ε0 = 0, then from equation R2-42 [361] t  ε = − b ln + 1 , [R2-43]  t1  and ε =

ε0 = ε0 eε / b , t / t1 + 1

[R2-44]

where t1 = b / a is unit time. By analogy to shear stress, FEDA [361] argues that logarithmic creep can occur if the stressdependent structural changes “compensate themselves (‘jumping’ of bonds)”, and may correspond to either the lack of time-dependent structural changes (in which case fluctuation of the activation energy controls the process) or “some sort of mutual compensation” of the time-dependent structural changes occurring at a specific shear-stress level in different creep axes. Having said this, in general, the structure of soils does change in the course of creep [361].

R2▪3 R2▪3▪1

Macrorheological models Basic elements

The simplest material models include [361]: • ideally e l a s t i c (HOOKEan) — σ = E ε where E is YOUNG’s modulus. This is represented symbolically as a s p r i n g . It is sometimes referred to as a TERZAGHI element [933]. 814



• ideally v i s c o u s (NEWTONian) — σ = μσ ε where μσ is the coefficient of normal viscosity (or, equivalently, β is the damping coefficient). This is represented symbolically as a d a s h p o t . • ideally p l a s t i c (SAINT VENANT [127]) — ε = 0 for σ < σc where σc is a threshold stress (or strength). When σ ≥ σc there is no restraint on the strain. (The strength, σc, can be described as the product of the pressure and the tangent of the shear strength angle [361].) Represented symbolically as a s l i d e r . Elastic and viscous elements may be combined in s e r i e s as a MAXWELL material [361]: ε = σ / μσ + σ / E . [R2-45] Such a material would exhibit a c o n s t a n t strain rate, ε , given a constant applied stress, σ, and so equation R2-45 models only s e c o n d a r y c r e e p , with the implication that the s t r a i n i s u n b o u n d e d in time [361]. Upon unloading, this material relaxes exponentially to a finite strain [361]. Non-linearity is commonly introduced in the form of an exponent, Δ (say), [611] ε = σΔ / μσ + σ / E . [R2-46] Combining the elements in p a r a l l e l gives a KELVIN–VOIGT material [361, 612]: σ = E ε + μσ ε . [R2-47]  Such a material would exhibit a d e c r e a s i n g strain rate, ε , given a constant applied stress, σ, and so it models only p r i m a r y c r e e p , asymptoting to a finite strain [361]. This material is non-dissipative, and relaxes exponentially to zero strain upon unloading [361]. Whereas the MAXWELL material models relaxation well and the KELVIN–VOIGT material models creep well, these two features can be combined in one model by adding a second elastic element in series with the parallel pairing of a KELVIN–VOIGT material, to give a ‘standard’ rheological model * [361]. This models creep in exactly the same way as a KELVIN– VOIGT material, but relaxation is different — this material still relaxes to zero strain, but the exponential decay follows an instantaneous elastic response, and this is deemed by FEDA to be a “realistic” representation (in the context of soils) [361].

R2▪3▪2

Application to consolidation

SHIRATO et alii [933] modelled the overall consolidation of clay–water mixtures using a series combination of an elastic spring element (for “primary consolidation”) and a KELVIN–VOIGT element (for creep). They used a continuity equation equivalent to [933]: ∂φ ∂φ ∂pS ∂  ρS ∂pS    [R2-48] + = φ2 ⋅  η α ⋅ ∂w  , ∂ ∂ ∂pS ∂t t w m       " primary consolidation"

in which t pS

*

creep

is the time [s], is the local particle “pressure” [Pa],

Variously described as a ‘HOOKE–KELVIN’ material, a POYNTING–THOMPSON material, or a ZENER material [361]. R2▪3 : Macrorheological models

815

D. I. VERRELLI

φ is the local solidosity, a function of both pS and (in the case of creep) t [–], w is the “mass of solids per unit sectional area” [kg/m2], is the solid phase density [kg/m3], ρS η is the viscosity [Pa.s], and αm is the local specific resistance (on a mass basis) [m/kg], to derive the following “tedious” [236, 237] solution for the case of initially uniform hydraulic pressure through the sample dewatered under a constant applied stress: h −h ε Uc ≡ 0 = h0 − h∞ ε∞ ∞    ( 2n − 1) i π  2  8 ~ t )] −   + ψ [1 − exp(− μ   exp C t = (1 − ψ) 1 − e 2           2 w0   n = 1 π ( 2n − 1)       creep 



[R2-49]

primary consolidation

in which Uc h n ψ i w0 Ce ~ μ

is the dimensionless change in height (or normalised strain) [–], is the height, with subscripts 0 and ∞ for the initial and equilibrium conditions [m], is a summation index [–], is the fraction of the overall equilibrium consolidation due to ‘creep’ * [–], is the number of drainage surfaces (typically 1 in filtration) [–], is the “total solids mass in mixture per unit sectional area” [kg/m2], is the coefficient of primary consolidation, being the ratio E1 φ ρS / μ αm (where E1 is the elastic modulus of the spring in series) [kg2/s.m4], and is the coefficient of “secondary consolidation” (i.e. creep), being the ratio of the

elastic modulus, E2, and viscosity, μσ, of the KELVIN–VOIGT element [1/s]. If Ce can be related to cv c [compare 933, 1014], then it can in turn be related to LANDMAN– WHITE dewatering parameters [605]. This phenomenological model was also used by CHANG and co-workers [236, 237]. It is typical that the rate of primary consolidation is initially much greater than the rate of ~ , as assumed in the above secondary consolidation (i.e. creep), so that (i π / 2 w0)2 Ce [ μ derivation [933]. Typical values for the parameters in the clay–water system described are ~ = 3.09×10‒5s‒1 [933]. Using these values ψ = 0.1, i = 1, w0 = 13.06kg/m2, Ce = 0.680kg2/s.m4, μ the following curves in Figure R2-3 may be plotted.

Figure R2-3 shows that the consolidation clearly takes place in two distinct stages. The derivative undergoes almost a step change from one function (power-law asymptote) to another at a time of approximately 240s, or 4min. The equations quoted fit the span as plotted. The equations for the asymptotes are in fact 0.03206 / t , as t → 0 dUc  , [R2-50] = −6 −5 dt 3 . 09 10 exp( 3 . 09 10 t ), as t × − × → ∞  implying that

*

816

Hence equal to the ratio of spring constants E1 / (E1 + E2) [237]. Appendix R2 : Behaviour of Sludge-like Matter


 0.0641 t , as t → 0 , Uc =  −5 − − × → ∞ 1 0 . 1 exp( 3 . 09 10 t ), as t 

[R2-51] ~

and the second asymptote can be seen to be the formula Uc = 1 ‒ ψ e − μ t [as in 236], i.e. simple e x p o n e n t i a l d e c a y . In terms of height the following form is predicted: ~ h = h∞ (1 + ψ∗ e − μ t ), as t → ∞ . [R2-52]

Time, t [s] 1.E-5

1.E-3

1.E-1

1.E+1

1.E+3

1.E+5

1.E+7

0.0

0.2 dU c/dt = 0.032t 0.4

-0.5005

1.E-02

2

R =1 Transition

1.E-04

0.6 1.E-06 0.8

Derivative, dU c/dt [1/s]

Normalised change in height, U c [–]

1.E+00

1.E-08 1.0

–3.E–5t

dU c/dt = 3.E–6e 2

R =1

1.E-10

Figure R2-3: The fractional consolidation, Uc, as a function of time, t, for a spring and a KELVIN– VOIGT element in series using the parameter values given in the text. The contribution of primary consolidation (no creep) is shown as the dash–dot curve. The derivative dUc/dt is also shown (the equations are least squares fits for the plotted spans).

For the parameters of SHIRATO et alii’s [933] sample, after about 1×103s (≈17min) the settling data p l o t t e d o n a l o g ( t ) s c a l e would suggest equilibrium was almost attained — the experimenter at that time may anticipate practical equilibrium will certainly be attained by (say) 1×104s. However, the complete plot shows that dewatering occurs up to O(105)s. (In the published paper [933] data up to 2.5×104s is shown.) This illustrates one of the disadvantages (or ‘key differences’) of plotting on a log(t) scale. However this is still often required due to the exceedingly long time required to achieve equilibrium for some samples, as the rate decreases steadily. Working at high pressures, CHANG et alii [237] found optimum flocculation of clay ~ increasing from about 0.003 suspensions allowed an increase in dewatering by creep, with μ to 0.007 [time units], indicating an increased rate (or earlier onset), and ψ likewise increasing R2▪3 : Macrorheological models

817

D. I. VERRELLI

from about 0.25 to 0.85 or higher, indicating that creep controls a greater proportion of the overall dewatering. The first change is attributed to the tendency for the surface charge to be nearly neutralised at the optimum flocculation condition, so the resistance to particles ‘creeping’ past one another was reduced [237]. The second change is attributed to the increase in aggregate strength and size, meaning that they do not dewater as far before forming a network of appreciable py [237], so that we would expect to observe an increase in the gel point, φg. Freeze–thaw conditioning of an activated sludge also led to a very large increase in ψ, from about 0.55 for the original material up to 0.89 after freeze–thaw *; these compare to 0.082 for ~ for the activated sludge is also 2.3μm kaolin and 0.38 for 4.5μm “clay” [238]. The value of μ much less than for the particulate kaolin or clay systems [238], and the same trend is expected for WTP sludges. Combining the MAXWELL and KELVIN–VOIGT material models in series is another alternative [361]. CHANG & LEE [238] observed that in the filtration of suspensions of fractal particles at long times (of order hours) a much higher dewatering rate than expected was observed — and appeared to be c o n s t a n t . This prompted the addition of another ideally viscous element, to end up with a KELVIN–VOIGT element in series with a MAXWELL element (although it is described as three elements in series) [238]. A significant problem with this model is that it does not predict a finite equilibrium cake height, but rather predicts that dewatering will continue indefinitely (albeit very slowly), which is clearly unphysical. CHANG & LEE [238] attempted to overcome this by defining a (somewhat arbitrary) cut-off time at which “all removable moisture has been forced out”; this then becomes another parameter in the model. According to SAHIMI [889], models including elastic (spring) elements are suitable for materials under shear or tension, but not compression, for which he recommends beam models; the distinction is not considered in the following analysis of fibre bundle models, and it is believed that the general trends will still be relevant. In comparison to the LANDMAN–WHITE theory, models involving series and parallel combinations of ideal elastic, viscous and plastic elements are more restricted in the range of behaviours they can describe. They are typically simpler analytically. The simplest models provide mediocre agreement for all materials; composite models with several basic elements can be designed to suit a specific class of behaviour, but are not as generically applicable as LANDMAN–WHITE theory; composite models with many basic elements could be designed that would describe almost any behaviour, but parameter optimisation may not yield a unique result, and insight into the physical process would be limited. There is no fundamental reason to believe that a material physically comprises a limited number of ideal macrorheological elements †: it is a conceptual artifice. *

Note that these represent relative importance of the stages of dewatering for a given sample. The freeze– thaw conditioned sample actually lost considerably less water than the original sludge on a mass basis [238].

†

Even in microscopic modelling (§2▪4▪7) it is doubtful that behaviours would reduce to those of the ideal elements described above.

818



A more general approach allows for n o n - l i n e a r model elasticity and viscosity relations (cf. §R2▪3▪1), introducing e.g. a certain time dependence [see 126]. This tends to lose the advantage of simplicity, and becomes more-or-less equivalent to ‘conventional’ phenomenological modelling [see 126].

R2▪3▪3

Fibre bundle models

A model has been investigated by HIDALGO, KUN, HERRMANN and co-workers [470, 471, 612] based on a conventional Fibre Bundle Model (FBM) with the following key properties [612]: • The macroscopic behaviour of the fibre bundle is viscoelastic, modelled as a KELVIN– VOIGT material (§R2▪3▪1), i.e. a spring and a dashpot in p a r a l l e l , aligned in the direction of the applied load. Use of simple models of this type is reasonable here, and can provide a good approximation of the response of real materials when the deformation is s l o w or s m a l l [352]. • Interaction of fibres is specified in terms of an adjustable load-sharing function, which can interpolate between the extremes of mean-field Global Load Sharing (GLS) and short-range Local Load Sharing (LLS). The function used is rij − γ Δσij = , [R2-53] rij −γ

 i≠ j

in which Δσij is the additional stress distributed to fibre i upon failure of fibre j, rij is the distance between the two fibres, and γ is a model parameter. GLS is implied by γ = 0 (load redistributed to all remaining fibres equally), and γ → ∞ implies LLS (entire load taken up by nearest fibre(s)). It has been demonstrated that effectively GLS exists for γ ( 2, γ T γcrit yields LLS, and 2 ( γ ( γcrit is a transition region, with γcrit in the range 3 [612] to 7 [471]. • The breaking strains of the population of fibres are defined by a probability distribution, such as the uniform distribution or the WEIBULL distribution, with cumulative density function P(ε). This viscoelastic FBM is intended to model uniaxial tensile loading [612], but could give useful inferences for compressive loading too. It is applied to heterogeneous materials that may be considered to be disordered [470], i.e. “systems formed by many interacting constituents, each one having statistical properties related to some breaking characteristics of the material, distributed randomly in space and/or time” [471]. Under steady external loading, “local stresses [...] are resolved in the form of avalanches of microscopic relaxation events”, and a “stationary macroscopic state” is attained, characterised by “scale-invariant microscopic activity” [612] in the case of partial material failure. A further feature of the model is that the fibres break one-by-one, which makes the model sensitive to the detail of the load-sharing function [612]. In the stationary state a power-law distribution of intervals between fibre breakages is obtained (with exponent depending on γ), as is observed for real materials [612]. For GLS, an analytical expression can be obtained, viz. (for externally applied stress σ0) σ0 / (1 ‒ P(ε)) = E ε + μσ ε ; [R2-54] none can be obtained for LLS [612].

R2▪3 : Macrorheological models

819

D. I. VERRELLI

Provided σ0 does not exceed a critical stress *, σc, ε asymptotes to zero, and ε asymptotes exponentially to a finite value, ε∞, as time progresses [612]. The characteristic time of the exponential relaxation is [612] [R2-55] trelax ∝ (σc ‒ σ0)‒1/2 . The value of ε∞ is obtained by setting ε = 0 so that [612] [R2-56] σ0 = (1 ‒ P(ε∞)) E ε∞ . It may be seen that as σ0 increases, ε∞ also increases and so (1 ‒ P(ε∞)) decreases; eventually an external stress is reached for which the otherwise equilibrium strain implies that all of the fibres are broken and P(ε∞) = 1. The threshold at which this occurs is σc. In the case of σ0 > σc, ε passes through a minimum (around ε∞ for σ0 → σc‒), after which the fibres fail increasingly rapidly until finally the system fails globally [612]. This increase in ε can be explained by the fact that eventually there are few enough fibres remaining that failure of just one becomes relatively more significant (i.e. Δσij in equation R2-53 increases). The time of failure (total creep–failure time) is given by [612] [R2-57] tfail ∝ (σ0 ‒ σc)‒1/2 , which has the same form as equation R2-55. When σ0 is only slightly larger than σc, the quasi-stationary state of ε ~ 0 is long-lived [612]. The shape of this trajectory of strain versus time is very similar to that depicted in Figure R2-1. The strain versus time relation may be solved analytically in the GLS case, and for uniformly distributed breaking strains between 0 and εmax, such that P(ε) = ε / εmax. Integrating equation R2-54 in nondimensionalised form as T

θ

0

1 0 4

 dT = 

1−θ dθ Σ − θ (1 − θ )

[R2-58]

yields † 1 1  1  θ(1 + S) − 2 Σ   4   ln   + ln 1 + θ 2 − θ   , Σ ≤ 1, with 0 ≤ θ ≤ (1 ‒ S) / 2 [R2-59a]  1 2  S  θ(1 − S) − 2 Σ   Σ    1 1  4 2  2θ − 1   −1  1   [R2-59b] T = tan −1   + tan   − ln 1 + θ − θ  , Σ > 1, with θ ≥ 0 S   S  2  Σ  S 

T =−

(

)

(

)

with T ≡ E t / μσ, θ ≡ ε / εmax, Σ ≡ σ0 / σc, σc = E εmax / 4 , and S ≡ (1 ‒ Σ)1/2. For this distribution of breaking strains the maximum value of ε∞, i.e. at σ0 = σc, is εmax / 2 (so that θ = 1/2). This is shown in Figure R2-4 for various stresses.

*

This is given by the static fracture strength of the fibre bundle [612].

†

The equation given for Σ ≤ 1 in the original paper [470] is incorrect.

820



Σ = 0.10

1.00

Σ = 0.20 Σ = 0.30

Dimensionless strain, ε /ε max [–]

0.90

Σ = 0.40 Σ = 0.50 Σ = 0.60

0.80

Σ = 0.70 Σ = 0.80

0.70

Σ = 0.90 Σ = 0.95

0.60

Σ = 0.998

0.50

Σ = 1.001

Σ = 1.000 Σ = 1.005 Σ = 1.01

0.40

Σ = 1.02 Σ = 1.03

0.30

Σ = 1.04 Σ = 1.05 Σ = 1.06

0.20

Σ = 1.07 Σ = 1.08

0.10

Σ = 1.09 Σ = 1.10 Σ = 1.20

0.00 0

10 20 30 40 Dimensionless time, t E / μ σ [Pa]

50

Σ = 1.30 Σ = 1.40 Σ = 1.50 Σ = 2.00

Figure R2-4: Behaviour of viscoelastic fibre bundles with GLS and uniformly distributed breaking strains for a range of dimensionless stresses, Σ.

The quasi-stationary state of very small strain rate obtained for stress slightly larger than σc could be approximated as linear creep, i.e. constant creep rate — as the curvature of ε(t) is at a minimum at these intermediate times — followed by tertiary creep (increasing strain rate) until ultimate failure [352]. However, FABENY & CURTIN [352] point out that this is only an a p p a r e n t (quasi-)steady-state, and that the underlying deformation m e c h a n i s m s are not necessarily at (quasi-)steady-state. It has been found that for GLS the model indicates a ‘second-order’ phase transition (continuous) of 1 / tfail at σc, and a first-order transition (discontinuous) for LLS [470]. In LLS the ultimate strength, σc, of the material is a function of the system size, N, going to zero as 1 / ln N [471] due to the increasing likelihood of the constituent fibres being somewhere so spatially distributed that the localised concentration of stress at the tips of a nucleated crack exceeds the strength of the fibres there, so that the crack continues to grow until ultimate failure of the material — i.e. a ‘runaway’ event [471]. The final “avalanche” is driven by a fibre at the perimeter of the dominant cluster of broken fibres, where the stress concentration is highest [471]. An alternative to the above viscoelastic fibre bundle model has also been investigated [611]. In this alternative, fibres are modelled as purely elastic until their stress-controlled failure, when they are treated as non-linear MAXWELL elements (cf. §R2▪3▪1) that both ‘slide’ and relax with respect to the surrounding matrix [611]. Thus, the broken fibres are able to bear a certain amount of the applied stress [611]. For the particular case of GLS with uniformly

R2▪3 : Macrorheological models

821

D. I. VERRELLI

distributed breaking stresses (between 0 and σmax), the response of the material to a constant applied stress shows a great deal of similarity to the case examined above, in that [611]: • a critical stress (the static fracture strength, σc) exists below which partial failure occurs and above which complete failure occurs; • for applied stresses just above the critical stress, the system experiences rapid fibre failure initially, followed by a plateau region of little change in strain, followed finally by an increasing strain rate up until ultimate failure; • universal scaling laws apply; provided the non-linearity of the MAXWELL elements is negligible, they have form identical to the previous case, namely trelax ∝ (σc ‒ σ0)‒1/2 for the relaxation after fibre breakage and tfail ∝ (σ0 ‒ σc)‒1/2 for ultimate failure. FABENY & CURTIN [352] investigated fibre bundle models with different macrorheological constitutive equations and obtained similar results. The breakage that occurs in FBM’s above the critical stress is reminiscent of the description of tertiary creep in real physical systems (e.g. metals [187]): [T]ertiary creep is the result of microstructural and/or mechanical instabilities. [...] defects in the microstructure [...] develop. These result in a local decrease in crosssectional area that corresponds to a slightly higher stress in this region. [Hence] the strain and strain rate in the vicinity of a defect will increase. This then leads to an increase in the number and size of microstructural faults [...].

R2▪3▪4

Parallel friction-element model

The establishment of force chains in the direction of the major principal stress [83, 585, 772, 794] is evocative of the FBM concept, except that the failure mode is different. For consolidating particulate cakes ADAMS, MULLIER & SEVILLE [83] suggested the use of a “parallel friction-element” model, in which each transitory chain was represented as a column that failed in shear. The failure mode is debatable. More interestingly, because the system is under c o m p r e s s i o n , when one column fails, “load paths bifurcate”, with the result that m o r e particles become load-bearing — or the number of ‘active’ columns increases as compression proceeds — which has the effect of reducing the maximum local stress [83]. Compaction is not necessarily isotropic [83] [see also 585, 753] (cf. ‘System anisotropy and osmosis’ in §2▪4▪5▪1(a)).

R2▪3▪5

Spring–block earthquake models

While FBM’s deal with strain and failure under tensile stress, analogous theories have been developed to model shearing processes during earthquakes [cf. 958]. Of present interest are the family of models originating with BURRIDGE & KNOPOFF [210] and thereafter extensively studied and modified [e.g. 454, 468, 757, 798, 958]. The models begin with the basic premise that: “An earthquake is a stick–slip frictional instability of a fault driven by steady motions of tectonic plates” [757]. The interaction between two parallel plates is then modelled as occurring via an array of interposed b l o c k s (in one or two dimensions), which are interconnected by c o i l s p r i n g s , and anchored to the upper plate, driven at a small, steady velocity, by (one or more) leaf springs [210, 454, 798, 958]. (The 822



plate velocity is small, whereas the spring reaction time is very short, so the slippage events are analysed under quasi-equilibrium conditions [210, 757] [cf. 958].) The blocks then interact with the stationary lower plate via a frictional mechanism [210, 798]. Most crucially the frictional force decreases with slip velocity in at least part of the domain, rendering the system dynamically unstable [210, 454, 757] [cf. 798]. (In suspension rheology terms, the model posits a s h e a r - t h i n n i n g material with an apparent y i e l d s t r e s s between the blocks and the lower plate.) Other mathematical terms (with corresponding physical realisations) may also be introduced, such as a ‘viscosity’ term proportional to slip velocity (realised as a vibrating string attached to the blocks) that accounts for energy dissipation by seismic radiation [210]. Instabilities in these spring–block models are able to propagate due to the block interconnectivity. When the stress on one block (experienced as the nett effect due to all attached springs) surpasses the frictional resistance, then it will slip; upon slipping the forces acting on neighbouring blocks through the coil springs will change [cf. 119], so that some of them might also slip in a ‘cascade’ effect [210], resulting in an ‘avalanche’ [468, 798]. Thus a spectrum of failures can be observed, from one block to the entire array, depending upon the ‘tuning’ of the model and the imposed relative motion of the plates. In spring–block models all of the elements can be identical *: the ‘chaotic’ behaviour is instigated by a slight randomness in the initial block placement [cf. 119] — leading to a distribution of initial stresses and strains [210, 454, 468, 958] (cf. the distribution of breaking strains or stresses specified in FBM’s). Some implementations of the model (using cellular automata) allow the extent of load redistribution to neighbouring blocks to be controlled (cf. GLS and LLS) [see 798]. In contrast to the FBM’s the system goes through a continuous c y c l e of localised f a i l u r e (slip) followed by r e c o v e r y (stick) and storage of elastic energy: a series of small failures eventually results in conditions that admit of the possibility of major failure, which more-or-less resets the system to a ‘relaxed’ state so that the cycle begins again [210]. This ‘natural’ tendency for the system to condition itself for massive failure indicates the same quality of self-organised criticality (§9▪1▪1▪2) as sandpiles et cetera, with power-law behaviour that implies the absence of an intrinsic lengthscale or timescale [468, 798] [cf. 454, 757, 958] [see also 119, 120, 906]. An interesting feature of at least some implementations of the model is that immediately preceding a major failure there is a gradual increase in occurrence of lesser failure events in the general vicinity, but a suppression in the immediate neighbourhood (called the ‘MOGI doughnut’ in earthquake research) [757]. Like the standard FBM’s, dewatering experiments in the present work considered the effects of imposed stresses. In contrast, the spring–block earthquake models described consider an imposed strain rate. Still, they are readily adaptable to stress-controlled scenarios. Furthermore, some dewatering operations do run in a strain-controlled set-up.

*

This corresponds to the ‘homogeneous’ version; a ‘heterogeneous’ version with different springs between different blocks can also be treated, but analysis is more complicated and the behaviour seems to be similar to the homogeneous case [210]. R2▪3 : Macrorheological models

823

SUPPORTING MATERIAL

825

DETAILED CONTENTS OF SUPPORTING MATERIAL

S1.

EARLY DEWATERING THEORY ............................................. 831

S2.

GENERAL PRINCIPLES OF KINEMATIC WAVES .................... 834

S3.

EXPERIMENTAL OBSERVATIONS OF LONG-TIME SETTLING ............................................................................. 836

S4.

DOUBLE-EXPONENTIAL VERSION OF LONG-TIME FILTRATION ASYMPTOTE .................................................... 840

S5.

STOCHASTIC SETTLING ANALYSIS ..................................... 841

S6.

JAR TESTING PRACTICE ....................................................... 843

S6▪1 Operation and physical configuration ............................................ 843 S6▪2 Motivation and interpretation ........................................................ 846

S7.

LIGHT ABSORBANCE ............................................................ 848

S7▪1 Principles ....................................................................................... 848 S7▪2 Visible light absorbance spectra ..................................................... 849 S7▪3 NOM-related ultraviolet absorbance peaks ..................................... 850 S7▪3▪1 Theory .........................................................................................................................850 S7▪3▪2 Analysis.......................................................................................................................851 S7▪4 Deviation from B E E R ’s law ............................................................. 854 S7▪4▪1 Case study: Yorkshire Water data..........................................................................855

S8.

COLOUR MEASUREMENT ..................................................... 856

S8▪1 Traditional determination of true colour ........................................ 856 S8▪2 Single-wavelength estimation ........................................................ 858 S8▪2▪1 Justification for wavelength specification ..............................................................858 S8▪2▪2 Variation by site.........................................................................................................862

Supporting Material

827

D. I. VERRELLI

S8▪3 Quantitative description of colour by standard colourimetry ......... 862 S8▪3▪1 Colour spaces .............................................................................................................862 S8▪3▪2 Important parameters ...............................................................................................863 S8▪3▪3 Fitting objective parameters to observer-measured colour .................................865

S9.

EVALUATION AND SELECTION OF SYRINGE FILTERS ......... 867

S9▪1 Interferences .................................................................................. 867 S9▪2 Light absorbance ............................................................................ 868 S9▪2▪1 True colour .................................................................................................................868 S9▪2▪2 Ultraviolet absorbance ..............................................................................................868 S9▪2▪3 Evaluation...................................................................................................................869 S9▪3 DOC ............................................................................................... 872

S10. MULTIPLE BATCH SETTLING ANALYSIS .............................. 874 S10▪1 Determination of compressive yield stress curve ........................... 874 S10▪2 Alternative fits for the dewatering parameters .............................. 877 S10▪3 Re-prediction of settling h(t) profiles ............................................ 882

S11. SLUMP TEST RESULTS .......................................................... 892 S11▪1 Strong (conditioned) sludge .......................................................... 892 S11▪2 Weak (unconditioned) sludge ........................................................ 893 S11▪3 Coloured water ............................................................................. 894

S12. CONTOUR SENSITIVITY ANALYSIS ..................................... 895

S13. FILTER PRESS MODELLING .................................................. 898 S13▪1 Methodology ................................................................................. 898 S13▪2 Alum sludges: dose effects ........................................................... 899 S13▪3 Alum sludges: pH effects ............................................................. 901 S13▪4 Selected alum sludges ................................................................... 902 S13▪5 Selected ferric sludges ................................................................... 903 S13▪6 Membrane resistance ..................................................................... 904 S13▪7 Validation against laboratory filtration ......................................... 905 S13▪8 Conclusions ................................................................................... 907

828

Supporting Material


S14. POLYMER CONDITIONER MIXING RECOMMENDATION OF WRc ................................................................................. 908

S15. BOOTSTRAP AND JACKKNIFE STATISTICS .......................... 913 S15▪1 Motivation .................................................................................... 913 S15▪2 Application ................................................................................... 914 S15▪2▪1 Bootstrap procedure..................................................................................................915 S15▪2▪1▪1 Constructing bootstrap data sets.....................................................................915 S15▪2▪1▪2 Correcting bias ...................................................................................................915 S15▪2▪1▪3 Accelerated bias-correction ..............................................................................918 S15▪2▪2 Jackknife procedure...................................................................................................919 S15▪2▪3 Optimising the accuracy of the estimate ................................................................920 S15▪2▪3▪1 Censoring bootstrap sample results................................................................920 S15▪2▪3▪2 Number of data points......................................................................................921 S15▪2▪3▪3 Number of bootstrap samples .........................................................................921 S15▪2▪3▪4 Random numbers ..............................................................................................922

S16. SILANISATION ..................................................................... 925

S17. BULK VISCOSITY .................................................................. 928 S17▪1 Estimation from physical properties .............................................. 929 S17▪2 Estimation from phenomenological observation ............................ 939

S18. BARRIER HOPPING THEORY ................................................ 941

S19. FILTRATION RIG FRAME EXPANSION .................................. 943

S20. ESTIMATION OF THE BULK MODULUS OF COMPRESSIBILITY, BS, THROUGH CENTRIFUGATION ......... 945

S21. METAL COMPLEXATION BY ‘FOREIGN’ ANIONS ................. 947

S22. PSEUDOBÖHMITE STRUCTURE AND COMPOSITION ........... 954

S23. OCCURRENCE OF IRON(II) ................................................... 956

S24. RELATIVE STABILITY OF HÆMATITE AND GOETHITE ........ 957

Supporting Material

829

D. I. VERRELLI

S25. CORRELATIONS OF dmax ....................................................... 960

S26. ESTIMATION OF G FOR INDUSTRIAL SCENARIOS............... 964 S26▪1 Mixing in pipes ............................................................................. 964 S26▪1▪1 Theory .........................................................................................................................964 S26▪1▪2 Laminar flow ..............................................................................................................965 S26▪2 Fluidised bed (floc blanket clarifiers) ............................................ 967 S26▪2▪1 Settling ........................................................................................................................967 S26▪3 Flow through deep bed filters ....................................................... 967 S26▪4 Filtration ....................................................................................... 968

A listing of tables and figures can be found at the front of this thesis.

830

Supporting Material

S1.

EARLY DEWATERING THEORY

FREE (1916) wrote a series of articles [notably 373, 375, 376, 377, 378] on the constitution of “colloidal slimes” and their settling and consolidation, published together with the work of RALSTON [notably 855, 856]. Significant insights included recognition of the following: • a continuum of behaviour from ‘true’ solutions, to colloidal systems, to gross particle suspensions [373] [cf. 303, 449]; • consequently, the increasing relevance of particle charge, BROWNian motion [378], and surface forces, but decreasing relevance of gravity [373] to fine-particle suspensions [see also 377]; • equivalence of behaviour of crushed-ore ‘slimes’ and other suspensions, including model kaolin suspensions [376]; • the importance of particle network self-weight in driving consolidation, thus creating concentration gradients in the settled bed, and leading to the importance of column height in settling investigations [376]; • nonuniform settling, in which particles sediment independently (according to their own size, shape and density) at very low concentrations, then constant-rate zone settling at intermediate initial concentrations, and at still higher concentrations consolidation [855] due to self-weight of the solids in the column; • the slowing of particle (or aggregate) settling due to hindrance [377, cf. 378] of neighbouring particles and especially due to support from below [376]; • the importance of particle arrangement, including aggregate structure, and (primary) particle size in determining the a m o u n t of pore space, the s i z e of the pores, and the c o n t i n u i t y (cf. tortuosity) of the pores — and thereby the compressibility and permeability [375]; • the importance of the degree of coagulation in increasing the effective particle size [373, 377, 378], thereby improving permeability [375] and enhancing settling rates, but reducing the final consolidation [376]; • the sensitivity of the degree of coagulation to impurity species [376]; • the impermanence of aggregate structure [378], yielding even to encounters with or the imposed weight of other aggregates [375], albeit that resistance to aggregate breakdown becomes appreciable at higher concentrations [376]; • likewise the susceptibility of aggregates to rupture in response to rough handling, such as stirring or shaking [376, 378]; • and finally the progressive disruption of aggregate structure following consolidation, permeation and filtration, and (partial) convergence of particle arrangement toward that of the uncoagulated system [375]. The insights are all the more impressive in view of the germinal state of colloid science at the time, with the serious works apparently existing almost exclusively in German, besides the rudimentary nature of generally available particle characterisation techniques [see 373, 378, 856] [cf. 449].

Appendix S1 : Early Dewatering Theory

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D. I. VERRELLI

COE & CLEVENGER (1917 *) [273] published another early study of coagulated suspensions, and observed that the upward flow of supernatant through the settling bed of mineral ‘slime’ was a special case of pore flow [742]. (Later observations on kaolin using x-ray imaging showed that the displaced supernatant initially leaves the bed through relatively large pores, and later through smaller “tubules” [742].) They developed solid and liquid mass balances for use in thickener design [281]. (This calculation was aided by development of YOSHIOKA, HOTTA, TANAKA, NAITO & TSUGUMI (1957) of a graphical solution technique [281]; this relied on extrapolation of the solid flux–density function, qS, (see equation 2-34) [218].) COE & CLEVENGER [273] were also the first to emphasise the need to design dewatering devices (thickeners) using material properties (rates †) corresponding to a range of ‘mass consistencies’ — or, equivalently, solidosities — rather than implicitly ‘extrapolating’ from a single characterisation [868]. However their advice has gone long and often unheeded [868]. They also emphasised the significance of the gel point (which they called “critical settling point”) [273]. This work was especially influential because it combined theoretical development, experimental justification, and practical guidance on unit design and operation. Nevertheless at least two significant flaws were present. Firstly, COE & CLEVENGER [273] essentially dismissed the occasionally observed higher equilibrium solidosity obtained by increasing h0 as an artefact [see also 1050] [cf. 995]. Secondly, they [273] made some dubious conclusions regarding channelling [362]. DEERR (1920) [298] had independently developed some of the same (correct) ideas as COE & CLEVENGER [273]. Key aspects discussed by him [298] include: • the idea of a settling tank as equivalent to “a plurality of vertical tubes [...] of great height in proportion to their diameter”, with an obvious inference for laboratory studies; • identification of distinct zones in a column of settling material, viz. supernatant (perhaps including a few ‘straggling’ particles), a plug of ‘freely’ sedimenting material at roughly the initial concentration (mostly in a dynamic balance, with constituent particles gyrating and moving both up and down according to the local current), and a bed of consolidating material that grows as additional material is deposited from the suspension; • nonuniform settling, in which particles settle independently (according to their own size, shape and density) at very low concentrations, then constant-rate zone settling at intermediate initial concentrations, and at still higher concentrations consolidation due to self-weight of the solids in the column. With application to soil consolidation under self-weight TERZAGHI (1925) [1012] recognised the load as being borne partially by the solid material and partially by hydrodynamic resistance (manifest as an ‘excess’ pressure in the liquid). py and KD 1856 were plotted as

*

Although latterly cited widely as 1916 [e.g. 742], the work was p u b l i s h e d in 1917 as the proceedings of a m e e t i n g held in September 1916. Internal journal citations [and 133] also use the p u b l i c a t i o n year (see e.g. p. 348 of the same volume). Note that FREE’s work was published prior to September 1916, and had been drafted in early 1915 [377].

†

Given that industrial thickening is usually limited by the system kinetics, limited attention was paid to equilibrium properties.

832

Appendix S1 : Early Dewatering Theory


functions of (average) void ratio, e, and methodologies were suggested for obtaining KD 1856 — through either constant strain or constant pressure experiments — and py [1012] [see also 1011]. TERZAGHI [1012] also outlined the extant methods of ‘sludge analysis’, which fell into three classes: separation by fluidisation; sedimentation; and settling in which the liquid pressure within the falling suspension is monitored using a standpipe [see 203, 928] (introduced by WIEGNER circa 1918). Another early discussion of sedimentation that foreshadowed the convention of modern theory in terms of measuring both equilibrium and kinetic data as functions of concentration was presented by EGOLF & MCCABE (1938) [338]. The equilibrium data were plotted as h∞(φ0 h0) [338], which is equivalent to Cφ∞D(py :z=0), with py the compressive yield stress; the kinetic data were plotted as [ηL h 0/Δρ](φ0/φ∞) [338], and a correlation was presented relating h 0 to the STOKES settling velocity, u° — taken together this could be expressed as я(φ0/φ∞), in which я ≡ u°/u. WORK & KOHLER (1940) [1128, 1129] extended the concept of fluid permeating an array of particles to the free-settling and hindered-settling regimes, and also presented kinetic data in terms of deviation from free settling as a function of ‘effective’ solidosity. RUTH and colleagues’ work throughout the 1930’s linking filtration k i n e t i c s to the concept of local cake resistance and membrane resistance [881, 883, 884] is frequently cited, although some was not published until 1946 [882]. The work [881, 882, 883] was informed by the publications of — inter alia — POISEUILLE, SPERRY (1916, 1917) and UNDERWOOD (1926, 1931), and later KOZENY (1927) and CARMAN (1938). Key advances include [882]: • recognition of the ‘universal’ nature of the dewatering process in both settling and filtration [see also 881, 884]; • development of the specific cake resistance concept, and distinction between local and cake-average values [881, 883, 884]; • emphasis of the role of membrane resistance [883], and inclusion of a term to account for it [881, 884]; • introduction of the concept of ‘dead’ pore volume (subject to later criticism [416]); • initial development of the compression–permeability cell; and • recognition that the sum of the liquid pressure drop * and solid stress at any instant is equal to the applied filtration pressure [883]. GRACE (1953) [416, 417], TILLER (1953, 1955), OKAMURA & SHIRATO (1955) and others later refined the compression–permeability cell design and methodology [see 932]. Selective reviews of historical settling and thickening theory appear in BUSTOS et alii [218] and CONCHA & BÜRGER [274].

*

Presumably this is the parameter that RUTH [882] intended by “hydrostatic pressure”. Appendix S1 : Early Dewatering Theory

833

D. I. VERRELLI

S2.

GENERAL PRINCIPLES OF KINEMATIC WAVES

The general theory of kinematic waves was first set out by LIGHTHILL & WHITHAM (1955) [663, 664], who coined the term, although the concepts originated around 100 years earlier. These waves are differentiated from other classes of waves (principally ‘dynamic’ waves) not by their shape per se, but rather by their method of propagation [663]. Pertinent features of kinematic waves are [663, 664]: • They can describe any system where: o the waves represent deviations or fluctuations of a ‘concentration’ (quantity per unit distance), k, and; o there is an “approximate functional relationship” () between this concentration and the ‘flow’ (quantity per unit time), q — and, optionally, the position, x. • They follow directly from the continuity equation,

∂k ∂t

+

∂q ∂x

= 0 (), where t is time,

and do not involve second derivative terms *. They therefore do not naturally diffuse. ∂q

d(uk )

• The wave travels with velocity c = ∂k = dk = u + k dduk , where u is the space-mean flow velocity at a point (u = q / k). o Waves are only able to travel forwards (i.e. in the same direction as the flow). Reflection is not possible. o c > u when mean flow velocity increases with concentration, and c < u when flow decreases with concentration. o The velocity of the undisturbed wave is constant, so waves propagate along straight ‘characteristics’. • Waves of different concentration propagate at different speeds, and thus may diverge in an ‘expansion’ (or ‘fan’), or coalesce into a ‘shock’. o Shock waves generally follow a curved path. o Discrepancy between c and u leads to gradual attenuation of a shock wave as it propagates †. In the general physical system, waves of kinematic and dynamic nature can both propagate: however one will generally dominate under a given scenario [663] ‡. In any case the presence of dynamic waves does not affect the propagation of kinematic waves [e.g. 663]. In certain systems minor flows may be added to or removed from the main flow. Provided that the resulting change in the main flow is ‘small’, a reasonable approximation is to simply adjust q — yielding a corresponding step in c [663, 664].

*

These can enter from the effect of acceleration, as in dynamic waves, or from inclusion in  of a first derivative of q or k [663].

†

The wave disperses forwards for c > u [663], and backwards for c < u [664]. The dispersion occurs with an equivalent diffusion coefficient of the order of c∞ Δc Δt, where c∞ is the ‘equilibrium’ wave speed, Δc is the maximum deviation in c, and Δt is the duration of the perturbation [664].

‡

N.B. For a situation in which dynamic waves attenuate much more rapidly than kinematic waves, the assumption that the former can be neglected is only valid at sufficiently long times [cf. 663].

834

Appendix S2 : General Principles of Kinematic Waves


LIGHTHILL & WHITHAM [663] emphasised that the model was not exact: for example — Normally some small time lag may intervene between adjustments of flow and concentration at a given point; or, again, the relationship between them may have only statistical validity.

Further on the last point [664]: The ‘continuous-flow’ approach represents the limiting behaviour of a stochastic process for a large ‘population’ [of quanta] [...].

In such cases q and k are taken as mean values [664]. Consideration of dewatering operations shows that, intuitively, movement of particles will slow as solidosity increases (conversely, flow of liquid will increase as porosity increases). On the other hand, higher φ would result in greater quantities of particle transport if the velocity could be held constant. The situation is analogous to traffic flow [cf. 664], and the trade-off results in appearance of a m a x i m u m in q with respect to k (or qS with respect to φ, for the present application) [cf. 617]. A number of different settling “modes” (and ‘submodes’) have been identified based on the appearance of points of inflection in the qS(φ) function — whose influence also depend upon φ0 [cf. 274, 617].

Appendix S2 : General Principles of Kinematic Waves

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D. I. VERRELLI

S3.

EXPERIMENTAL OBSERVATIONS OF LONG-TIME SETTLING

DEERR (1920) [298] had deduced the same f o r m of relationship as equation 2-105 for settling of arbitrary suspensions, with most experimental work on ‘aluminium hydroxide’ along with sugar precipitates. DEERR’s [298] proposed correlation was intended to apply from the moment the initial suspension had settled completely into the bed, say t1, until a later time when the settling rate has become “slow”, say t2 — in the reported work t2 ~ 90min. (Immediately this indicates that the formulation is n o t intended to represent true long-time a s y m p t o t i c behaviour.) We may write this [cf. 298, 1050]: h − h2 = (h1 − h2 ) e − γ (t − t1 ) , [S3-1] where h1 and h2 correspond to t1 and t2, and γ ~ e1 = 1 / E2 and (h1 – h2) exp(t1) ~ Φ f1 by comparison with equation 2-105. A key feature of DEERR’s [298] analysis is that h1, t1 and h2 are obtained directly from experimental observation, so that only γ is a fitting parameter. DEERR’s [298] own calculations revealed that for the two examples reported γ is not truly constant even in the constrained domain t1 ≤ t ≤ t2. The two examples also confirm that settling is still ongoing at time t2 [see 298]. It is possible to recreate predictions according to equation S3-1 by optimising γ to yield the least sum of squares of the residual errors. This computation reveals that equation S3-1 yields a good correlation in the domain t1 ≤ t ≤ t2, slightly better than a simplistic logarithmic fit, and substantially better than a power-law fit (although these latter two fits can be improved by shifting the time scale). Yet an important detail to be observed is that the fit of equation S3-1 following this procedure is worst precisely at the latest times. Based on an observed trend, ROBERTS (1949) [868] proposed that the rate of water removal from a sludge was directly proportional to the amount of water remaining, expressed as time-varying mass “dilutions”, D(t) = 1 / x – 1: d ΔD = −γ ΔD , [S3-2] dt where ΔD ≡ D(t) – D(t→∞) and γ is a constant [274]. By comparison with the definition of φ (equation 2-2), and recalling that in settling φ h is constant, by conservation of mass (or volume), it can be shown that equation S3-2 is consistent with the asymptotic exponential decay predicted by USHER, SCALES & WHITE [1061], equation 2-105, with γ ≈ e1 = 1 / E2. ROBERTS’s [868] analyses were conducted on metallurgical ‘slime’ data of COE & CLEVENGER (“C&C”) [273] and on new settling data for “flocs” of “raw cement mix” (d0 ~ 30μm). There are some important points to mention in relation to ROBERTS’s paper [868]: • Equation 2-105 was fit not just to the long-time data, but in fact to essentially all of the settling data from circa the time at which the material becomes fully networked throughout the column. The C&C data showed a fall only ~90% of its purported

836

Appendix S3 : Experimental Observations of Long-Time Settling


•

•

• •

equilibrium, and the settling velocity when terminated was still of order ~10% of the initial rate; ROBERTS’s own data gave a closer approach to equilibrium [see 868]. The C&C data comprised just five points, and can be shown to be just as well modelled by a logarithmic fit to h(t) as it was by the exponential fit to ΔD(t). Eight data points were used for the cement raw mix data, and the exponential model yielded a slightly better fit to reconstructed h(t) data. There is no evidence that the C&C data is real experimental data. In the cited source [273] it is presented simply as an “illustration of the method” (p. 371). There is passing similarity to data for a “siliceous” pulp with d0 ~ 74mm (p. 367) and for a gold mill ‘slime’ (p. 378) [273]. In any case, the empirical data which the illustration most closely resembles (Example A:3) includes an intervention mid-way where water was drawn off and the partially settled bed s t i r r e d up [273], raising doubts over its applicability here. (No interventions are mentioned for ROBERTS’s own data.) The equilibrium height was treated as an experimental fitting parameter, and adjusted to maximise the agreement with equation 2-105. Despite the description of ‘flocs’, the settling tests were practically complete within days. The slowest settling velocities were of order 10–7m/s. (For comparison, settling in the present work sometimes c o m m e n c e d at a speed of this order of magnitude, and was terminated after more than 100 days at settling rates less than 10–9m/s.)

YOSHIOKA, HOTTA & TANAKA (1955) claimed either * that γ = γ∗ / φg h0 [218] or that γ = γ∗ / φ0 h0 [1050], with γ∗ constant for a given material. There is no obvious theoretical rationale for  h0 −2 [1061] †, this variation in γ. On the contrary, the foregoing theory suggested that e1 ∝ implying rather that γ ∝ h0 2 . TORY & SHANNON (1965) [1050] investigated the correlation of ROBERTS [868] (which they erroneously conflated with DEERR’s [298]) and the amendment due to YOSHIOKA et alia (1955). They demonstrated that the latter amendment was necessary to avoid false inferences [1050]. TORY & SHANNON [1050] claimed to have validated the aforesaid amendment experimentally [218]. Certainly the amendment may have improved the correlation, however the data show that estimates of the ‘constant’ γ∗ varied by a factor of 1.5 over 36 experiments on CaCO3 slurries; the solid phase mass was varied over a factor of 19, although h0 was varied over a factor of just 4.1 [1050]. It should also be noted that channelling was observed in several runs [1050]. TORY & SHANNON [1050] were critical of ROBERTS’s [868] implications that samples with φ0 ≥ φg should follow logarithmic consolidation for all time, and that no concentration profiles would thereby develop in the bed.

*

The former option presumably assumes that φ0 < φg. The latter option seems more plausible. The original paper is in Japanese and not readily available; however, the SciFinder Scholar (American Chemical Society, 2005–2007) abstract indicates that raking was employed. Contrary to claims [in 1050] neither ROBINSON [869] nor WORK & KOHLER [1128] state or even imply a comparable relation.

†

 h∞ 2 , by equation 2-127; however, in gravity settling equation 2-97 allows either In filtration (at least) E2 ∝

 h∞ or h0 ∝  h∞ 2 , depending upon the form of py(φ). h0 ∝ Appendix S3 : Experimental Observations of Long-Time Settling

837

D. I. VERRELLI

BEHN [133] undertook an analysis in line with ROBERTS [868], but it is rather compromised by the c o n t i n u a l s h e a r i n g imposed on his settling systems (degassed digested sewage sludge) throughout the column [see e.g. 107, 842, 928]. Aside from this and the inherent issue with treating h∞ as an adjustable parameter, the experimental data showed falls only ~80 to 93% of their purported equilibria, and the settling velocity when terminated was still ~6 to 21% of the initial rate [133]. BUSTOS et alii [218] found BEHN & LIEBMAN’s (1963) justification of BEHN’s [133] application of equation S3-2 to be “unconvincing”, and noted treatment of h∞ as a “fudge factor”. Nevertheless, they [218] also claimed much experimental support for the correlation. FITCH [362, 363] discussed long-time settling (or thickening) behaviour with the aid of TORY plots, which are simply plots of h (h). In the later discussion [363] a schematic plot was drawn which illustrated the proposed linear relationship between h and h (implying exponential decay of both h (t) and h(t)). However, examination of the empirical basis for the plot [362] is less convincing: the decrease in settling rate at long times is in fact highly nonlinear, but is expediently split into a ‘transition’ of arbitrary shape (potentially affected by channelling) followed by a presumed linear decay of settling rate with h (exponential with t) to the final, steady state [see 362]. What is especially interesting about the TORY plots is that they do exhibit an extended domain of approximately linear h (h) behaviour in the earlier ‘KYNCH’ region, i.e. in h i n d e r e d s e t t l i n g before consolidation effects become significant [362]. On the basis of the foregoing, it appears plausible that it is t h i s region, rather than true long-time consolidation, that has often been modelled with the exponential decay of h(t). See the settling modes described by BÜRGER & TORY [205] for an illustration of the possibility of a discontinuity in the h(t) profile when the free-settling zone (with material at φ0) disappears into a predominantly hindered settling regime. BEHN [133] seems to imply that analyses by ROLLASON (1913) and EGOLF & MCCABE (1937) [338] supported the longish-time exponential decay model he discussed. Yet BEHN [133] goes on to incorrectly state that the latter relationship is linear on log–log co-ordinates, and subsequently implies that a power-law relationship exists for h(t) and that it corresponds to logarithmic behaviour! Furthermore EGOLF & MCCABE [338] actually describe a p o w e r - l a w model of the ‘falling rate period’, and imply that t h i s is what ROLLASON (1913) showed. The discrepancy arises due to the imprecise description of both exponential [868, 1050, 1061] * and power-law [338] models as “logarithmic” (they plot linearly on log–linear and log–log co-ordinates, respectively). The agreement of EGOLF & MCCABE’s [338] power-law fits with the data varies from poor to good, although this may be at least partly due to the ranges they attempted to fit, as well as the rigor in optimising the fit.

*

838

Under the heading “logarithmic behaviour” ROBERTS [868] described the settling as of “logarithmic decrement” type, which at least is more evocative for the reader, who may draw an analogy to (say) the “log reduction” of microbes described in hygiene literature [e.g. 59]. Appendix S3 : Experimental Observations of Long-Time Settling


WORK & KOHLER [1128, 1129] obtained good agreement with a power-law model to longertime h(t) settling profiles of CaCO3 and ‘alumina’ slurries. They did continuously stir their samples, justified on the grounds that otherwise channel formation would ‘interfere’ with the results [1128, 1129]. In this study, too, settling was terminated while still quite far from the equilibrium state. The result of most interest for the present work is that the various suspensions exhibited t w o sequential power-law regimes (with significantly different exponents) after the initial constant-rate settling [1128, 1129]. Intuitively, this is expected to correspond to a change in dominant settling mechanism, such as from h i n d e r e d s e t t l i n g to c o n s o l i d a t i o n of a particulate network [cf. 205] — WORK & KOHLER [1128, 1129] described the material in the first power-law regime as “fluid” and that in the second regime as “plastic” and akin to soil undergoing consolidation. HARRIS, SOMASUNDARAN & JENSEN [450] stated that the latter phase of settling could be described by “first-order decay kinetics”. Although this might be expected to yield simple exponential decay of h(t), a literal reading of their differential equation yields the reciprocal of exponential decay in h(t). However, they [450] actually presented the integrated form as double-exponential decay. One justification of the “first-order kinetics” [450] was a paper by CHAKRAVARTI & DELL [233], but this paper actually dealt implicitly with the instantaneous concentration profiles at early times, and did not consider h(t). The curve was fit to experimental data over a very short range only [450], for which agreement might be attained with other forms with different asymptotic behaviour. In geomechanics and soil science a range of views are held, as indicated in §R2▪2.

Appendix S3 : Experimental Observations of Long-Time Settling

839

D. I. VERRELLI

S4.

DOUBLE-EXPONENTIAL VERSION OF LONG-TIME FILTRATION ASYMPTOTE

Equation 2-124 was simplified significantly to obtain equation 2-125, which has first-order accuracy. The same treatment can be extended to include the first two terms:         lim  tc + ln (Φ f ) − t  + exp 9 tc + ln (Φ f ) − 9 t  , [S4-1a] − ≈ exp V V 0 1 t→∞ ∞  E2  E2 E2  E2           constant = E1 / E2   constant = 9 E4 / E2  or, in the notation of equation 2-125b: E −t  9( E4 − t )  lim  + exp  . E3 − V ≈ exp 1 [S4-1b] t→∞  E2   E2  E1 and E4 are clearly defined as E1 ≡ tc + E2 ln (Φ f0 ) ,

[S4-2a]

E4 ≡ tc + 9 E2 ln (Φ f1 ) .

[S4-2b]

It was stated in §2▪4▪5▪6 that |fi+1| < |fi|. Nevertheless, the logarithm suggests that it is quite possible (but not guaranteed) that E4 > E1; this would mean that the second term would be more important than the first term at ‘early’ times (still with t > tc). Nonetheless, the first term controls the behaviour at very long times, shown by: lim t→∞

(

)

(

)

9

E3 − V ≈ e E1 / E2 e − t / E2 + e 9 E4 / E2 e − t / E2 .

[S4-3]

The major difficulty with introducing yet another parameter, namely E4, is the method of its estimation. Or, more precisely, the method of o p t i m i s a t i o n of the parameter estimates. A simple approach would be to solve for E1, E2 and E3 as described in §2▪4▪5▪6, and then obtain E4 by minimising the error in     E − t  E  . t = E4 − 2 ln  E3 − V − exp 1 [S4-4]  9 E2    actual      first estimate   This should be compared with equation 2-125b. If V∞ were known exactly, then the term labelled ‘actual’ would represent the true value of V∞ ‒ V , while the term labelled ‘first estimate’ would be a first-order estimate of V∞ ‒ V . The residuals from implementation of the first-order form of the asymptote, equation 2-125b, are predicted to decay exponentially, in accordance with equation S4-3. In practice V∞ is not usually known exactly, and is estimated as E3. However equation S4-4 might still provide a useful indication of the self-consistency of the model estimates. A more rigorous scheme would seek the global optimum by allowing all parameters to vary simultaneously (in concept, at least).

840

Appendix S4 : Double-Exponential Version of Long-Time Filtration Asymptote


S5.

STOCHASTIC SETTLING ANALYSIS

One important branch of dewatering theory that has unfortunately been neglected despite interesting developments over its long history is the field of s t o c h a s t i c m o d e l l i n g . The genesis of this approach lies in observations that fluctuations in the settling velocities of even identical particles, in a region of given solidosity, can be considerable [1049] — not to mention variations in polydisperse systems [205]. This mechanism gradually induces a ‘smoothing’ of the solidosity profile, and a blurring of the (erstwhile discontinuous) interfaces [cf. 205, 218]. For very small particles such manifestations are known to arise from BROWNian motion, and can be modelled as (FICKian, molecular) diffusion processes; for the larger particulates considered here the process is thus sometimes termed ‘ h y d r o d y n a m i c d i f f u s i o n ’ [1049]. An alternative to conventional d e t e r m i n i s t i c models of diffusion (partial differential equations which may be solved analytically or numerically) is to employ s t o c h a s t i c models. This approach was pioneered by PICKARD & TORY (1972), with subsequent development driven primarily by TORY with continuing contributions by PICKARD and colleagues such as KAMEL and HESSE [218, 1049]. These stochastic and diffusion processes are formally equivalent [205] — although in the stochastic model described below it is strictly v e l o c i t y that ‘diffuses’ [1049]. The stochastic modelling application has become known as a ‘PICKARD–TORY process’ (or model) [1049]. In general, the movement of a given particle has a significant random component, which is generated i n d e p e n d e n t of the motion of neighbouring particles; yet the parameters of the statistical distribution sampled d e p e n d on the current state of the local environment [1049]. The approach is conveniently applied to the problem of one-dimensional batch settling through use of a three-parameter MARKOV model [1049]. (Five parameters are required to model settling in three spatial dimensions [1049].) This is then solved in what is effectively a Monte Carlo (discrete numerical) method, where stochastically-generated particle trajectories (‘WIENER processes’) are repeatedly computed and the results of many simulations combined [1049]. The three parameters are the mean, variance and autocorrelation of the particle velocities, and are naturally functions of solidosity [218, 1049]. The solidosity is taken as a ‘surrogate’ for configuration; the fact that each solidosity represents many different configurations is accounted for by inserting appropriate random variation [1049]. The algorithm can advantageously be arranged such that each parameter takes as its argument a local weighted average of solidosity that incorporates information about neighbouring regions [218]. The mean and variance reflect the steady-state distribution of particle velocities, which is GAUSSian [1049]. The autocorrelation of velocities decays exponentially [1049]. Settling can then be described by a “stochastic differential equation” in terms of the velocity, which is a (rescaled) instance of the ‘FOKKER–PLANK equation’ — a second-order, parabolic partial differential equation, also known as the ‘KOLMOGOROV forward equation’ — with a ‘drift’ (i.e. convection) term and a diffusion term [see 1049]. Formulation of the problem as a stochastic differential equation makes it much easier to solve numerically [1049]. The threeAppendix S5 : Stochastic Settling Analysis

841

D. I. VERRELLI

parameter model implementation is almost the same as the well-known ORNSTEIN– UHLENBECK model, and has well-characterised statistical properties [1049]. It has a simple fundamental structure, and can be expressed in nondimensionalised form as a function of just one parameter [see 1049]. The stochastic modelling approach is a generalisation of KYNCH’s method (§2▪4▪3) [1049] [cf. 205, 218]. Unlike KYNCH’s model, it is able to capture the variation of particle velocity with time and the variance in the velocities of identical particles in a suspension [1049]. Advantages of this approach over conventional so-called continuum modelling are that variables in the real system such as solidosity and velocity are recognised as varying continuously * [1049], and ‘deterministic chaos’ — manifest in the large-scale correlated motions † (e.g. §2▪4▪3▪2, §9▪1▪1▪1(b)) and in fluctuations or variance in settling velocities — is effectively simulated (cf. approximated) by appropriate substitution of random processes [cf. 218]. It also provides a deeper physical insight into actual trajectories and velocities of individual particles [1049]. Advantages of the approach over micromechanical modelling are that computation is vastly more efficient, so that much larger system sizes (e.g. ~106 particles) can be handled with ease [218, 1049]. Also micromechanical modelling requires much more than three (or five) parameters to describe the process, especially where more complicated systems are to be modelled, e.g. settling of a suspension of cylinders [218]. A ‘hydrodynamic diffusion’ model would also assume the particles execute a random walk through the suspension (superimposed on the bulk drift), meaning that velocity is not continuous (the position variable is not differentiable) [1049]. The main disadvantage is that the neglect of this field of research has meant that information about the values of the parameters (and trends in their behaviour) has been lacking [218, 1049]. This deficit is slowly being addressed [218], although care must be taken to ensure the resulting estimates are not biased [see 205, 1049]. An advantage in this effort is that it is possible to estimate the model parameters (to predict dynamic behaviour) from steady-state observations [1049]. The preferred implementation of the model is limited to describing systems in which the velocity distribution is GAUSSian: this becomes a poor approximation at ‘high’ solidosity (where treatment of the random component of individual particle velocities as independent — i.e. uncorrelated — also becomes erroneous) [1049] — with the critical value presumably being lower for aggregated systems. (Implementation of f i r s t - o r d e r autocorrelation i s supported by experimental observations [1049], yet in theory this too may not accurately represent all systems.) A further potential issue is the prediction of unbounded variance in velocity as the system size increases [see 218, 1049].

*

Nonetheless, with appropriate parameter choice, ‘interfaces’ can still be practically identified as thin regions in which system properties (e.g. solidosity) vary rapidly [218] [cf. 205].

†

These effects are expected to be more pronounced in larger containers [218] [cf. 1049]. In extreme cases the velocity distribution becomes significantly skewed (i.e. non-normal) [1049], and so cannot be modelled by the implementation described above — although the principle of stochastic modelling is generic, and a suitable non-normal model could be developed.

842

Appendix S5 : Stochastic Settling Analysis


S6.

JAR TESTING PRACTICE

Section 3▪3▪3 introduced the concept of jar testing, and the protocol followed in the present work. Numerous alternative implementations are described in the literature, as the following survey illustrates.

S6▪1

Operation and physical configuration

In jar testing some industrial practitioners add the alkali (or acid) before dosing coagulant [229, 436]. Industrially it appears to be more common to dose the alkali following the coagulant — although in certain circumstances the reverse sequence may work better [see 503] — and that is reflected in the above protocol. An outline of selected recommended or implemented configurations from the literature is presented in Table S6-1. A historical sketch of rig development was provided by CORNWELL & BISHOP [283]. Although not explicitly stated, proprietary jar mixers are likely to have been used in most of the references [e.g. 430, 557]: these are typically unbaffled, of square cross-section, 1.0 to 2.0L in volume and fitted with centred paddle impellers for mixing [e.g. 503, 557, 968]. The preference for square jars appears to be related to a combination of distortion-free viewing and a desire for greater turbulence and reduced vortexing compared to unbaffled cylindrical beakers [503, 557]. In studies evaluating rapid mix speed, intensities up to 10000rpm [503] and 16000s‒1 [90] have been used. In practical applications very high mixing intensities are typically achieved with static in-line mixing elements. STOOPS [979] notes that static in-line mixers impart a large amount of energy over only 1 to 2s. Static mixers are not suited to fluctuations in treatment chemical flowrates (accurate dosing pumps are required [e.g. 979]), or for plants experiencing significant seasonal fluctuation in process flow requiring a large turndown ratio [754].

Appendix S6 : Jar Testing Practice

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D. I. VERRELLI

Table S6-1: Key specifications implemented or recommended for jar testing in the literature. (a) Specifications based on impeller speed.

Jar volume and shape a [L] 1.0 to 1.5   2.0  1.5

Sample volume [L] 1.0 1.5 1.0 1.0

c

0.08 1.0 1.0 2.0 1.0



1.0



1.0 2.0

 

1.0 2.0

2.0



2.0



0.5

c

0.8 1.0 0.8 1.0

200 80 300 200

1.0

1.0 ~2.0

0.6

844

Rapid mix Slow mix Intensity Duration Intensity Duration [rpm] [min] [rpm] [min] 120 1 ~20 ~20 100 1 40 then 20 10 + 10 100 2 20 20 b 6 15 1+ 200 5 50 20 100 2 30 20 1 30 100 3 40 20 200 4.5 40 17

200

2 0.5 10 1 1 1.5

100 100 to 200 100 to 200 150 150 100 200 300 400 100 140 100 100

1 ~0.2 ~0.2 1 3 1 1 1 1 5 3 3 2

40

20

30 30 30

10 15 10 to 20 15

24 Tapered Tapered 30 20 40 20 30 30 40 40 40 35

20 20 20 20 20 10 14 15 10 20 to 30 30 15 15


Settling Reference time [min] ~15 [28] 30 [79] 60 [159] 15 [229] 120 [236] 30 [251] 180 [300] 30 [333] 10 [355, 1055] [cf. 623] 15 [389] [413] [430] [436] [518] 10 [524, 525, 526] 120 [533] 20 [557] 20 [557] 30 [569] 40 [578] 55 [597] 15 [685] 15 [827] [861] [997] 30 [1082] 30 [1085] 60 [1116]


Table S6-1 continued. (b) Specifications based on characteristic velocity gradient.

Jar volume and shape a [L] 5.0 2.0

Sample volume [L]



2.0



1.0

1.0 0.8

Rapid mix Slow mix Intensity Duration Intensity Duration [s‒1] [min] [s‒1] [min] 292 3 to 5 21 30 d 389 1 34 480 1 18 14 (220rpm) (25rpm) 70 to 400 1 (or 2b) 20 to 50 30 300 to 500 0.25 to 2 Tapered 518 ~0.1 to 1 23 10 to 60 (400rpm) (50rpm)

Settling time [min]

15 60 30

Reference

[111] [367, 369] [478] [521] [979] [1140, 1141]

Notes a  = square or rectangular,  = cylindrical. b Extra time allowed if polymers dosed sequentially. of stators (i.e. baffles) endorsed [236, 557]. d “long enough to form full-grown flocs” [369].

c

Use

In the ‘slow mix’ stage the goal is to maximise the aggregation rate without engendering excessive break-up [518]. A configuration favoured by some workers, and which may more closely replicate industrial conditions, is to more gradually vary the stirrer speed. In practice tapered mixing would be achieved by connecting mixing compartments in series [754] — or, equivalently, installing baffles into a large chamber. (In most real plants, end baffles or similar are used to prevent mixing energy from being transferred through to the clarification stage [1113].) KAWAMURA [557] recommends the ‘tapered’ mixing protocol presented in Table S6-2 (see also IVES [518]). This may be varied around the optimum coagulant dose, covering velocity gradients of 15, 30, 45 and 60s‒1, and mixing times of 10, 20, 30 and 40min [557]. However the mixing time should sum to at least 15min, with a target G.t value of around 5×104 [557]. Table S6-2: Tapered mixing protocol suggested by KAWAMURA [557].

G [s‒1] 60 30 15 N/A

Mixing speed [rpm] 70 40 25 Sum

t [min] 7.5 7.5 5.0 20.0

G.t [–] 2.7 × 104 1.4 × 104 4.5 × 103 4.5 × 104

Table S6-3: Tapered mixing protocol suggested by HUDSON & WAGNER [503]. Summer data corresponds to a dose of 3.4mg(Fe)/L, without lime, with 12NTU raw water at 21°C. Winter data corresponds to a dose of 5.2mg(Fe)/L, plus lime, with 57NTU raw water at 4°C.

G [s‒1]

Sum Note

a

Summer 60 34 14 N/A

t [min] Winter 60 23 11 N/A

2 6 ~22 ~30 a

G.t [–] Summer Winter 3 7.2 × 10 7.2 × 103 1.2 × 104 8.3 × 103 4 1.8 × 10 1.5 × 104 3.8 × 104 3.0 × 104

Test values between 10 and 40min [503].


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D. I. VERRELLI

HUDSON & WAGNER [503] presented a similar protocol, as in Table S6-3. This was applied to 2L samples of natural raw water in square jars [503]. STOOPS [979] also describes a tapered slow mixing protocol for jar testing, varying from 80 down to 20rpm. However, he allows the slow mix operation to be carried out over as little as 5min, or up to 30min (often 10 to 20min) [979]. “Common” values of G in the slow mix stage are 10 to 80s‒1 [979]. MONK & WILLIS [754] recommend values of G selectable in the range 15 to 80s‒1. The settling time is specified based on industrial hydraulic loading rates (cf. residence times) [503]. Clarifier design values range from about 1cm/min to 5cm/min or more [282, 557, 754]. Laboratory-generated aggregates derived from alum coagulation of coloured, low-turbidity water may have somewhat lower settling velocities, in the range 0.6 to 2.4cm/min [111, 116] (these velocities are high in the sense that one expects design values to incorporate a safety margin, but low in the sense that treatment conditions studied in the research work included sub-optimal regimes that would not be implemented in industry).

S6▪2

Motivation and interpretation

The jar test results may be evaluated by considering whether treatment t a r g e t s such as those in Table S6-4 were met. Many other parameters can be monitored, such as TOC [229]. EIKEBROKK et alia [340] nominate residual metal concentrations as the “critical parameter” with respect to minimum dosages of metal-based coagulants. Table S6-4: Examples of treatment objectives in jar testing [229].

Parameter

Jar test treatment objective Direct filtration Sedimentation Dissolved air floatation Metal residuals [μg/L] < 50 < 400 < 1000 Turbidity [NTU] < 0.1 <2 <2 Colour < 5 mg/L Pt units > 60% reduction > 60% reduction A254nm [% reduction] 30 > 30 > 30 Floc size [754] ‘pinpoint’ ‘large’ ‘large’ The jar testing products — i.e. supernatant and sludge, or flocs — can be processed further in other bench-scale experiments, for example filtration. For the supernatant, 8μm [503] or 11μm [557] filters can be used to generate a prediction of filtered water quality * (the first portion of filtrate is discarded). For the sludge, assessments of dewaterability can be made [e.g. 191]. BACHE and co-workers [115] have found that optimum conditions based on supernatant evaluation in jar testing also yield roughly optimal floc properties.

*

846

The pore size of a regular sand filter bed is approximately 10 to 15μm [557]. Appendix S6 : Jar Testing Practice


Jar test results should be used for comparison only with other jar testing results. Full-scale plant data may give performance that is better or that is worse than jar testing carried out under the same nominal conditions [see 503]. An example of an effect that is not well modelled in jar testing is the “incidental” flocculation that occurs in large plants while the water stream passes through a conduit from the flash mixing basin to the slow mixing basins (“flocculators”) [1113]. Although jar testing may be conducted with the motivation of determining ‘optimal’ treatment conditions, the outcome can be subjective. If only one process parameter and one response variable were involved, and the response exhibited a (local) optimum at a certain value (or range) of the manipulated parameter, then an objective decision could be made. However, in practice a number of treatment parameters may be adjusted (e.g. dose, pH) with different consequences for a number of response variables (e.g. colour, turbidity) some of which may not exhibit local optima — i.e., there may always be a (slight) improvement in going to more extreme values of the treatment parameter. This being the case, it is common to establish rules of thumb that seek to obtain ‘nearoptimum’ responses for a few key variables by adjusting only a couple of treatment parameters (in a given study). The acceptance of near-optimum results avoids money being spent on essentially negligible improvements of treatment. There is also a need to consider the starting conditions (or baseline). While only a couple of response variables may be optimised, others will be constrained to satisfy relevant guidelines or regulations. BACHE et alia [116] defined an optimum dose as the minimum to achieve 95% colour reduction. Turbidity removal is another popular parameter [503, 557].


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D. I. VERRELLI

S7. S7▪1

LIGHT ABSORBANCE

Principles

The absorbance, Asample, reported in spectrophotometric measurements is defined by the intensity of illumination in the absence (I0) and presence (I ) of the sample [451]: Asample = log10(I0 / I ) . [S7-1] The transmittance, T, is given simply by T = I / I0 [451]. Absorbances of interest may range from about 0.001 up to 3.0 *, corresponding to transmittances of about 99.8% down to 0.10%. The cell pathlength or sample concentration may be adjusted so as to attain a value of Asample within this range [334] (see below). Maximum measurable absorbance is limited by stray light and the signal to noise ratio [451]: the instrument used in the present work can be considered accurate for Asample < 3.5 [421]. It is usual to subtract from the sample absorbance a b a c k g r o u n d , or ‘reference’, absorbance (here purified water in a ‘matched’ sample cell). The quantity that is obtained, A, could be called the specific absorbance [cf. 515]: A ≡ Asample ‒ Areference . [S7-2] This is useful for isolating the contribution to absorbance of the solute by subtracting the absorbance due to the solvent (and to the sample cell itself et cetera). The BOUGUER–LAMBERT law states that absorbance is proportional to the pathlength of the through the sample, l [451, 572]. To facilitate comparison, absorbances are often standardised to a common pathlength of (say) l = 10mm. Normalising the specific absorbance yields the l i n e a r a b s o r b a n c e (or linear absorption coefficient) [515]: A ≡ A / l , [S7-3] ‒1 with units of (say) cm . For brevity, A will be called simply ‘absorbance’ hereon in. BEER’s law states that specific absorbance of a solution is proportional to the concentration of the absorbing solute, C, at “reasonably low concentrations” [451]. This is typically combined with equation S7-3 in the BEER–BOUGUER–LAMBERT law [417, 515, 836]: A=ΥCl, [S7-4] where Υ is the molar absorptivity (or molar absorption coefficient [515]), popularly called the ‘extinction coefficient’. The proportionality of A with C need not be assumed when correlating against a series of standard solutions (e.g. for colour), hence: A = f(C) , [S7-5] where f represents some arbitrary function — see §S7▪4 for discussion. Absorbance peaks when the energy of the incident light, which is inversely proportional to the wavelength, corresponds to the difference in energy between two allowed states of the

*

848

The U.S. Standard Methods [334] specify ranges of 0.005 to 0.9 for UV absorbances (253.7nm) and 0.005 to 0.8 for visible light (~456nm); these are conservative estimates of instrument capability. Appendix S7 : Light Absorbance


absorbing molecule [451]. The ‘natural bandwidth’ of such a measured peak is defined as “the width (in nm) at half the height of the sample absorption peak” [451]. Similarly, the incident light for any chosen wavelength actually spans a narrow range of wavelengths described by the ‘spectral bandwidth’ (SBW) [see e.g. 451]. In the present work natural bandwidths were exceptionally broad (e.g. §S7▪3▪2), so use of a moderate SBW was permissible [see 451]. For a scan that progresses stepwise with a constant increment (or decrement) in wavelength, the spectrophotometer manufacturer recommends that the SBW be at least three increments wide [421] to avoid losing information about absorbance b e t w e e n the designated wavelengths. Although temperature can affect absorbance measurements [451, 515], the laboratory variation is unlikely to be significant [cf. 421].

S7▪2

Visible light absorbance spectra

Visible absorbance spectra for raw and treated waters are relatively simple to fit, due to their high degree of smoothness. Several workers [139, 193] have fitted * water absorbance spectra to an exponential function: A = K e–P.λ , [S7-6] where both K and P are curve-fitting parameters. For a wide range of waters including both fresh and sea waters BRICAUD, MOREL & PRIEUR [193] found that P varied † between 0.010 and 0.020nm–1. From the spectra published by KIRK [572] for inland and coastal waters (freshwater and seawater) BRICAUD, MOREL & PRIEUR [193] computed P values of 0.013 to 0.016nm–1. The raw water analysed by BENNETT & DRIKAS [139] could be fitted by P values of 0.011±0.001nm–1, with lower values corresponding to higher colours. KIRK correlated Australian inland waters with P = 0.016nm–1, DAVIES-COLLEY & VANT correlated 11 New Zealand lakes with P = 0.019nm–1, and CUTHBERT & DEL GIORGIO correlated ‡ 20 Quebec lakes § with P = 0.017nm–1 [291]. Results in the present work show that the absorbance of MIEX eluate may be fitted with power laws of the form: A = K λ–P , [S7-7]

*

BRICAUD, MOREL & PRIEUR [193] found two separate regions of exponential law behaviour, namely from 200 to 250nm, and from 275 to 700nm. While they predicted reasonable results for an exponential fit between 350 and 700nm, in the end their regression was carried out only from 375 to 500nm.

†

Variation was reduced for samples from the same source: an area influenced by industrial or domestic effluents had P = 0.012nm–1, and a coastal area affected by fluvial discharge had P = 0.013nm–1 [139, 193].

‡

Correlation was carried out pairwise for absorbances (or absorbance coefficients) between 250nm and 440nm [291].

§

True colour from < 5 to 85mg/L Pt units [291]. Appendix S7 : Light Absorbance

849

D. I. VERRELLI

in which P was approximately 7.0±0.5. A possible decrease in P with increasing colour may have been due to experimental uncertainty *. The absorbance spectra were fitted less well by exponential curves. The inverse-power fit suggests a material with a r a n g e of relaxation (or response) times [cf. 906], which is intuitively appropriate for the present application.

S7▪3

NOM-related ultraviolet absorbance peaks

It is also interesting to consider curve-fitting the absorbance spectra in the ultraviolet region, where the ‘hump’ associated with the presence of humics or NOM occurs. As described in §3▪4▪1▪3, in order to obtain a summary parameter, conventionally only the ultraviolet absorbance at around 254nm is measured (or recorded). However this does not necessarily correlate with the true (average) peak in ultraviolet absorbance due to those compounds.

S7▪3▪1

Theory

It is difficult to deconvolute the component peaks in a spectrum. It may be assumed that the spectrum is made up of a set of narrow to broad peaks, some noise, and some scattering (or other cut-off phenomenon) at the lowest wavelengths. The fitting is more conveniently defined with respect to w a v e n u m b e r , which is simply the reciprocal of the wavelength, conventionally in cm–1. Individual peaks are then modelled as normal or GAUSSian distributions in 1/λ [597]. This is modelled as IA ~ N(1/λ, σ2) , [S7-8] in which 1/λ is the mean wavenumber, and σ2 is the variance. Scattering may be modelled as proportional to some inverse power of the wavelength, IS ∝ (1/λ)m , [S7-9] † and the exponent m is taken as equal to 4 for particle sizes small compared to the wavelength of incident light (including RAYLEIGH scattering ‡) [33, 506, see also 739]. For

*

The curve fitting took place over different wavelengths: from 425 to 750nm for the most highly coloured sample (where absorbances at lower wavelengths were off the scale), to 300 to 600nm for the most diluted sample (where absorbances at high wavelengths were too small to be adequately resolved).

†

I.e. particle sizes of no more than 5 to 10% of the incident wavelength [796, 801]. In the limit for very small particles (with polarisability independent of wavelength, so proportional to V [506]) the forward scattering is proportional to V2 / λ4, where V is the volume of a particle [796], while absorbance is proportional to V / λ [amended from 506]. If absorbance occurs, then it will dominate the behaviour as V → 0 [506].

‡

RAYLEIGH scattering is described by the equation IS =

8π α λ4 r 2

2

(1 + cos 2 θ)I 0

in which IS and I0 are the scattered and incident intensities, respectively, θ the angle between the incident and scattered rays, r is the distance from the scattering centre to the detector, and α is the ‘polarisability’ of the particle [506, 801]. For our purposes only forward scattering, with θ = 0, is of interest. RAYLEIGH scattering is a relatively simple type of scattering pertaining to small particles, however it makes some assumptions about particle properties besides size [506].

850

Appendix S7 : Light Absorbance


particle sizes on the order * of the wavelength of incident light more complex relations apply (MIE theory) [506]. For very large † particles, distinct refracted and reflected beams result [506, 801]. The general result is that the exponent m decreases as the particle size increases [1041] ‡. Adjustments may be made for particles that are not simple spheres [540] and for collections of such particles in various sizes [506]. Numerous special cases are considered by VAN DE HULST [506]. However it may be noted that corrections for particle size and shape are negligible for forward scattering [796]. These individual components are weighted and then summed to (hopefully) reproduce the experimental curve. It is convenient to apply the weights for the scattering function(s) inside the exponent, so that they also normalise the wavelength; it has been found that the following set of three terms is sufficient to model spectra from 230 to 460nm with reasonable accuracy: I = (wS/λ)m + wA1 IA1 + wA2 IA2 [S7-10] m 2 2 ~ (wS/λ) + wA1 N(1/λ1, σ1 ) + wA2 N(1/λ2, σ2 ) , in which the wi terms are the weights. In practice each of the three terms represents the superposition of contributions from many NOM species acting in the same ‘mode’ [see 597].

S7▪3▪2

Analysis

Applying the fit of equation S7-10 to four different spectra by least squares regression yielded the parameters given in Table S7-1. The spectra and their suggested components are plotted in Figure S7-1 and Figure S7-2. The scattering is only significant at the lowest wavelengths, and the question may arise how important is the choice of the domain over which the spectrum is to be fitted. The choice of a lower limit of 230nm is a practical choice that includes the majority of the peak data (as the λ are all significantly larger than 230nm, with sufficiently small σi2), and a good portion of the cut-off in absorbance. Below this wavelength the absorbance continues to increase rapidly for all samples, and the sample transmittance is too low for the instrument to detect accurately. It is notable that the λ2 values corresponding to the second (smaller) absorbance peak associated most directly with the hump or peak in the experimental spectra are all quite consistent (irrespective of raw water date), in the range 2 6 2 ± 4 n m , and are not significantly affected by the treatment with either coagulant (there is a small increase in λ2 upon treatment).

*

I.e. particle sizes in the range 10 to 150% of the incident wavelength [801].

†

At a ratio on the order of 10, the laws of geometric optics begin to apply [33].

‡

BABINET’s Principle suggests that for particles very large compared to the incident wavelength forward scattering is proportional to V4/3 / λ2 [506]. This result appears consistent with a separate derivation for “very large spheres” [506]. Appendix S7 : Light Absorbance

851

D. I. VERRELLI

Table S7-1: Ultraviolet absorbance curve-fit parameters (used in equation S7-10).

Sample code Sample description

A Raw water (Winneke)

C Raw water (Winneke)

2004-09-15

B 1.6L of A, treated with 80mg(Fe)/L at pH ~ 7.3 (2004-11-24)

2005-04-05

D 48.4L of C, treated with 79mg(Al)/L at pH ~ 6.3 (2005-08-17)

Sample date Scattering wS [nm] m [–] Absorbance 1 wA1 [–] λ1 [nm] σ1 [–] Absorbance 2 wA2 [–] λ2 [nm] σ2 [–] Humic peak [nm]

227.1 23.24

224.4 32.69

226.1 30.84

225.4 40.82

0.0006205 265.6 0.0006725

0.00006102 287.0 0.0004803

0.0003981 265.1 0.0006270

0.00005133 290.0 0.0003940

0.00009757 258.2 0.0002857 N/A

0.00006561 262.3 0.0002737 264

0.0003981 261.8 0.0002163 259

0.00003401 265.0 0.0002034 265

It can be seen that the λ2 values of the component peaks are highly consistent with the experimental humic peaks (spectrum A exhibited only a ‘hump’). This data suggests that a value of around 2 6 2 n m may be most appropriate to characterise the humic content of raw and treated waters. This value is consistent with the 260nm wavelength used for detection of NOM by NEWCOMBE & COOK [778]. The values are below those associated with NOM aromaticity (~280nm) [553, 554, 647] and maximum susceptibility to chlorination (272±4nm) [657]. There is no indication of a constituent peak at ~330nm, typical of fresh ferric solutions (ascribed to Fe2 species) [325]. Other metals are not expected to interfere [see 597]. Values of σ2 are not significantly affected by the treatment process (there is a slight decrease), but are significantly different for the two dates. The λ1 values for both raw waters fall in the same range as the λ2 values (tending to be slightly larger). However the λ1 values exhibit a significant increase following water treatment, to around 289±2nm. Values of σ1 are significantly decreased by the treatment process, and are similar on the two dates (with different coagulants). The exponent, m, for the absorbance cut-off is unexpectedly high, in the range 23 to 41, with a tendency to increase following treatment. This may suggest either that MIE scattering is occurring (with the RAYLEIGH scattering effect at higher wavelengths too small to identify) or that some other mechanism is prevailing. Spectra from a number of other samples also exhibit humic ‘peaks’ rather than the more usual ‘humps’, permitting more accurate curve fitting.

852



1.000

A : Raw water 20040915 Inverse power

0.900

Gaussian 1

0.800

Gaussian 2 Sum

Aλ [10/m]

0.700

B : 80mg(Fe)/L; pH 7.3 Inverse power

0.600

Gaussian 1

0.500

Gaussian 2 Sum

0.400 0.300 0.200 0.100 0.000 200

250

300

350

400

450

λ [nm] Figure S7-1: Absorbance spectra and components thereof for a raw water and the supernatant resulting from coagulation of the raw water with ferric chloride at 80mg(Fe)/L, pH ≈ 7.3.

KORSHIN, LI & BENJAMIN [597] developed a somewhat different model, comprised of three GAUSSian terms, associated with different excitation modes — and no scattering term. It was hypothesised that the centres of all three peaks would remain constant, and these were found to be at ~180, ~203, and ~253nm for NOM in various raw and treated natural waters [597]. The accuracy of these values seems open to question given that they are practically identical to the (known) bands of benzene, on which the model was based. It may be possible that the assumption of small peak overlap and specification of initial ‘guesses’ for the peak centres in the iteration procedure combined to return parameters close to the starting values. Besides that, their spectra [597] showed only indistinct shoulders [see also 456, 512], so that uncertainty (or flexibility) in their fitting parameters was presumably greater than in the present case.


853

D. I. VERRELLI

0.700

C : Raw water 20050405 Inverse power

0.600

Gaussian 1 Gaussian 2 Sum

Aλ [10/m]

0.500

D : 80mg(Al)/L, pH 6.3 Inverse power

0.400

Gaussian 1 Gaussian 2 Sum

0.300 0.200 0.100 0.000 200

250

300

350

400

450

λ [nm] Figure S7-2: Absorbance spectra and components thereof for a raw water and the supernatant resulting from coagulation of the raw water with aluminium sulfate at 79mg(Al)/L, pH ≈ 6.3.

In conclusion, curve fits were obtained for the region of the humic peak in UV–visible spectrophotometric absorbance scans for the first time. The absorbance peak associated most directly with the hump or peak in the experimental spectra is centred consistently on 262±4nm. This lies between the common UV measurement point of 254nm and the range associated with aromaticity and chlorine susceptibility, viz. ~272 to 280nm.

S7▪4

Deviation from B E E R ’s law

Apparent non-linearities in the correlation between absorbance of visible light at a particular wavelength (or wavelengths) and true colour may be expected due to: • the presence of turbidity; • errors in absorbance or true colour determination (including operator or instrument bias);

854



• change in the underlying (population) correlation o over the data collection period *, o across a number of locations, or o with respect to different water treatment conditions; • inherent non-linearities manifest as deviations from BEER’s law for the water samples. Scattering of light due to particles passing through a 0.45μm filter “becomes significant” for wavelengths of light below 400nm [139], and so this may constitute a lower bound on possible wavelengths for true colour measurement. Filtration down to 0.2μm is an alternative, but is rarely used in practice [139]. BENNETT & DRIKAS [139] found that estimation of true colour from 456nm absorbance assuming a linear relation would introduce a negative error (i.e. overestimate) for low colours and a positive error (i.e. underestimate) for high colours. The errors were of magnitude ≤ 20% at this wavelength, but varied significantly from close to zero at the pseudo-isosbestic point of 570nm to much larger errors at 400nm and into the ultraviolet range [139]. The nature of these errors imply that absorptivities calculated from samples of high colour are likely to be greater than those for samples of low colour. BENNETT & DRIKAS [139] suggested that this phenomenon may be due to aggregation effects causing a deviation from BEER’s law. Similarly, the Yorkshire Water data [124, 1105] a l l predict a positive intercept of true colour at zero 400nm absorbance — albeit that not all are statistically significant. An alternative explanation may be that the sample absorbances include an underlying low, nearly-constant contribution due to fine particulates.

S7▪4▪1

Case study:

Yorkshire Water data

The raw data [124] used by WATTS et alia [1105] has been analysed together. This data consists of paired true colour and 400nm absorbance data for 0.45μm filtered water samples from nine sites in Yorkshire from August 1997 to June 1998 [1105]. Absorbances were measured in a spectrophotometer (reported in m–1), while true colour (reported in Hazen ~ mg/L Pt units) measurement was performed by a computer robot [124, 1105]. It was desired to further analyse the data statistically to test for possible curvature in the relation between 400nm absorbance and true colour. A detailed statistical analysis [with reference to 755, 886, 1096] was inconclusive. Numerous combinations of polynomial models and sites suggested the existence of significant curvature in the raw data — however the result did not hold for individual sites, and the orientation of the purported curvature was not consistent, varying according to the choice of independent and dependent variables. It would appear that curvature effects are less important than variation in samples at a given site and between different sites.

*

Especially in the event of extreme weather, such as drought or flooding. Appendix S7 : Light Absorbance

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D. I. VERRELLI

S8. S8▪1

COLOUR MEASUREMENT

Traditional determination of true colour

The human eye responds to wavelengths from 380 to 760nm, with a maximum sensitivity at 556nm [139]. This peak sensitivity corresponds to the yellow (or greenish-yellow [334]) spectral region that is especially relevant to colouration of natural waters [139]. The platinum–cobalt visual comparison method proceeds with the estimation of colour, referenced to a set of standards, in “mg/L Pt units” [4]. The standards are composed of an approximate 2:1 mixture of platinum and cobalt salts [4, 270, 334]. A 1000mL stock solution with a colour of 500 mg/L Pt units is prepared from the equivalent of 500mg of Pt as potassium hexachloroplatinate (IV) (K2PtCl6), 1.00g of crystallised cobalt (II) chloride hexahydrate (CoCl2·6H2O), 100mL of concentrated hydrochloric acid, and distilled water [4, 270, 334]. In the present work pre-prepared 500mg(Pt)/L platinum–cobalt standards (Hach, U.S.A.) were used for true colour calibration. The stock solution is diluted with purified water to produce the reference standards according to Table S8-1. Table S8-1: Concentrations of standard platinum–cobalt colour solutions.

Colour [mg/L Pt units] 5 10 15 20 25 30 40 50 60 70 100

Dilution Used in ISO 7887:1994 [mL of stock / 50mL] [4] 0.5 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 10.0

Yes Yes No Yes No Yes Yes Yes Yes Yes No

Used in 2005 U.S. Standard Methods [334] Yes Yes Yes Yes Yes Yes Yes Yes No No Yes

Using matched 50mL NESSLER tubes in tall form (~20cm *), the sample is compared against the various reference standards by observation looking down the tube toward a white or “specular” surface [4, 334]. If the sample colour exceeds 70 mg/L Pt units, then it must be diluted with distilled water. This can introduce errors if particulate material dissolves in the diluted sample [139]. Fortunately, such an effect would be minimal provided that dilution is carried out after

*

856

CROWTHER & EVANS [290] used a sample depth of 110mm. Appendix S8 : Colour Measurement


filtration (or centrifugation). The pH (and temperature) must be measured after the final dilution. Colour is strongly dependent upon pH, and is also influenced by temperature [4]. For this reason the pH at which a colour measurement is made must be recorded. The temperature may be recorded. For rigorous investigation it may be advisable to a d d i t i o n a l l y measure all colours at a common pH (e.g. 7, given by the current U.S. Standard Methods *) through appropriate addition of acid (HCl) or base (NaOH) †, especially if the raw values lie outside the range 4 to 10 — or even to determine the colour response across a range of pH values [334]. However it must be noted that these values “may not reflect the colour of the water in situ” [139] — it is recommended that the sample at its original pH a l s o be analysed [334], as this is what the ‘consumer’ will see. Experimentally the specification of the standard pH value too close to 7.0 may not be practical. SINGLEY, HARRIS & MAUDLING [943] published a nomograph which suggested that the r e l a t i v e variation of colour ‡ with pH was not significantly affected by the ( a b s o l u t e ) amount of colour present, nor by the particular value of pH (i.e. only the pH change). However they stated that dependence on pH “becomes less important as the colour value decreases” below about 50mg/L Pt units [943]. (Although BLACK & CHRISTMAN [157] reported the opposite finding, re-analysis of their raw data revealed that the identified trend was not statistically significant §.) Furthermore, a separate figure in their paper [943] implies that the influence of the pH on the measured colour decreases as the pH decreases, being negligible for many purposes below about pH 4 or 5; a similar trend was observed by BLACK & CHRISTMAN [157], who added that the process was reversible. It is also noted that many natural and finished (i.e. treated) waters have pH values close to the standard pH value in any case, and little colour change occurs upon pH adjustment [943]. Correlations with other water properties may also be improved when original pH is retained [456]. Finally, it was observed that pH adjustment on the desired scale is often subject to experimental error [943]. For these reasons no pH adjustment was carried out for the colours reported in the present work. All samples were at room temperature when analysed — no temperature artefacts were seen.

*

An alternative ‘standard’ pH is 8.3 [155, 159] or 8.4 [157], chosen as being “a representative value for finished waters” [943]. Previous editions of the U.S. Standard Methods [270] quoted a reference pH of 7.6, which was presumably a practical compromise in view of the difficulty in adjusting sample pH to 7.0.

†

These should be sufficiently concentrated as to keep the resulting volume change below 3% [334].

‡

It was not made clear whether this was strictly true colour, or apparent colour.

§

Removing one (the smallest colour change) of the points from their data set of ten points simultaneously reduced the magnitude of the trend and reduced its coefficient of determination, R2, from 0.2 to 0.0. Appendix S8 : Colour Measurement

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D. I. VERRELLI

S8▪2 S8▪2▪1

Single-wavelength estimation Justification for wavelength specification

Measuring absorbance at only a single wavelength has the disadvantage that it can only be used reliably to characterise samples of a certain colour. It is important to remember that this is also true of conventional visual comparison, which many absorbance-based measures seek to emulate. CROWTHER & EVANS [290] found that the absorbance spectra for several surface waters and groundwaters, along with their colour-causing constituents (typically humates and lignins for the former, and iron and manganese salts for the latter), were all similar. However the trends they exhibited were not shared by standard platinum–cobalt suspensions they examined. Some studies have determined colour by using real water samples as ‘standards’ and correlating their o p e r a t o r - a s s e s s e d colour with their absorbance at wavelength λ. If the method of colour determination is used in which colour is equated to that of a platinum–cobalt standard of equal absorbance, then the wavelength at which the absorbance is measured is especially important. Different wavelengths will predict very different true colours, as shown by the ratio of normalised absorbances in Figure S8-1. HONGVE & ÅKESSON [487] demonstrated that raw water absorbances at 410nm, 450 to 460nm, and 490 to 500nm are, on average, equal to those of a matched reference solution of platinum–cobalt (consistent with the results of BJÄRNBORG). Between 400 and 500nm, colours computed at two different wavelengths could differ by as much as a factor of 2.5 from each other: from 30% too low (at 400nm) to 80% too high (at 427nm) [487]. (CUTHBERT & DEL GIORGIO [291] found far greater differences in the range 300 to 440nm: potentially a factor of > 4 difference in colour estimates.) See also Figure S8-1. Of the three possibilities mentioned, HONGVE & ÅKESSON [487] preferred 410nm, where the absorbance is higher. This recommendation has been adopted by a number of investigators, especially in Norway [e.g. 400]. Looking in more detail at the results of STARK, presented by HONGVE & ÅKESSON [487], a wavelength that will correlate correctly with visual colour comparison lies b e t w e e n 450 and 465nm. Linearly interpolating over each sub-domain and minimising the squares of the errors yields 460nm as the wavelength of best correlation. CROWTHER & EVANS [290] identified three light source specifications: 412nm, 460nm, and a range 405 to 450nm (from a broad-band filter). They found that the “integrated” result from the broad-band filter gave the best correlation. The 460nm wavelength yielded acceptable results, while the 412nm wavelength yielded inferior results in their assessment. It is noteworthy that Hach provides a (nominally) 455nm interference filter assembly module for (approximate) colour measurement [19]. Experimental measurements showed that the transmittance exceeds 10% for wavelengths between 450 and 464nm.

858

Appendix S8 : Colour Measurement


Normalised absorbance, Aλ /A 400nm [–], and ratio thereof [–]

10

1

0.1

0.01 350

Platinum–cobalt Median platinum–cobalt Raw and coagulated water Median water ~Upper bound on ratio Median water / median Pt–Co ~Lower bound on ratio

400

450

500

550

600

Wavelength, λ [nm] Figure S8-1: Absorbances for raw and coagulated water, and for platinum–cobalt colour standards, all normalised such that A400nm is plotted as unity. In this range the water absorbance spectra vary approximately exponentially (green).

HAUTALA, PEURAVUORI & PIHLAJA [456] recommended that true colour be correlated by absorbance measurements at either 410nm or 465nm, with the latter yielding the most favourable results for natural water samples (at their original pH values). For some wavelengths the correlation between operator-observed colour and absorbance was greater when the water sample was analysed at its natural pH (~5.7), while for others it was greater when the pH was adjusted (to 7.0) [456]. As each sample contains a different proportion of species that absorb most strongly at a given wavelength, there is no universal rule for adjusting the pH. Comparisons [456] indicate that in many cases it is preferable not to adjust the pH at all. BENNETT & DRIKAS [139] surveyed analytical methods of colour determination in use in 1993 around Australia and in Britain and the U.S.A., as well as those recommended by instrument manufacturers. Light absorbance methods which were referenced to the platinum–cobalt colour scale variously used wavelengths of 395nm, 400nm (in two cases), 420nm, 436nm,


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D. I. VERRELLI

455nm, or 465nm (as in STEVENSON [see 456]) [139]. Additionally, KIRK’s determinations were carried out at 440nm [139], described in 1992 as “the most frequently used” wavelength for spectrophotometric determination of colour [291]. (Other wavelengths have been proposed for correlation with properties other than true colour [see 456].) BENNETT & DRIKAS [139] converted absorbance profiles measured spectrophotometrically into “transmission response profiles” (TRP’s) based on illuminant A, a standard light source representative of incandescent light globes * [see 260], and the spectral sensitivity of the average human eye. Despite the greater rigour of TRP computation, it was recognised that correlation with absorbance at a single wavelength is more practical in many laboratories [139]. BENNETT & DRIKAS [139] concluded: Only wavelengths in the region 445–470nm however, will produce results which agree with comparator measurements and minimise the dependence on water composition.

Correlation with absorbance at 456nm was recommended, with an absorptivity of 0.027m‒1.(mg/L Pt units)‒1 [139]. BENNETT & DRIKAS [139] showed by normalisation of raw water absorbance spectra by true colour † that use of this s i n g l e w a v e l e n g t h would introduce a negative error (i.e. overestimate) for low colours and a positive error (i.e. underestimate) for high colours, with each of these having a magnitude of ≤ 20%. (See also §S7▪4.) Analysis of their data [139] indicates that selection of a wavelength of 460nm would bias the accuracy in favour of lower colours. However, this may be appropriate for examination of raw waters of low colour and treated waters, given that BENNETT & DRIKAS [139] looked exclusively at raw waters, some of which had colours of > 150mg/L Pt units. By analogy to the results of CROWTHER & EVANS [290], BENNETT & DRIKAS [139] found that averaging absorbances over the range 445 to 470nm yielded an improvement in accuracy, but which was classed as “marginal” and “of no significant advantage”. In examining scans of the platinum–cobalt standards (see Figure S8-2), it can be seen that there is a definite, broad peak at about 460nm, whereas e.g. 410nm and 490 to 500nm each correspond to positions on the sides of a peak. These locations mean that the middle wavelength domain is preferred — BEER’s law can be expected to be more applicable for peak absorbances. In contrast raw and treated water generally have no discernable absorbance peak in the visible spectrum, and indeed can be fitted quite well by exponentials (see §S7▪2). From the gradients of the spectra, selection of 460nm should minimise any errors arising from bias in the instrument wavelength. Furthermore, of the three options mentioned, the ∂Aλ relative difference between the gradient for water and for platinum–cobalt colour ∂λ standard is highest at 410nm, implying an undesirable amplification of errors at that wavelength.

*

Illuminant D65, corresponding to natural light [see 260], may have been a better, less colour-biased choice.

†

The normalised spectra exhibited an isosbestic point at about 570nm, which “reflects the matching of water colours to the standard in the yellow spectral region” [139].

860



1.0

mg(Pt)/L

0.9

500 71.5 60 50 40 30 20 10 5 1

Absorbance, Aλ [10/m]

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 200

300

400

500

600

700

Wavelength, λ [nm] Figure S8-2: Absorbance of platinum–cobalt colour standards.

Following publication of the research discussed above, the new “ p r o p o s e d ” singlewavelength method was introduced into the 2005 U.S. Standard Methods [334]. The wavelength of interest may be specified from 450 to 465nm, with 456nm being especially recommended — no spectral bandwidth (SBW) provision is stated, but in the alternative methods a maximum of 10nm is stipulated [334]. Calibration is against standard platinum– cobalt solutions of dilutions as in Table S8-1. In industry it is common to use a single wavelength of 400nm for colour measurements correlated against platinum–cobalt standards [95, 475]. Absorbance measurements at 400nm are more usefully used unmodified, as by EGGINS, PALMER & BYRNE [337] and in the pre1989 European Community water supply (water quality) regulations [1105]. The European Community requirement for treated water absorbance at 400nm to be below 1.5 per metre was “considered to be equivalent to” 20 mg/L Pt units of true colour [1105]. This implies an absorptivity at 400nm of 0.075m‒1.(mg/L Pt units)‒1.


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D. I. VERRELLI

The 1993 Japanese Drinking Water Test Methods published by the JWWA advised ‘colour’ measurements be carried out using absorbance at 390nm [477]. This measurement has been criticised as producing a result that is “different from [the] human sense” [477].

S8▪2▪2

Variation by site

CUTHBERT & DEL GIORGIO [291] note that absorptivities at 440nm for lakes in Quebec and Sweden were “similar”, but were “significantly different” to those for Tasmanian lakes: the latter had, on average, the highest true colour — up to 600mg/L Pt units — and the lowest absorptivities. WATTS et alia [1105] presented linear regressions for absorbance and true colour at nine sites in Yorkshire. 400nm absorptivities ranged from 0.077m‒1.(mg/L Pt units)‒1 to 0.090m‒1.(mg/L Pt units)‒1 [1105]. At two sites a non-zero (positive) true colour at zero absorbance remained significant at the 99% level, so the absorptivity is undefined [1105]. Analysis of the raw data [124] showed that a further two sites had non-zero (positive) true colour intercepts at the 95% level of confidence. See also §S7▪4▪1. Conversion factors applied previously in the Yorkshire Water district varied somewhat, and are equivalent to the following absorptivities at 400nm [124]: • 1/15 ≈ 0.066m‒1.(mg/L Pt units)‒1 in West Yorkshire — largely surface water from upland acid moorlands • 1/12 ≈ 0.083m‒1.(mg/L Pt units)‒1 in North Yorkshire — water abstracted from springs, rivers, and boreholes • 1/10 ≈ 0.100m‒1.(mg/L Pt units)‒1 in South Yorkshire — upland acid moorlands, with a few boreholes Enhanced colours are expected in regions whose soils have significant proportions of peat, in particular the upland areas [1105]. A decision has since been made to standardise the conversion factor, equivalent to an absorptivity of 1/12 ≈ 0.083m‒1.(mg/L Pt units)‒1 [124]. (Recall that in the present work an absorptivity of 0.088m‒1.(mg/L Pt units)‒1 was found at 400nm.)

S8▪3 S8▪3▪1

Quantitative description of colour by standard colourimetry Colour spaces

A multitude of colour systems (or colour ‘spaces’) have been developed over time to quantitatively represent perceived colour. There are numerous systems for describing colour, including: • “RGB” — a colour cube where a colour is defined in terms of its (nominally) Red, Green and Blue components — often with each component quantified on a scale from 0 to 255 (i.e. 28 graduations each, for a total of 23×8 = 224 = 16777216 colours). • CMYK — similar to RGB, but using Cyan, Magenta, Yellow, and Black. 862



• MUNSELL — parameters of hue, lightness (or ‘value’), and chroma [1134]. A number of other colour spaces were developed by the CIE, of which the established and recommended varieties are published as technical reports [260 or revised edition] *, which form the basis of a number of international and national standards [see 1093]. Important CIE systems are [260, see also 1134]: • XYZ — colour is represented by the intensity of its component tristimulus values X, Y and Z, corresponding to stimulation by hypothetical † supersaturated red, green and blue pure colours. • xy — chromaticity defined based on normalised X, Y and Z (so z = 1 – x – y), with lightness given by unscaled Y. Used as the basis of one method for measuring colour by the U.S. Standard Methods [334]. • u′ v′ — similar to xy, but with chromaticity co-ordinates normalised according to human colour perception; lightness is given by unscaled Y. • L∗u∗ v∗ — similar to u′ v′, but with chromaticity co-ordinates further normalised according to human colour perception and lightness given by L∗ (scaled Y); called “CIELUV”. Of the above colour spaces, the one most suited to describing colour as perceived ‡ in human vision is CIELUV [173, 260]. The major part of its improvement over the u′ v′ system is the provision made for the effect of the illuminant § [260]. CIELUV is especially suited to the analysis of transmitted light [173], such as through a (fluid) solution — distinct from light reflected from a (solid) surface.

S8▪3▪2

Important parameters

Numerous terms are used in the description of colour, many of which can be considered either exact or approximate synonyms [cf. 1134]. The colour parameters or terms in Table S8-2 specify approximately equivalent properties.

*

Ironically, the two authoritative colour science references [260, 1134] are printed in black & white.

†

Each hypothetical supersaturated single-wavelength colour is constructed as the sum of a spectrum of colours, where the colour intensity of the spectrum varies according to the wavelength.

‡

The differences are akin to those between the dB and dB(A) scales of audiology.

§

The CIE and other sources describe numerous illuminants, however the most useful, relevant and commonly used standard is D65, which represents “a phase of daylight with a correlated colour temperature of approximately 6500K” [173, 260, cf. 334]. Appendix S8 : Colour Measurement

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D. I. VERRELLI

Table S8-2: Approx imat e equivalencies and related terms for colour space parameters [173, 260, 334, cf. 1134].

CIE Lightness

Saturation

Hue-angle

Note:

a

Alternative Value Brightness a Relative brightness Luminance (Light) intensity a Chroma Excitation purity Colorimetric purity Chromaticness Dominant wavelength Hue

Plain-English Lightness/darkness Amount

Examples 99.9

Brightness/dullness a (Colour) intensity a Colourfulness

0.007 0.5% Pastel

‘Colour’

Greenish-yellow 570nm 85°

Some terms are ambiguous unless associated with a specified colour scheme.

The following parameters have been precisely defined by the CIE and can be uniquely established for a given sample and illuminant [260]: • Excitation purity (1931) [%] — fraction displacement away from the illuminant (pure ‘white’ *) in the direction of the chromaticity envelope (pure colour). • Colorimetric purity [%] — a modification of the excitation purity to decrease the influence of the illuminant. • Dominant wavelength [nm] — the intersection of the line extrapolated from the illuminant through the sample point to the chromaticity envelope. • Hue — a descriptive nomenclature (e.g. “Yellowish green”, “Yellowish orange”), assigned according to the dominant wavelength. and specifically within the “1976 Uniform Colour Space” — i.e. compatible with CIELUV: • L∗, CIE 1976 lightness — the adjusted ratio of the Y component of the sample stimulus intensity to that of the illuminant (conventionally defined as identically 100). • suv, CIE 1976 u,v saturation — like purity, this measures a displacement of the sample point away from the illuminant on the chromaticity diagram; a measure of “the [...] degree to which a chromatic stimulus [or sample] differs from an achromatic stimulus [or reference] regardless of their brightness” [1134]. • C∗uv, CIE 1976 u,v chroma — a measure of “the [...] degree to which a chromatic stimulus [or sample] differs from an achromatic stimulus [or reference] of the same brightness” [1134]. • huv, CIE 1976 u,v hue-angle [°] — an alternative to the dominant wavelength or hue, where the hues are described by angles (up to 360°) on a disk. Of these quantifiers, L∗ appears to be the least sensitive to the illuminant chosen. Typical values of the parameters are illustrated for several samples in Table S8-3.

*

864

Of course, the whiteness of the illuminant can vary. Appendix S8 : Colour Measurement


Table S8-3: Typical values of colourimetric parameters. Sample ‘A’ is Winneke raw water (collected 2004-07-05); sample ‘B’ is sample A plus 1.25% dMIEX; sample ‘C’ is sample B treated with 80mg(Al)/L at pH ≈ 6.4. The illuminant is D65.

[mg/L Pt units] [10/m] A254nm A400nm [10/m] A460nm [10/m] True colour [mg/L Pt units] A700nm [10/m] A405–450nm [10/m] Excitation purity (1931) [%] Colorimetric purity [%] Dominant wavelength [nm] Hue L∗, CIE 1976 lightness u∗ v∗ suv, CIE 1976 u,v saturation C∗uv, CIE 1976 u,v chroma huv, CIE 1976 u,v hue–angle u′ v′ x y Intersection on envelope, x Intersection on envelope, y X Y Z

S8▪3▪3

[°]

Platinum–cobalt std. 500 5 9.9979 3.8656 3.5149 0.0447 1.3487 0.0135 506 5 0.0059 0.0002 1.5685 0.0158 85.45 1.48 89.79 2.35 579.1 573.8 Yellow Greenish Yellow 86.62 99.82 58.0435 0.6636 92.1572 2.4833 1.25736 0.02575 108.9128 2.5704 57.8 75.0 0.2494 0.1983 0.5502 0.4703 0.4782 0.3151 0.4689 0.3320 0.5064 0.4704 0.4927 0.5285 70.61 94.45 69.23 99.53 7.81 105.82

Water samples A B C 0.6335 2.4369 0.2084 0.0601 0.2456 0.0111 0.0231 0.1038 0.0041 9 39 1 0.0021 0.0073 0.0011 0.0389 0.1660 0.0070 2.56 11.02 0.41 4.08 16.54 0.66 573.3 574.1 572.4 Greenish Greenish Greenish Yellow Yellow Yellow 99.27 96.82 99.84 1.0293 4.9667 0.1287 4.3040 17.3008 0.7046 0.04458 0.18590 0.00717 4.4253 17.9996 0.7163 76.5 74.0 79.6 0.1986 0.2018 0.1979 0.4717 0.4821 0.4689 0.3167 0.3303 0.3133 0.3342 0.3508 0.3299 0.4673 0.4726 0.4608 0.5316 0.5263 0.5381 92.98 86.64 94.60 98.13 92.00 99.60 102.50 83.64 107.73

Fitting objective parameters to observermeasured colour

In a small trial, suv was found empirically to correlate best with perceived ‘colouredness’ of raw waters. The trial involved visual comparison of raw water spiked with dialysed MIEX eluate (“dMIEX”, see §6▪2▪1) and platinum–cobalt standards of various dilutions by an (‘untrained’) panel. The colourimetric parameters of sample–reference pairs judged visually to have ‘equivalent’ colouration were computed based on spectrophotometric measurements, and suv appeared to be the most influential parameter. It is also possible to conceive of some function that involves more than one CIE parameter. In particular, an analogy can be drawn between the “true colour” of raw or treated water and the “redness rating”, Rredness, used to describe soil colour: Rredness = (10 – H) C / V , [S8-1]


865

D. I. VERRELLI

(H, C, and V are the hue, chroma and value * used in the MUNSELL Colour System) because it has been found to vary almost linearly with hæmatite concentration [280].

*

866

That is, the shade of colour, its intensity, and its lightness (respectively) [280]. Appendix S8 : Colour Measurement


S9.

EVALUATION AND SELECTION OF SYRINGE FILTERS

Measurement of the sample true colour, absorbance, or dissolved organic carbon (DOC) requires the removal of turbidity and particulate organic matter in a ‘pre-filtration’ operation prior to measurement. Syringe filters are commonly used for this task, and were employed in the present work. While these devices have several advantages, a number of concerns remain in relation to the potential for interference with the sample properties. The following sections provide guidelines to assist in syringe filter selection, and also demonstrate the appropriateness of the syringe filters used in the present work. A membrane pore size of 0.45μm was employed for convenience, on account of its suitability for DOC, true colour and light absorbance applications, as discussed below.

S9▪1

Interferences

There are three main sources of potential error in pre-filtration of water samples [e.g. 553]: 1. S o l u t e a d s o r p t i o n . This can be reduced by discarding an initial portion of filtrate, as per previous editions of the U.S. Standard Methods [270]. This assumes that the adsorption sites on the filter become ‘saturated’ with solute. Some workers contend that this does not significantly affect true colour measurement *. 2. C o n t a m i n a t i o n b y f i l t e r . This can likewise be reduced by discarding an initial portion of filtrate. The current U.S. Standard Methods [334] recommendation for true colour direct that the filters be rinsed before use (with pure water) and the filtrate monitored. This assumes that loose matter in the filter is cleaned out by the preliminary filtration. One report suggests that such contamination is more significant for glass or paper-based filters, and less significant for polymeric membranes [487]. Contamination due to leaching or dissolution of chemical residuals from the membrane can also occur [553]. 3. P a r t i c l e b r e a k - t h r o u g h . BENNETT & DRIKAS [139] found that the turbidity of filtrate from 0.45μm filters rises initially as the volume of water filtered increases, which they attributed to “progressive blocking of filter pores”. After a significant volume of water had been filtered (of order > 0.1m3/m2), the turbidity of the filtrate exhibited a tendency to decrease [139]. The extent of particle breakthrough varied between filter brands [139]. Particle break-through was found to be negligible following filtration through 0.10μm filters [139]. However, given that true colour is d e f i n e d (in the ISO 7887 standard [4]) as the colour of the filtrate following 0.45μm filtration, it is

*

E.g. HONGVE & ÅKESSON [487] seem to attribute colour reduction upon filtration to retention of (some of the larger) particles in the water. Appendix S9 : Evaluation and Selection of Syringe Filters

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D. I. VERRELLI

possible that filtration to lower sizes may remove some of the true colour due to removal of an additional colloidal fraction to which coloured compounds may be adsorbed [139]. The work of BENNETT & DRIKAS [139] indicates that interference with true colour is negligible provided the turbidity value (in NTU) is less than 2% of the colour (in mg/L Pt units) *. If necessary, the sample may be refiltered. A further concern is the formation of a dense filter cake that effectively reduces the pore size of the filter, so that the pre-filtration yields an ‘excessively pure’ filtrate. As a general rule paper filters should not be used for pre-filtration, to avoid contamination of the sample with organic paper fibres [979].

S9▪2

Light absorbance

Scattering of light due to particles passing through a 0.45μm filter “becomes significant” for wavelengths of light below 400nm [139]. Given that this is at the extreme of human vision (380 to 760nm [139]), it seems unlikely that this would interfere with ‘manual’ colour determinations. However, absorbance of light by particles can still be significant at higher wavelengths, which can lead to errors when the reference standard is particle-free.

S9▪2▪1

True colour

ISO 7887 [4] defines true colour as the remaining colour that is measured after passing the sample through a 0.45μm filter. The latest U.S. Standard Methods [334] do not prescribe a single means of separating the suspended matter: usually 0.45μm membrane filtration (cellulose acetate, 22 or 47mm diameter) is recommended; glass fibre filters are an alternative for routine testing (typically 40 to 60μm equivalent pore size [e.g. 270]); filters of pore size ~0.2μm or even smaller may sometimes “be needed to remove colloidal particles [e.g.] Mn or Fe oxides”. Centrifugation is no longer recommended. For comparison, by progressive membrane filtration BLACK & CHRISTMAN [157] found that the majority of colour-causing colloids in raw water were of size 4.8 to 10nm. The U.S. Standard Methods [334] additionally specify that the filters should be held in assemblies made of either glass, poly(difluoromethylene) [cf. 548], or stainless steel — to minimise contamination.

S9▪2▪2

Ultraviolet absorbance

Ultraviolet absorbance measurements are of interest in their own right, but are also required for the evaluation of SUVA. Separate recommendations have been developed for each. Particles are removed by filtering with a 0.45μm filter, as per U.S. EPA Method 415.3 [846]. The U.S. Standard Methods [334] recommends various alternatives for filtration, including

*

868

This limits the absorbance due to turbidity to contribute no more than about 20% of the total absorbance [139]. Appendix S9 : Evaluation and Selection of Syringe Filters


glass (free of organic binder) depth filters of nominal pore size 1.0 to 1.5μm, and poly(difluoromethylene) [cf. 548], polycarbonate, and silver membranes. A 2002 survey by KARANFIL, SCHLAUTMAN & ERDOGAN [555] found that in practice many laboratory workers use alternative filters: both different pore sizes (0.2 to 1.6μm) and different materials (nylon, cellulose, PES, et cetera). KARANFIL, ERDOGAN & SCHLAUTMAN [553] re-examined this issue from the perspective of minimising interference with the readings. In contrast to the high sensitivity of the DOC measurements, measurements of A254nm were significantly affected only by polyamide (nylon) membranes, this being due to adsorption rather than leaching — fulvic acids adsorbed more strongly than humic acids [553]. Some workers omit the filtration entirely for low-turbidity samples [555], although experience has shown that absorbance is sensitive to even fairly low levels of turbidity (e.g. from filter membrane failure) .

S9▪2▪3

Evaluation

Experiments showed that for filtration through a 0.45μm nylon filter the initial portion of filtrate tended to have a slightly higher ultraviolet absorbance (Figure S9-1), and possibly colour (Figure S9-2), than the following portions of filtrate. This suggests that additional organic material is able to pass through the filter in the initial portions of filtrate, before a layer of captured material on the filter surface adds additional resistance, consistent with the particle break-through described by BENNETT & DRIKAS [139] (mechanism 3 in the list from p. 867) or contamination by the filter, especially leaching, described by KARANFIL, ERDOGAN & SCHLAUTMAN [553] (mechanism 2). The results confirm that for increased accuracy the initial portion of filtrate should be discarded. Subsequent portions of filtrate showed fairly steady absorbances, even after filtering relatively large volumes, with a possible tendency towards a marginal increase. If this is a real phenomenon, then it would presumably be due to additional break-through, perhaps of previously retained material, possibly due to the increased pressure that must be applied and/or degradation of the membrane. The results indicate that the ‘volumetric capacity’ of the membrane is not exceeded under the conditions described. In no case was any clear evidence of solute adsorption (mechanism 1) found *. Employing syringe filters with nominal diameter of 25 to 26mm, the practice of discarding the first 25mL of filtrate was found to result in absorbance spectra which were practically indistinguishable for PES and SFCA membranes (Figure S9-3). The largest variations occurred in the ultraviolet range, but were not significant. This indicates that interference by the membrane with the measurement is negligible, and matches the findings of KARANFIL, ERDOGAN & SCHLAUTMAN [553].

*

The only candidate for such behaviour is the 400nm absorbance of the treated water: deviation in the absorbance of the first portion of filtrate m a y have been dominated by extractables from the filter despite some adsorption of organics, while for the immediately following portions of filtrates adsorption of organic matter m a y have come to dominate any deviation from the ‘correct’ value. Appendix S9 : Evaluation and Selection of Syringe Filters

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D. I. VERRELLI

Ultraviolet absorbance, A 254nm [10/m]

0.400 0.350 0.300 0.250 Raw water at 254nm 4mg/L Al at 254nm

0.200 0.150 0.100 0.050 0.000 0

12.5

25

37.5

50

62.5

75

87.5 100

Volume passed through filter [mL]

0.040

0.0040

0.035

0.0035

0.030

0.0030

0.025

0.0025 Raw water at 400nm Raw water at 460nm 4mg/L Al at 400nm 4mg/L Al at 460nm

0.020 0.015

0.0020 0.0015

0.010

0.0010

0.005

0.0005

0.000

Treated water absorbances, A 400nm and A 460nm [10/m]

Raw water absorbances, A 400nm and A 460nm [10/m]

Figure S9-1: Ultraviolet light absorbances of progressive filtrate portions. Filter is a Bonnet 0.45μm NYLON filter of nominal diameter 25mm. Raw water collected from Winneke WTP on 2003-12-02 was treated with aluminium sulfate and settled overnight.

0.0000 0

12.5

25

37.5

50

62.5

75

87.5 100

Volume passed through filter [mL]

Figure S9-2: Visible light absorbances of progressive filtrate portions. Filter is a Bonnet 0.45μm NYLON filter of nominal diameter 25mm. Raw water collected from Winneke WTP on 2003-12-02 was treated with 4mg(Al)/L and settled overnight*.

*

870

Absorbances of treated water at 400 and 460nm are typically considerably higher i m m e d i a t e l y after coagulation, prior to extended settling, even taking into account the subsequent filtration of the samples. Appendix S9 : Evaluation and Selection of Syringe Filters


0.80

Supernatant: Pall 0.45μm sterile(R) PES Acrodisc

0.35

Supernatant: Sartorius 0.45μm sterile(EtO) SFCA Minisart

0.30

Supernatant: Millipore 0.10μm sterile(EtO) PVDF Millex-VV — after PES/SFCA Supernatant: La-Pha-Pack 0.45μm non-sterile Nylon ProFill

0.25

Supernatant: La-Pha-Pack 0.45μm non-sterile Nylon ProFill — REPEAT Raw water: Pall 0.45μm sterile(R) PES Acrodisc

0.20 0.15

Raw water: Millipore 0.10μm sterile(EtO) PVDF Millex-VV — after PES

0.10

0.70 0.60 0.50 0.40 0.30 0.20

0.05

0.10

0.00

0.00

200

300

400

500

600

Raw water absorbance, Aλ [10/m]

Supernatant absorbance, Aλ [10/m]

0.40

700

Wavelength, λ [nm] Figure S9-3: The effect of different filters on absorbance (first 25mL of filtrate discarded). Raw water collected from Winneke WTP on 2004-06-02 was treated at 5.0mg(Al)/L and pH ≈ 5.0 and settled overnight. All syringe filters had nominal diameters 25 to 26mm. Active diameters: Sartorius 26mm; Millipore 22mm; La-Pha-Pack 22mm; Pall 19mm. Membrane materials: PES = polyethersulfone; SFCA = surfactant-free cellulose acetate; PVDF = poly(1,1-difluoroethylene) [548]; Nylon = polyamide. Sterilisation methods: R = gamma radiation; EtO = ethylene oxide.

The results for the nylon filter show a decrease in ultraviolet absorbance, which is consistent with the findings of KARANFIL, ERDOGAN & SCHLAUTMAN [553] that nylon filters adsorb NOM fractions more strongly than any other membrane material studied, even after passing relatively large volumes of filtrate, and for this reason are to be avoided. The discrepancies with the nylon membranes were most pronounced around 254nm — the most commonly reported wavelength — and the hump in the spectra, which can perhaps be characterised by an underlying peak in the vicinity of 262nm (see §S7▪3); hence the interference is of practical significance.

Appendix S9 : Evaluation and Selection of Syringe Filters

871

D. I. VERRELLI

S9▪3

DOC

A steering committee examining the issue of DOC quantitation in natural waters wrote [138]: Seawater contains a spectrum of organic structures ranging in size from small molecules (approximately 10–10m) to whales (approximately 10+1m). By convention, those components of this continuum which pass through a 0.2–1.0μm filter are defined as being dissolved; the retained moiety is particulate.

The implications of the range of permissible filter pore sizes for measured DOC (and UV absorbance) would usually be negligible, though it could be significant in some cases [555]. LEENHEER & CROUÉ [647] recommended precisely 0.45μm filters. A number of laboratories that “normally” use filters do not filter samples of low turbidity (e.g. < 1NTU) prior to DOC measurement [555]. WRUCK [1132] conducted tests on three Sartorius syringe filter devices with different membranes and sterilisation procedures. No significant difference between ethylene oxide (EtO) and gamma-radiation (R) sterilised devices was found. Polyethersulfone (PES) membranes gave lower leaching values in the first 25mL of deionised water filtrate (0.1mg(C)/L), compared to glass fibre plus cellulose acetate (GF+CA) membranes (0.6mg(C)/L). However the TOC readings of the next 25mL of filtrate (i.e. after wasting the first 25mL) showed no significant difference for the two membrane types, and were within the expected instrument measurement error (0.04mg(C)/L and 0.02mg(C)/L respectively). KARANFIL, ERDOGAN & SCHLAUTMAN [553] conducted extensive tests on a range of proprietary membranes and glass filters and arrived at the following recommendations: • In general, avoid hydrophobic surfaces (and pure polyamide (nylon)) so as to minimise membrane fouling *. • Wash filters with at least 100mL of pure water. • Prefer membranes of either polyethersulfone (PES) or poly(1-methylethylene) (PP [548]) †. • Discard the first portion of filtrate — up to 65mL for nylon membranes, but as low as 3 to 8mL for PES and PP membranes. Volumes have been converted to equivalents for a filter with an a c t i v e area of 25mm diameter, as approximately for the syringe filters typically used in the present study. Some of the above recommendations are not practical. In particular, the large wash volumes have not been found to be necessary. It would seem that the portion of sample that is filtered and discarded also serves adequately as the wash water. This procedure was practised by around 10% of respondents to a 2002 survey [555].

*

In their study of apple juice microfiltration with 0.2μm membrane filters RIEDL, GIRARD & LENCKI [866] found that the reduced f o u l i n g l a y e r r e s i s t a n c e with PES and PVDF was associated with their increased inter-pore surface roughness on a micron to sub-micron scale (being made up apparently of spherical and leaf-like aggregates, respectively) in comparison to polysulfone (PS) and nylon (which were smooth), and was n o t attributed to hydrophobicity.

†

As only a finite number of proprietary membranes could be tested, the recommendations were limited to membranes from specific manufacturers. This is because of the possibility that membranes generated from the same precursors may perform differently due to differences in the production process, e.g. use of binding agents, solvents used, and cleaning of the filter during or after production [552]. However the results suggest that the membrane material will at least give a good initial indication of performance.

872

Appendix S9 : Evaluation and Selection of Syringe Filters


In summary, generally syringe filters with PES and surfactant-free cellulose acetate (SFCA) membranes have been used, with the wash volume assumed subsumed into a total 25mL initial filtrate wasting. It is possible for other aspects of the pre-filtration configuration to affect the DOC readings, including the filter housing and sample container. To validate the materials used, leaching tests were performed on purified water using various membranes, and different sample containers were used. (As filtration may result in a decrease/increase in organic carbon due to adsorption/desorption of carbonaceous material onto/from the filter, blanks for DOC calibration should be filtered in the same way as the samples [334].) The gamma-radiation sterilised poly(1-methylethylene) sample containers were not found to add to baseline DOC readings, nor was rinsing of the sample containers found to be necessary. Filtrate from Sartorius Minisart 16555K 26.0mm diameter, 0.45μm syringe filters sterilised with ethylene oxide (EtO) was found to initially be compromised. These units have surfactant-free cellulose acetate (SFCA) membranes in a methyl methacrylate butadiene styrene (MBS) terpolymer housing. The first 25mL of filtrate had a DOC increase of about 0.5mg(C)/L, and about 0.4mg(C)/L for the first 50mL. The third 25mL portion (i.e. after passing 50mL) showed no increase in DOC *. It was concluded that discarding the first 25mL of sample should be adequate for avoiding overestimation of DOC values for these filters. The same volume of filtrate discard was also adopted for Pall Acrodisc 18.9 and 27.2mm diameter †, 0.45μm syringe filters, which are constructed of PES membranes in PP housings, as leaching from these materials should be below the levels from the SFCA filters.

*

In fact, an insignificant decrease of 0.2mg(C)/L was recorded.

†

Sold according to their nominal diameters of 25 and 32mm (part numbers 4614 and 4654), respectively. Appendix S9 : Evaluation and Selection of Syringe Filters

873

D. I. VERRELLI

S10. MULTIPLE BATCH SETTLING ANALYSIS S10▪1

Determination of compressive yield stress curve

An alum sludge (80mg(Al)/L, pH 8.6: see Table 3-8) underwent the alternative compressive yield stress analysis described in §3▪5▪1▪2. Table S10-1 describes the individual settling tests. Table S10-1: Individual settling tests.

Cylinder A B C D

φ0 [–] 0.001420 a 0.001114 b 0.000754 b 0.000414 b

h0 [m] 0.211 0.248 0.248 0.247

h∞ [m] 0.168 0.176 0.137 0.086

Notes a The measured values for this test were φ0 = 0.001399 (material loaded) and φ0 = 0.001315 (based on material unloaded). However the lower estimate is highly inconsistent with the measured volumetric dilutions of approximately 100, 77.9, 53.4, and 29.4%. The ‘corrected’ value of φ0 gives consistent mass dilutions of 100, 78.4, 53.1, and 29.2%; using 0.001315 implies discrepant mass dilutions of 100, 84.7, 57.3, and 31.5%. Even 0.001399 gives slightly high values, namely 100, 79.6, 53.9, and 29.6%. b Based on material unloaded.

Although Table S10-1 shows that test A commenced at a different (lesser) height compared to the other three tests, this should not affect the analysis. However, test A also has the greatest initial solidosity, which is in fact nearly equal to the gel point estimated by B-SAMS (based on this one test) — cf. Table S10-4. For this latter reason test A has been excluded from all but one of the multiple-settling analyses that follow. Fit parameters shown in Table S10-2 were obtained for various combinations of equations by minimising the sum of the squares of the residuals. Table S10-2: Fitting parameters for multiple batch settling experiment analysis.

Curve fit: Test A a b R2 φg

874

ωtotal = a h∞2 + b h∞ Included Excluded 0.005635 0.004304 0.0006752 0.0007992 0.9525 0.9992 0.0006752 0.0007992

ωtotal = a h∞2 Excluded 0.009361 N/A 0.9019 0

Appendix S10 : Multiple Batch Settling Analysis

ωtotal = a h∞b Excluded 0.003168 1.4106 0.9979 0


The following observations can be made about the curve fitting: • Excluding test A as an outlier gave better fits. However the effect of its inclusion on the predicted gel point was comparatively small. • The quadratic equation gave the best fit. The variable-power fit was also very good. The power-of-two fit was poor. • The value of b computed for the variable-power fit was of the same order as those quoted in §2▪4▪5▪3(f). An analysis using a piece-wise linear fit between the data points and the origin was also carried out for comparison, and is included in the accompanying graphs (Figure S10-1, Figure S10-2, and Figure S10-3).

0.00030

0.00025

ω total [m]

0.00020

Experimental data Experimental outlier Quadratic fit Power-of-two fit Variable-power fit Quadratic fit with outlier Piece-wise linear fit

0.00015

0.00010

0.00005

0.00000 0.00

0.05

0.10

0.15

0.20

h ∞ [m] Figure S10-1: Curve fits of data from four batch settling experiments on the same material at different dilutions.


875

D. I. VERRELLI

0.0025

φ ∞|z =0 = dω total/dh ∞ [–]

0.0020

0.0015

0.0010 Quadratic fit Power-of-two fit

0.0005

Variable-power fit Quadratic fit with outlier Piece-wise linear fit

0.0000 0.00

0.05

0.10

0.15

0.20

h ∞ [m] Figure S10-2: Variation in solidosity at the bottom of the bed as a function of bed depth from curve fits of data from four batch settling experiments on the same material at different dilutions.

The principle of parsimony [e.g. 464, 755] directs that the model yielding the best fit with the minimum number of fitting parameters be used. It can be seen that the one single-parameter model yields a poor fit, while the two dual-parameter equations yield significantly better fits. However, the variable-power fit predicts a zero gel point! Hence it was determined that in this case the most suitable fit was the quadratic equation (with zero-order coefficient equal to zero) with the data from test A omitted. Although this means that the estimated gel point (0.00080) is less than the initial solidosity of test B (0.00111), so that in principle test B cannot be included in the analysis, it is evident from the accompanying charts that inclusion of test B does not significantly affect the outcomes. For example, it can be shown that exclusion of test B shifts the estimated gel point up slightly to approximately 0.00089 (cf. Table S10-4 following).

876



4.5

Quadratic fit Power-of-two fit

4.0

Variable-power fit

3.5

Quadratic fit with outlier Piece-wise linear fit

p |z =0 [Pa]

3.0 2.5 2.0

p |z =0 = 2501.7(φ ∞|z =0) – 2.1615

1.5

R2 = 0.9938

1.0 0.5 0.0 0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

φ ∞|z =0 [–] Figure S10-3: Variation in particle pressure as a function of solidosity, both at the bottom of the bed, from curve fits of data from four batch settling experiments on the same material at different dilutions.

S10▪2

Alternative fits for the dewatering parameters

In the preceding section the compressive yield stress was estimated for an 80mg(Al)/L, pH 8.6 laboratory sludge (see Table 3-8) using the multiple-test procedure described in §3▪5▪1▪2. It is of considerable interest to compare the result of the multiple-test procedure with the results of the outputs from B-SAMS for each of the settling tests taken individually: see Figure S10-4. Recall that the latter is the ‘default’ methodology in the present work. Using the low-solidosity multiple-test data, it was necessary to use some interpolation between the largest concentration in this data and the lowest concentration obtained at the high solidosity end obtained from filtration data (the filtration data remains valid). Two


877

D. I. VERRELLI

simple interpolations were included for the purpose of comparison, namely an e x p o n e n t i a l fit and a l i n e a r fit. In view of the approximate power-law behaviour suggested by the log–log plot, the two forms of interpolation may be considered as indicative limits of the true py(φ) profile. The final sediment heights obtained from the analysis described were validated by comparison to those predicted by equations 2-102 and 2-103, and the discrepancies for tests B, C, and D were less than 3% (Table S10-3). Table S10-3: Error in h∞ using equation 2-102 only, or 2-102 and 2-103 depending on φ0.

Without accounting for φ0 > φg Accounting for φ0 > φg

Test A 17.4% 3.6%

Test B 6.3% 0.3%

Test C 6.0% 5.6%

Test D 10.8% 10.8%

In Figure S10-4 there are two features of especial interest. One is the differences in curvature displayed by the various curves. The other is the estimated gel points. Notice that all of the estimates of φg obtained from B-SAMS are greater than the respective φ0 value, with the margin increasing going from test A to test D (this follows from assumptions regarding φ0 inherent to B-SAMS; see §3▪5▪1▪1). There is a clear trend for the gel point computed by B-SAMS to decrease as φ0 is decreased. Furthermore, the φg prediction from the multiple-test analysis lies below even the lowest of these. Numerical values are summarised in Table S10-4. Table S10-4: Gel points estimated by B-SAMS based on each settling test taken individually, and by multiple-test analysis.

Estimated φg

B-SAMS A 0.001498

B-SAMS B 0.001308

B-SAMS C 0.001135

B-SAMS D 0.000985

Multi-test 0.000799

Given the curves for the compressive yield stress that have been presented, it is of interest to compare the corresponding hindered settling function curves. The default B-SAMS curves are readily available. In order to obtain further comparison curves, test C was selected as a case study, as this was the intermediate case in the fitted tests B, C, and D. Taking the raw batch settling data and curves Cd (default B-SAMS) and cE (multiple-test composite with exponential interpolation) from Figure S10-4, the two corresponding R(φ) curves were manually adjusted until the predicted batch settling profiles each matched closely the raw settling data (see §S10▪3 following). The results are presented as curves Cb and Cc in Figure S10-5.

878



1.E+3 1.E+2 1.E+1

p y [kPa]

1.E+0 1.E-1

A: B: C: D:

φ 0 = 0.00142, h 0 = 0.211m φ 0 = 0.00114, h 0 = 0.248m φ 0 = 0.000754, h 0 = 0.248m φ 0 = 0.000414, h 0 = 0.247m

cE: composite p y with exponential interpolation to high φ data cL: composite p y with linear interpolation to high φ data d: default B-SAMS single-test fits

1.E-2

Raw data Multi–test analysis Ad Bd Cd Dd cE cL

1.E-3 1.E-4 1.E-5 1 E-4

1 E-3

1 E-2

1 E-1

φ [–] Figure S10-4: Compressive yield stress computed using B-SAMS for individual settling tests A, B, C and D compared to a multiple-test analysis. The multiple-test analysis is presented as a composite curve, with exponential (E) and linear (L) interpolation alternatives.

The R(φ) curve was not adjusted beyond solidosities greater than the lowest obtained from filtration data, ~0.011. Of course, alterations beyond the greatest solidosity in the modelled settling test, i.e. that at the base at equilibrium (~0.0020 for test C, the middle point in Figure S10-4), will not affect the predictions of the settling profile, h(t). It can be seen that to achieve a good match between the predicted and experimental settling data a much steeper form of the R(φ) function in the vicinity of φg was required: namely, R(φ) increases rapidly up until slightly above the gel point, and the curve is near vertical. Eventually a value of R is reached that is close to that of the lowest filtration point, so that the R(φ) curve then turns through almost a right angle into a virtual plateau region — it is a s s u m e d that R(φ) increases m o n o t o n i c a l l y with φ. However, it is physically possible for this condition to be invalid, e.g. with formation of rapidly-settling clusters as the concentration is increased.


879

D. I. VERRELLI

1.E+15 1.E+14 1.E+13 Ad Bd Cd Dd Cb Cc

R [Pa.s/m²]

1.E+12 1.E+11 1.E+10 1.E+09

A: B: C: D:

1.E+08 1.E+07 1.E+06 1.E+05 1 E-4

φ 0 = 0.00142, h 0 = 0.211m φ 0 = 0.00114, h 0 = 0.248m φ 0 = 0.000754, h 0 = 0.248m φ 0 = 0.000414, h 0 = 0.247m

b: R modified to fit C based on B-SAMS p y c: R modified to fit C based on composite p y d: default R obtained from B-SAMS single-test fits

1 E-3

1 E-2

1 E-1

φ [–] Figure S10-5: Hindered settling function computed using B-SAMS for individual settling tests A, B, C and D compared to the results of manually adjusting R to match settling curve C using either compressive yield stress curve Cd (default B-SAMS) or cE (multiple-test analysis) of Figure S10-4.

It is also clear that the two forms of py(φ) chosen, which are very different throughout the range of φ of interest, have had very little effect on the R(φ) curve selected as producing the best h(t) fit for test C. Having obtained py(φ) and R(φ), the solids diffusivity, D (φ), can readily be obtained: see Figure S10-6. For the curves obtained directly from B-SAMS this can be done using an analytical derivative based on the known fitting equation for py(φ). For the data based on the composite curve of the multiple-test analysis, the function py(φ) is not described analytically, and so numerical methods have been used, including (importantly) to smooth the R(φ) curve when interpolating.

880



1.E-06

D [m²/s]

1.E-07

b: R modified to fit C based on B-SAMS p y c: R modified to fit C based on composite p y d: default R obtained from B-SAMS single-test fits E: exponential interpolation to high φ data L: linear interpolation to high φ data

1.E-08

1.E-09

Ad Bd Cd Dd Cb CcE CcL

A: B: C: D:

1.E-10 1 E-4

φ 0 = 0.00142, h 0 = 0.211m φ 0 = 0.00114, h 0 = 0.248m φ 0 = 0.000754, h 0 = 0.248m φ 0 = 0.000414, h 0 = 0.247m

1 E-3

1 E-2

1 E-1

φ [–] Figure S10-6: Solids diffusivity computed using B-SAMS for individual settling tests A, B, C and D compared to the results of manually adjusting R to match settling curve C using either compressive yield stress curve Cd (default B-SAMS) or cE (multiple-test analysis) of Figure S10-4.

It is clear that all of the results obtained directly from B-SAMS are very similar, with the only significant difference being at the lowest concentrations due to the divergent estimates of φg. In contrast the curves based on manually-adjusted R(φ), Cb, CcE and CcL, are quite different from each other and are collectively very different to the default B-SAMS results. Note that some of the features discriminating the curves based on manually-adjusted R(φ) are purely numerical artefacts. For φ > 0.011 all curves should be taken as identical. (These differences arise primarily because the smooth B-SAMS fit to the filtration data was not used for the composite curves.) The instantaneous steps in D (φ) are not artefacts per se, but arise because the interpolations in py(φ) were not required to have a continuous first derivative. All of the D (φ) curves have been obtained from smoothed numerical differentiation of py(φ) except for Dd and Cb, where results of analytical differentiation were prepended. Let us return to a key point that was made earlier: for prediction of h(t), only values of φ up to that at the base will affect the solution. For all cases considered here that value is less than


881

D. I. VERRELLI

~0.0025, and less than ~0.0020 for test C (cf. Figure S10-4 and Figure S10-11). That is, the modifications that can be directly justified lie below this solidosity, and any changes above that concentration are a consequence of the interpolation that is therefore required. Considering firstly the similarities between curves Cb, CcE and CcL, it is interesting that they all appear to possess an initial d o w n w a r d slope from their respective gel points up to about 0.00133 — which is apparently due to the slope implicitly set by the m a n u a l l y s p e c i f i e d R(φ) (as in Figure S10-5). (The solids diffusivity is identically zero below the gel point.) In contrast the slope of D (φ) is p o s i t i v e in this region for all of the d e f a u l t BSAMS curves. The adjusted curves also (therefore) all predict lower solids diffusivities up until the high end of the φ domain, where all curves converge. In the domain 0.0023 ≤ φ ≤ 0.011, between the multiple-test batch settling data and the filtration data, the strong influence on D (φ) of the type of py(φ) interpolation is evident. Given the need to somehow link the low-φ and high-φ regions, it is plain that the exponential py(φ) interpolation provides the better match of gradient at either end, leading to minimal discontinuities. The linear interpolation introduces a massive step change to the solids diffusivity curve, which is not physically realistic. However, it is useful in demonstrating the r a n g e of variation that could be possible, and the s e n s i t i v i t y of the solids diffusivity curve itself to interpolation in py(φ) — or R(φ) — which is often overlooked [e.g. 787]. The modified B-SAMS solids diffusivity curve, Cb, most closely resembles the shape of the unmodified curves in the region of interpolation, also being concave-down on the plot.

S10▪3

Re-prediction of settling h(t) profiles

The final piece of analysis that can be performed on these sets of data is to examine whether the R(φ) curves that were carefully adjusted so that the predicted batch settling behaviour matched experimental observation in test C (Figure S10-9) also yield improved predictive power for the other tests, A, B and D (Figure S10-7, Figure S10-8, and Figure S10-10, respectively). Note that the gel point curves in a given plot do not all relate to the same estimated φg value. An overview of the modelling details is provided in Table S10-5. The nomenclature is as presented in the previous section. For the parameter pair based on multiple-test analysis, the exponential interpolation (cE) was generally used, which is smoother at the lower junction — however the effect of choosing instead the linear interpolation (cL) is mostly negligible in the following, where they are generically listed as curves “c”. A cursory inspection of the predictions shows that several yielded inaccurate final heights (also recorded in Table S10-5). To facilitate a ‘fair’ comparison of the effects of adjusting R(φ), the entire py(φ) and R(φ) curves were jointly shifted to higher or lower φ so as to obtain better agreement of the predicted final height — these are denoted with a p r i m e , as in Ab′ et cetera. In each case the TBS code (§3▪7▪1) * was run within Mathematica 5.0, with the (initial) number of height increments in the numerical solution (J) equal to 250. This yields reasonably good *

882

With minor modifications and amendments by me for the present work. Appendix S10 : Multiple Batch Settling Analysis


precision, with computer processing times ranging from just 3h (Ab′) up to 190h (Ac) for prediction of 107s of settling *. Table S10-5: Overview of input parameters for h(t) predictions from various sources. Predicted (output) equilibrium heights, ĥ∞, are included here for convenient comparison with observed h∞.

h0 [m] h∞ [m] φ0 [–] φg :B-SAMS X [–] d: Default B-SAMS test C

Test A 0.211 0.168 0.001420 0.001498

Test B 0.248 0.176 0.001114 0.001308

Same as 

Same as 

ĥ∞: 0.213m

ĥ∞: 0.197m

Test C 0.248 0.137 0.000754 0.001135  py: B-SAMS C R: B-SAMS C ĥ∞: 0.135m

Test D 0.247 0.086 0.000414 0.000985 Same as  ĥ∞: 0.078m

d′: As for , but φ Same as  Default B-SAMS As for , but φ As for , but φ test C s h i f t e d shifted (+0.00037) shifted (+0.00017) shifted (–0.00012) ĥ∞: 0.168m ĥ∞: 0.176m ĥ∞: 0.135m ĥ∞: 0.086m  b and b′: p : same as  y As for , but φ As for , but φ Optimised BAs for , but φ R: optimised to SAMS test C shifted (+0.00037) shifted (+0.00017) shifted (–0.00012) predict test C h(t) (shifted) ĥ∞: 0.168m ĥ∞: 0.176m ĥ∞: 0.135m ĥ∞: 0.086m  c and c′: py: multi-test As for  Optimised multi- As for , but φ As for  R: optimised to test composite shifted (+0.00016) predict test C h(t) (shifted) a ĥ∞: 0.168m ĥ∞: 0.177m ĥ∞: 0.135m ĥ∞: 0.087m a Note: φg :multiple-test ~ 0.000799. Figure S10-9 clearly shows the superior fits in the consolidation phase of test C that have resulted from ‘manual’ modification of R(φ) to suit the respective py(φ) curves. Because the default B-SAMS curves (“d”) overestimated the rate of settling at l o n g times, it was necessary to significantly increase R(φ) at intermediate solidosities (φ > φg :B-SAMS C ≈ 0.00114) to obtain agreement. It can be expected that this will therefore lead to decreases in the predicted settling rates for tests A (φ0 = 0.00142) and B (φ0 = 0.00114) at s h o r t times — provided that they are not shifted in φ. One reason for the original mismatch of the Cd prediction at intermediate-to-long times is that relatively high solidosities arise in this phase (cf. Figure S10-11), whereas B-SAMS is unable to extract R(φ) estimates in the h(t) tail based on fundamental dewatering theory. Thus the behaviour in the consolidation region is effectively given by a B-SAMS interpolation.

*

Computation times tended to increase in the order Xb′ ( Xb ( Xd′ ( Xd ( Xc′ ( Xc. In general, computations also followed D ( B ( A, C; however for the fastest (Xb′ and Xb) this order was reversed. Appendix S10 : Multiple Batch Settling Analysis

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D. I. VERRELLI

The unshifted default curves (Ad, Bd, Dd) show poor to extremely poor predictive power. Predictions Ad and Bd behave as if the gel point has been severely underestimated — so that the ‘solidness’ of the material is overestimated, and little settling is predicted — while Dd behaves as if the gel point has been overestimated. Contemplation of Figure S10-4 shows this to be a reasonable interpretation. In an attempt to discriminate between the influence of kinetic and equilibrium effects, both py(φ) and R(φ) were shifted in φ to the extent shown in Table S10-5 so as to ‘correct’ for the ‘error’ accruing from using test C as the basis and obtain better agreement for the predicted final height of the given test. This generated the new predictions Ad′, Bd′ and Dd′. The shifted default predictions, somewhat surprisingly, all share similar characteristics: they predict the initial kinetics reasonably well, but uniformly overestimate the settling rate at intermediate-to-long times. The ‘intermediate’ times at which divergence appears to commence correspond roughly to the points at which the gel point curve meets the top interface. The predictions also clearly underestimate the settling rate at the longest times, but that is less surprising given that the solidosities in tests A and B are almost entirely above the highest φ for which B-SAMS extracted R(φ) based on test C (viz. φs = 0.001136); beyond this, interpolation is used. (Also, the model presumes the existence of a non-close-packed equilibrium and the absence of creep, whereas the experimental data do not necessarily support this.) Using the “b” parameters to predict settling in tests A, B and D raised the same problems as encountered for the “d” parameters. Although changes in the kinetics have occurred, these could not be clearly distinguished from the mismatch in equilibrium specification (predictions were computed, but are not shown here). Thus, again the parameters were translated in φ — by the same amount as previously — to yield the new specifications Ab′, Bb′ and Db′. It is both surprising and intriguing that in all cases the s h a p e of the manually adjusted R(φ) function leads to better predictions of the settling over the duration of the experiment — the shifting in φ notwithstanding. This strong similarity suggests that a consistent cause is responsible, which might correspond to a failing in the computation of R(φ) by B-SAMS, or to the existence and importance of an additional, unaccounted-for mode of dewatering (e.g. ‘creep’ or ‘synæresis’) at intermediate-to-long times. Reviewing the performance of the dewatering parameters extracted using only test C, it can be seen that the predictions are highly sensitive to shifts in φ. When these equilibrium discrepancies are ‘corrected for’ by translating both py(φ) and R(φ), then the effect of R(φ) is emphasised (although the f o r m of py(φ) does still have a little influence). It was revealed that the settling rate at intermediate-to-long times was universally underestimated in the BSAMS results, and the manual adjustments made based on test C were also valid for the other three tests. Lastly, we examine the predictions made using the composite py(φ) curves derived from multiple-test analysis paired with corresponding R(φ) curves optimised to match the raw test C settling data. As should be expected, the equilibrium performance of the predictions was excellent for Bc, Cc, and Dc — with no shifting in φ. Recall that it was tests B, C and D that were included in 884



the multiple-test analysis, while test A was excluded on the grounds of an excessive φ0, as discussed at the beginning of this appendix. This would have instilled a high degree of confidence in the shape of py(φ) were it not for the mismatch between the corresponding ĥ∞ and h∞ for test A. Table S10-6: Effect of the interpolation (or extrapolation) of the compressive yield stress at intermediate solidosity on the predicted equilibrium height for test A. The final observed height was 0.1681m.

Designation AcE AcL Ac(extended) Ac(flat) Ac′E

Form of py(φ) at intermediate φ Exponential interpolation Linear interpolation Continuation of low-solidosity function (then step) Horizontal (then step) Exponential interpolation

Translation in φ None None None

ĥ∞ [m] 0.1866 0.1853 0.1866

None +0.00016

0.1759 0.1681

It has been noted that the particular interpolation (referred to earlier as cL and cE) was immaterial for most of the predictions. Evidently test A covers the highest solidosities, and so is actually affected by the interpolation to a minor degree. This is outlined in Table S10-6. It is plain that the difference between linear and exponential interpolation, in terms of ĥ∞, is very small. Also, the exponential interpolation is negligibly different from the result obtained by continuing the low-solidosity py(φ) function over the full calculation range. (Note that these three all underestimate h∞: although creep might be suggested as an unaccounted-for mechanism to explain the additional settling observed, it is not clear how this could apply to test A when it does not apply to the other tests in the same way.) Even the physically unrealistic limit of a plateau in py(φ) is unable to match the observed h∞. Only shifting the compressive yield stress to slightly higher solidosities achieves the desired outcome. Note that the effect of this shift is massive around the gel point: φg shifts from 0.00080 to 0.00096 (+20%), so that py(0.00096) drops from 0.24Pa to 0.00Pa (–100%). Of course, test A involves only solidosities above the gel point, but the same trend applies that decreases at φ0 = 0.00142 (py drops from 1.18 to 0.81Pa (–31%)) are proportionally much greater than at the maximum solidosity where φ → 0.00242 (py drops from 4.4 to 3.8Pa (–14%)) *. The same trend also applies to R(φ) when it is shifted in the same manner. As with the “b” curves, for the “c” predictions R(φ) was optimised to match the test C observations. There is a likeness between the two manually adjusted curves (see Figure S10-5), with the steep increase in R around the gel point to very large values. Although this permitted excellent agreement between the prediction and the observations for the ‘training data’ of test C, the performance in terms of kinetics for the other tests was unfavourable.

*

In fact the asymptotic solidosity at the base changes when the compressive yield stress curve is shifted, viz. from the stated 0.00242 to 0.00261 (+8%), whereas the pressure experienced remains constant with py → 4.4Pa in both cases (±0%). (It is not obvious why 0.00242 does not shift by +0.00016; it can only be assumed to be due to assumptions inherent in the TBS code.) Appendix S10 : Multiple Batch Settling Analysis

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D. I. VERRELLI

There was a strong trend for the settling rate to be underestimated for tests commencing at higher solidosity (Ac or Ac′, and Bc) but overestimated for the test with lower φ0 (Dc). There appear to be four possible explanations for this discrepancy: 1. Test A is aberrant. 2. Optimising R(φ) to suit test C does not yield a unique solution. An alternative optimised form may exist which simultaneously yields favourable predictions for the other three tests. 3. Significant creep occurs at long times. 4. The ‘effective’ gel point is a function of the initial solidosity, as reported by BSAMS. There is no tangible reason to discount the accuracy or validity of the observations of test A, the present discussion notwithstanding. Prima facie the existence of a universal optimum seems unlikely, given the sweep of candidate R(φ) functions trialled, and being mindful of constraints that R(φ) be monotonic and reasonably ‘well-behaved’.

0.25

Height, h [m]

0.20

0.15

Raw Ad Ad Ad' Ad' Ab' Ab' Ac Ac Ac' Ac'

0.10

0.05

0.00 1 E+2

1 E+3

1 E+4

1 E+5

1 E+6

1 E+7

Time, t [s] Figure S10-7: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — t est A. Suspension heights (first in legend) and isoconcentration curves for φg (second in legend) are shown for each scenario.

886



0.25

Height, h [m]

0.20

0.15 Raw Bd Bd Bd' Bd' Bb' Bb' Bc Bc

0.10

0.05

0.00 1 E+2

1 E+3

1 E+4

1 E+5

1 E+6

1 E+7

Time, t [s] Figure S10-8: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — t est B. Both suspension heights (first in legend) and isoconcentration curves for φg (second in legend) are shown for each scenario.

The existence of creep could be consistent with overestimation of the settling due to ‘plastic’ deformation in concert with very high values of R corresponding to the solidosities occurring at long times. Such interpretation is inspired by the trend whereby application of the test C data to systems of higher solidosity leads to underprediction of the settling rate early on, implying that the steepness of the specified R(φ) function is excessive.


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D. I. VERRELLI

0.25

Height, h [m]

0.20

0.15

0.10

Raw Cd J=250 Cd J=250 Cb J=250 Cb J=250 Cc J=250 Cc J=250

0.05

0.00 1 E+2

1 E+3

1 E+4

1 E+5

1 E+6

1 E+7

Time, t [s] Figure S10-9: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — t est C. The solid lines are suspension heights, the isoconcentration curves for φg are shown as broken lines.

The ‘effective’ gel point may be a function of φ0, although the multiple-test analysis demonstrates that B-SAMS indications of such dependence across a l l tests is not necessarily correct. Nevertheless, based on the evidence presented here, a shift in the gel point is able to account for the observed settling patterns. Furthermore, this can also explain predictions Bc and Dc, in so far as the multiple-settling analysis may have — perhaps ‘artificially’ — removed the need to shift the composite py(φ) curve, but not the need to shift R(φ). It is anticipated that suitable translation of R(φ) with respect to φ for Bc and Dc, and further translation for Ac, would permit the predicted settling curves to match the observations. In summary of the findings here, prediction of gravity batch settling is highly sensitive to the specified gel point, and indeed the ‘effective’ gel point appears to shift in sympathy with increases or decreases in φ0. This is reflected both in default B-SAMS output and in prediction of settling at higher or lower φ0.

888



0.25 Raw Dd Dd Dd' Dd' Db' Db' Dc Dc

Height, h [m]

0.20

0.15

0.10

0.05

0.00 1 E+2

1 E+3

1 E+4

1 E+5

1 E+6

1 E+7

Time, t [s] Figure S10-10: Comparison of transient sediment height predictions from various py(φ) and R(φ) combinations with experimental data — t est D . Both (falling) suspension heights and (initially rising) isoconcentration curves for φg are shown for each scenario.

The multiple-test analysis results in quite a different estimate of the py(φ) curve from those obtained through separate analysis of individual tests in B-SAMS. At this time it is not clear which method of analysis is to be preferred, given uncertainties surrounding the importance of creep (and so the proper equilibrium bed height to use) and the constancy or otherwise of the gel point. It may be that the multiple-test analysis implicitly resolves the shift in gel point for py(φ), but not for R(φ).


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A B C D 0.000

0.050

0.100 0.150 φ [%]

0.200

0.250

Figure S10-11: Estimated range of solidosities occurring in tests A to D (based upon compressive yield stress from multiple-test analysis); the corresponding gel point is shown as a divider.

The discrepancies between the predicted h(t) profiles — based chiefly on data obtained from test C — and the raw data for tests A, B and D have three potential causes. The simplest issue is the fact that the s o l i d o s i t i e s embodied in test C do not cover the full domain of solidosities seen in the other tests. Namely, in test A and test B higher solidosities are seen, while in test D lower solidosities are initially present. This is illustrated in Figure S10-11. However, this does not seem a likely explanation for the discordance between predictions and observations, because the default B-SAMS predictions (the “d” curves) are equally accurate across the four tests. The second potential cause is the form of the p y ( φ ) curve. Certainly this can adversely affect the predicted settling behaviour if it is misspecified (compare also curves CcX to curve Cb in Figure S10-6), with sensitivity often greatest in the region of φg (cf. the filtration prediction in §S13); yet the final heights are accurately predicted for each of the four tests. While the errors could be arising because of misspecification in the domain of the i n i t i a l solidosities, from Figure S10-11 the foregoing would imply that the most accurate predictions could be made for test A, which plainly is not the case. Moreover, greater deviation of the predictions is seen where R(φ) was manually adjusted, irrespective of whether the default B-SAMS form of py(φ) (the “b” curves) or the composite based on multiple-settling-test analysis (the “c” curves) was used — especially clear for test B. Besides which, these predictions show least discrepancy in test D at early times, where solidosities are lowest. So the final aspect considered to account for the poor prediction is R ( φ ) . As foreshadowed, this parameter appears to be the factor controlling the agreement or otherwise of the h(t) profile predictions — which should not be surprising, given that it is the purely kinetic dewatering parameter. Concentrating on the predictions based on manually-adjusted R(φ) (curves “b” and “c”), recall that the estimates of R were sharply increased at moderate-solidosity (φ T 0.00114) in both cases — converging towards the default as φ → 0.011 (see Figure S10-5) — so as to better match the long-time settling behaviour of test C. From Figure S10-11 it is expected that such changes would most affect the early settling behaviour of tests A and B, whereas 890



test D should be essentially unaffected. This is indeed reflected in the actual predictions, where the short-time settling rates in tests A and B are severely underestimated. It has been posited that py and R are material properties, in which case it should be possible to find a pair of py(φ) and R(φ) curves that accurately predict the settling of this sludge at any initial solidosity or height. As seen, a single settling test cannot be uniquely deconvoluted to a pair of py(φ) and R(φ) curves, and consistent pairs may not accurately predict settling for alternative initial conditions. The present analysis suggests that no universally-correct pair of py(φ) and R(φ) functions can be found for this material — representative of WTP sludges in general — although its existence cannot be absolutely excluded. It seems likely that the mismatch in prediction Cd (Figure S10-9), is actually due to c r e e p like effects (cf. §9▪3▪2, §R2▪2▪3). Thus the manual adjustments to R(φ) to obtain predictions Cb and Cc may have erroneously attempted to encapsulate creep phenomena in a plasticyielding model (i.e. the model of LANDMAN and WHITE). If creep is present then the extent of settling due to plastic yielding would be overestimated, implying that py(φ) is underestimated: settling can still occur, by the creep mechanism, when φ > φ∞. (It is notable that to force B-SAMS to output the same gel point as obtained from the multiple-test analysis, viz. 0.00080, it is necessary to base the computation on a final height * of 0.1922m for test C, corresponding to lower equilibrium solidosities for the given load.) Creep would also enhance the long-time settling rates. Although prediction Cd appears to rather overestimate the long-time settling rate, such superficial assessment is misleading, as the presence of creep would require that the compressive yield stress curve be shifted to lower solidosities. Behaviours and mechanisms that may be relevant to creep are further discussed in §9▪3▪2, §S3, §S17, and §S18. Future work could investigate the effect of truncating the settling data set used for estimating the dewatering parameters, or a similar adjustment, as a means of incorporating an allowance for creep at long times.

*

This parameter can be adjusted separately to adjust the computed gel point without truncating the set of observed h(t) data. Appendix S10 : Multiple Batch Settling Analysis

891

D. I. VERRELLI

S11. SLUMP TEST RESULTS The following photographic sequences support the discussion of conventional subaerial and novel subaqueous slump tests in §3▪6.

S11▪1

Strong (conditioned) sludge

Figure S11-1: Subaerial slump tests. Final height ≈ 13mm  Slump ≈ 12mm. Minor leakage in first image is not significant for the purposes of this experiment.

Figure S11-2: Subaqueous slump tests. Final height ≈ 26mm  Slump ≈ –1mm (INVALID). Note: sample lifted up with cylinder until water surface reached (see centre image).

892

Appendix S11 : Slump Test Results


S11▪2

Weak (unconditioned) sludge

Figure S11-3: Subaerial slump tests. Final height ~ 2.5mm  Slump ~ 22.2mm (INVALID).

Figure S11-4: Subaqueous slump tests. Final height ~ 13mm  Slump ~ 12mm. Note: final height taken as lowest point of top surface of slumped column. The images in the bottom row were adjusted (contrast, colouring, et cetera) using IrfanView software (IRFAN SKILJAN, Jajce, Bosnia and Herzegovina; version 3.95) in order to better discern the sludge outline.


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D. I. VERRELLI

S11▪3

Coloured water

Figure S11-5: Subaerial slump tests. Final height ~ 2.5mm  Slump ~ 22.5mm (INVALID). Note: glass surface was on a slight incline in this test.

Figure S11-6: Subaqueous slump tests. Final height ≈ N/A  Slump ≈ N/A (Not applicable). Final image shows dispersion after about one minute of standing.

894



S12. CONTOUR SENSITIVITY ANALYSIS A number of contour plots were presented in §5▪5, which summarised the variation of φ (or R) as a function of coagulant dose and coagulation pH for fixed values of R (or py). The question may be asked as to how ‘reliable’ these contour maps are. Two approaches may be adopted: variation of contour algorithm parameters; or removal of individual data points. Brief testing (not presented) indicates that adjustment of algorithm parameters either yields only minor changes to the estimated contours (e.g. interpolation without “blending” in gradient estimates; surface tautness adjustment) or else highly implausible results (e.g. use of spline or hyperboloid gradients for interpolation). It may be concluded that the recommended settings were robust (as stated) [1104], and use of unsuitable algorithm parameters gave information on the algorithm rather than the data. Thus the removal of individual data points recommends itself. This is reminiscent of jackknifing (see §S15▪2▪2, p. 919) and outlier or leverage analysis in linear regression [e.g. 755], except that here only a few ‘high-influence’ data points will be removed, and no quantitative statistics will be computed. Two apparently influential samples were identified: • 5.0mg(Al)/L and pH = 4.9; • 10mg(Al)/L and pH = 6.0. The latter sludge was fully characterised, whereas no high-solidosity R data was obtained for the former. It was found that removing these points (separately) from the data sets for each contour plot only had a significant effect on the plot showing variation of φ with dose and pH for R = 5×1010Pa.s/m2. Figure S12-1 and Figure S12-2 show the result of removing each of the identified highinfluence points on the contour estimation, overlaid on the original plot.

Appendix S12 : Contour Sensitivity Analysis

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100

0.00175 0.00150

0.00175

0.00125

Dose [mg(Al)/L]

0.00150

0.00100 0.00100 0.00125 0.00125

10

0.00125 0.00150

0.0065 0.00150

0.00175

0.00175 0.00200

0.00200 0.00225

0.00225

0.00250

0.00250

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure S12-1: Effect of removing the low-dose, low-pH data point on the contour plot of φ at R = 5×1010Pa.s/m2 for laboratory alum sludges as a function of dose and pH. The co-ordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines. Full data set results are shown in pale grey (cf. Figure 5-11).

It can be seen that the contour plots are highly sensitive to each of the two points. Removing the pH 4.9 point (Figure S12-1) results in a drastic change from more-or-less horizontal contours to roughly ‘C’-shaped contours. This would imply that the poorest behaviour centred on 10mg(Al)/L and pH 6.0 (emphasising the influence of this point!) and at slightly higher dose and pH values. Except for low pH, the tendency for φ to pass through a minimum is retained. Removing the 10mg(Al)/L point (Figure S12-2) results in a change from essentially horizontal contours to more vertical contours above 10mg(Al)/L. This would mean that the pH effect was more important than the dose effect. The previous trend for φ to increase again at high doses is weakened considerably, but still evident.

896



100

0.00175 0.00175

Dose [mg(Al)/L]

0.00150

0.00100

0.00125

0.00125

10

0.00125 0.00150

0.00150 0.00175 0.00200 0.00225 0.00250

1 4.0

5.0

6.0

7.0

8.0

9.0

pH [–] Figure S12-2: Effect of removing the 10mg(Al)/L, pH 6 data point on the contour plot of φ at R = 5×1010Pa.s/m2 for laboratory alum sludges as a function of dose and pH. The co-ordinates of the underlying data are plotted as small squares. Approximate solubility limits of Al are shown as dashed lines. Full data set results are shown in pale grey (cf. Figure 5-11).

The two altered data sets presented demonstrate the specific sensitivity of this dewatering characteristic, φ at R = 5×1010Pa.s/m2, to the two identified samples. Certain of the previously identified features were retained, but some new features also arose. The new features were not necessarily indicative of real material properties, but rather were more likely to be artefacts due to the reduction in data coverage. As already stated, the other contour plots showed less sensitivity to exclusion of specific data points. On the other hand, data for the pH 4.9 sample was unavailable for two plots: it may be that inclusion of this data would alter the form of the contours. Likewise, there was generally a fairly large region around 25mg(Al)/L at pH 7 to 9 and at pH 5 in which contours were estimable only by interpolation from distant points. Thus it would be beneficial to characterise more sludges at a couple of key points to confirm the indicated trends.


897

D. I. VERRELLI

S13. FILTER PRESS MODELLING The past conclusions regarding the effect of coagulant dose and coagulant pH on the dewatering parameters py(φ) and R(φ) provided useful pointers for WTP design and operation. However, quantification of dewaterability variation in terms of throughput would enable the past conclusions to be validated in a practical context, would permit conclusions to be drawn on the relative importance of py and R, and would confirm the magnitude of the dewaterability variation in processing terms. An advantage inherent in the use of the compressive yield stress, py(φ) and hindered settling function, R(φ), parameters is that these can be used to describe dewatering behaviour across the entire domain of φ, from settling through to thickening, from centrifugation to filtration. In previous chapters conclusions have been reached in terms of the effects of coagulation conditions upon the dewaterability of the resultant sludge. For example, dewaterability of alum WTP sludges has been reported to deteriorate at high coagulant doses and at high coagulation pH values.

S13▪1

Methodology

In order to illustrate in more practical terms the respective advantages or disadvantages of the range of coagulation conditions, the experimentally derived py(φ) and R(φ) data have been used as inputs to a filtration model. This model predicts the transient dewatering of the given material in a flexible-membrane filter press. Such a press normally operates in two stages: first, material is pumped under pressure into the cavities and some dewatering occurs as liquid passes out through the filter cloth; second, the inflow line is shut off and a bladder is inflated at high pressure to ‘squeeze’ the cake against the filter cloths. Key model parameters are set out in Table S13-1. Dewatering of representative alum and ferric sludges has been modelled for a flexiblemembrane filter press operating at pressures of 100 and 300kPa for the fill and ‘squeeze’ stages (respectively), fed at the various gel points of the materials. The pressures are more typical of the laboratory filtration rig, and lower than an industrial WTP filtration press would use.

898

Appendix S13 : Filter Press Modelling


Table S13-1: Key flexible-membrane filter press model parameters.

Parameter Δpfill, the first-stage pressure Δpsqueeze, the second pressure h0, initial cavity half-width φ0, inlet solidosity Δtload, time to load empty cell Δtramp1, time to reach Δpfill Δtfill, time from loading until inflow line shut off Δtramp2, time to reach Δpsqueeze Δtsqueeze, squeeze time Δthandle, handling time ηL rmembrane, membrane resistance group

Value 100kPa 300kPa 15mm φg 0s 0s 3600s

Comments Arbitrary value Maximum available from experimental data This is a typical industrial value [973, 976] Set equal to the gel point, as if from a thickener Subsumed into Δthandle Assumed instantaneous, considering Δpfill is small Short compared to industry, but Δpfill is smaller too

0s varies 1800s ~0

Δpsqueeze – Δpfill is small Modelling continues until equilibrium approached Turnaround time for unloading, cleaning, checking Industry measurements are of order 1011Pa.s/m [974, 976]

Initially it was thought appropriate to set all of the input solidosities, φ0, to the same value, viz. some value at which none of the materials would be gelled. It was soon apparent that this meant some materials were loaded well below their gel point, with the result that the cake that could practicably be obtained would be excessively thin. Hence, instead all materials have been fed into the filter, in the model, at their respective gel points. This has the advantage of more accurately simulating the situation where the filter is fed from the underflow of a clarifier or thickener. It has the disadvantage of emphasising the importance of the gel point in the prediction, such that the prediction is highly sensitive to misspecification of φg. Although LANDMAN & WHITE [629] predicted optimum solid-phase throughput to occur where the filtration time was equal to the handling time, that analysis did not take into account some practical realities such as material added during the ‘fill’ stage and constraints on the final filter cake solidosity.

S13▪2

Alum sludges: dose effects

Results in Chapter 5 have shown that (very) low alum coagulant doses produce a more compressible material, which also has faster dewatering kinetics. Above a dose of 5 to 10mg(Al)/L, for the low to moderately coloured waters investigated, the precipitated alum was seen to dominate dewatering behaviour, and behaviour was less favourable. Naturally it was expected that this would be reflected in the predictions obtained for industrial dewatering devices and conditions. The conditions selected for modelling, above, were expressly chosen to cover the whole domain from φg to φ∞(300kPa), to try to ‘average’ the characteristics of the complete py(φ) and R(φ) curves in this domain, and avoid undue emphasis of any localised features or artefacts.


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1.0E-7

mg(Al)/L Lab.: 84 Lab.: 10 Lab.: 5 Lab.: 1.5 Plant: 1.9

Solids throughput, φ 0.Q [m/s]

9.0E-8 8.0E-8

pH 6.1 6.0 6.0 6.0 6.1

7.0E-8 6.0E-8 5.0E-8 4.0E-8 3.0E-8 2.0E-8 1.0E-8 0.0E+0 0.000

0.050

0.100

0.150

Average output solidosity, Cφ fD [–] Figure S13-1: Solids throughput as a function of final average cake solidosity for various alum doses.

As it turns out, the results of the filter press modelling (Figure S13-1) do not show unambiguous agreement with the general conclusions reached earlier. Two aspects that are consistent are the similar, favourable properties of the two sludges coagulated at the lowest alum doses (1.5 and 1.9mg(Al)/L), and the less favourable performance of the sludge coagulated at the highest alum dose (84mg(Al)/L). However it was not expected that the predicted throughputs for intermediate doses of 5 and 10mg(Al)/L would be so low. Closer inspection of the original data (presented in §3▪5▪4, §5▪3▪1▪1) indicates that there are two separate effects that account for these results. First, in the case of the 5mg(Al)/L sludge, while the compressive yield stress did not show any significant deviations from the 84mg(Al)/L sludge, the computed R at high solidosities (as obtained from filtration rig experiments) was somewhat higher. In fact, the divergence is greatest above 100kPa. Hence, although the 5mg(Al)/L sludge has a slightly h i g h e r throughput for low output solidosities, as the output solidosity increases the influence of the slower kinetics becomes more important, so that the throughput decreases more sharply than for the 84mg(Al)/L sludge, and at the higher solidosities of industrial interest the 900



predicted throughput is significantly lower. The divergence accelerates in the ‘squeeze’ phase, where the applied pressure difference in the model has been stepped up from 100 to 300kPa. Second, in the case of the 10mg(Al)/L sludge the computed gel point, φg, is much lower than for the 84 and 5mg(Al)/L sludges (0.0015 compared to 0.0024 and 0.0034), and appears to be an underestimate; as a consequence the R(φ) curve for this sludge at low values of φ is shifted to the left, so that effectively R(φ) is overestimated. This leads to the proposition that the above two features of the intermediate-dose sludges — namely overestimated R above 100kPa for the 5mg(Al)/L sludge and underestimated φg for the 10mg(Al)/L sludge — do not represent the true material properties. It is anticipated that in the absence of these two features the throughput predictions would be s i m i l a r for the intermediate- and high-dose sludges, reflecting the previous conclusions that above 5 to 10mg(Al)/L the precipitated coagulant dominates dewatering behaviour. The predictions shown above are a useful illustration of the perils of relying upon model predictions without examining the input data. The predictions above particularly highlight the sensitivity of throughput calculations to R. Even apparently negligible differences on the typical log–log plots of R(φ) — say 20% — may seem important in the context of results such as shown in Figure S13-1. This reinforces the conclusion that for filtration in industrial WTP applications the limiting factor is the kinetics, as quantified by R(φ) with φ → φ∞, rather than the equilibrium state, quantified by py(φ∞).

S13▪3

Alum sludges: pH effects

Figure S13-2 shows the throughput predictions for a range of alum WTP sludges where the dose has been held at approximately 80mg(Al)/L and the pH has been varied from 4.8 to 8.6, with one plant sample plotted for comparison. Unlike Figure S13-1, this chart essentially reflects the dewatering behaviour deduced from py(φ) and R(φ) and reported previously (§5▪4). The dewatering is optimal at pH ~ 6, and progressively deteriorates as the pH is increased up to a value of 8.6. There is also a reduction in throughput when the pH is reduced to pH 4.8.


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D. I. VERRELLI

1.0E-7

mg(Al)/L Lab.: 80 Lab.: 80 Lab.: 84 Lab.: 80 Plant: 1.9


9.0E-8 8.0E-8

pH 8.6 7.6 6.1 4.8 6.1

7.0E-8 6.0E-8 5.0E-8 4.0E-8 3.0E-8 2.0E-8 1.0E-8 0.0E+0 0.000

0.050

0.100

0.150

Average output solidosity, Cφ fD [–] Figure S13-2: Solids throughput as a function of final average cake solidosity for alum sludges coagulated at various pH values.

S13▪4

Selected alum sludges

Figure S13-3 shows a compilation of selected alum sludge throughput predictions for various dose and pH combinations to facilitate comparison of the influence of the two mechanisms. Much as was found for the underlying py(φ) and R(φ) data, the effect due to coagulant dose seems most critical in the low-dose range, when there is a transition from dominance of the raw water constituents to dominance of the precipitated coagulant.

902



1.0E-7

mg(Al)/L Lab.: 80 Lab.: 84 Lab.: 80 Lab.: 1.5 Plant: 1.9


9.0E-8 8.0E-8

pH 8.6 6.1 4.8 6.0 6.1

7.0E-8 6.0E-8 5.0E-8 4.0E-8 3.0E-8 2.0E-8 1.0E-8 0.0E+0 0.000

0.050

0.100

0.150

Average output solidosity, Cφ fD [–] Figure S13-3: Solids throughput as a function of final average cake solidosity for a selection of alum sludges coagulated under various conditions. (Compilation from Figure S13-1 and Figure S13-2.)

S13▪5

Selected ferric sludges

Throughput predictions for a selection of ferric sludges produced under a representative range of conditions are presented in Figure S13-4. These predictions show little variation for the laboratory samples, irrespective of the coagulant dose or pH — the main difference lies in the higher maximum output solidosity that is achievable for the lower-dose material. However all of the laboratory sludges exhibit lower throughputs than the plant sludge samples that were produced under conditions of low coagulant dose and unusually high pH.


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1.0E-7

mg(Fe)/L Lab.: 80 Lab.: 80 Lab.: 5 Plant: 2.2 Plant: 1.5


9.0E-8 8.0E-8

pH 7.3 5.6 5.6 8.7 9.0

7.0E-8 6.0E-8 5.0E-8 4.0E-8 3.0E-8 2.0E-8 1.0E-8 0.0E+0 0.000

0.050

0.100

0.150

0.200

0.250

Average output solidosity, Cφ fD [–] Figure S13-4: Solids throughput as a function of final average cake solidosity for a selection of ferric sludges coagulated under various conditions.

S13▪6

Membrane resistance

In industrial filter presses membrane resistance has been measured to be much greater than in the laboratory rigs, and so it is of interest to estimate the importance of this resistance for WTP sludge filtration, and to confirm that trends for (otherwise) readily and poorly dewaterable sludges still hold true. Figure S13-5 plots throughput predictions for negligible membrane resistance (1Pa.s/m) and for a typical industrial membrane resistance (5×1010Pa.s/m, cf. Table S13-1). The higher membrane resistance dominates filtration behaviour when it is included in the model. Despite the large reduction in throughput, the two sludges are affected in roughly the same way, and so the distinction between them is retained. While it is desirable to incorporate the effects of membrane resistance into any quantitative estimate of throughput, uncertainty exists as to the appropriate value to use. Given that the relevant trends appear to be largely unaffected by the inclusion or exclusion of a membrane

904



resistance term of industrial magnitude, membrane resistance has not been included in the estimates computed in the remainder of this appendix.

1.0E-7


9.0E-8 8.0E-8 7.0E-8

mg(Al)/L Lab: 1.5 Lab: 1.5 Lab: 80 Lab: 80

pH

η L.r membrane

6.0 6.0 8.6 8.6

1Pa.s/m 50GPa.s/m 1Pa.s/m 50GPa.s/m

6.0E-8 5.0E-8 4.0E-8 3.0E-8 2.0E-8 1.0E-8 0.0E+0 0.000

0.050

0.100

0.150

Average output solidosity, Cφ fD [–] Figure S13-5: Influence of membrane resistance on filter throughput predictions for alum sludges of good and of poor dewaterability.

S13▪7

Validation against laboratory filtration

The laboratory sample generated at 84mg(Al)/L and pH ~ 6.1 was chosen for validation. This sample was characterised by duplicate stepped pressure ‘compressibility’ tests, with no evident errors or artefacts. Membrane resistances for laboratory membranes were experimentally estimated by colleagues as part of this project. rmembrane varied from 3×109m–1 for a new 0.8μm mixed cellulose esters membrane to 1×1011m–1 for a 0.1μm nylon membrane [603]. The actual membrane resistance for the runs in question, using 0.22μm PVDF membranes, was estimated to be approximately 4×1011m–1 (or, equivalently, ηL rmembrane ~ 4×108Pa.s/m,


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D. I. VERRELLI

assuming liquid viscosity ηL ~ 0.001Pa.s, as for water).

This was carried out using the

(V )

method applied by STICKLAND [976], among others, in which the slope of a plot of d t2 1 is dV

equal to ηL rmembrane / 2 Δp [cf. 1006]. Although the estimated membrane resistance was higher than previously determined for other laboratory membranes, it is lower than typical industrial filter cloth resistances, and did not greatly affect the filter modelling predictions. Initial model outputs (not presented here) were poor predictors, underestimating both the rate and extent of filtration. The predicted behaviour was significantly affected when the model timestep was reduced, but not nearly enough to account for the discrepancy with the experimental data. The primary reason for the mismatch was sensitivity to the curve-fits to the dewatering parameter data applied by B-SAMS. In the case of the compressive yield stress, the fitted py(φ) curve did not pass directly through the experimental point at 5kPa, but rather passed slightly to the left of it, implying underestimation of φ∞ at 5kPa, and hence underestimation of the extent of dewatering. Shifting the entire py(φ) curve by a constant factor corrected this problem, and gave acceptable agreement in the extent of filtration at equilibrium. In the case of the hindered settling function, the fitted curve passed directly through the point corresponding to 5kPa, with φ∞ ~ 0.022. There was no experimental data between here and φ ~ 0.0025, yet models used feeds with initial solidosity φ0 ~ 0.006 to 0.009, meaning that the entire rate computation depended on a single interpolation across a wide span. Although B-SAMS fits a smooth curve between the points at φ ~ 0.0025 and 0.022, this is only one of an infinite number of possible interpolations. In particular, a lower-lying interpolation appears reasonable, and would predict faster filtration behaviour. Anecdotal evidence within the group suggests that sometimes the R(φ) estimations from settling data extend upwards to high values of R and φ beyond the range of strict validity of the computation; were that true here, then the left-hand interpolation point would be shifted down greatly in R (and only slightly in φ), leading to an overall downwards shifting of the R(φ) curve in the interpolated region. The main outcomes of this validation work are twofold: • Accurate quantitative dewatering predictions are reliant not only upon correct measurement of the dewatering parameters, but also upon curves used to fit the data smoothly and to interpolate between low- and high-solids data. o It is relatively straightforward to force functional curves to more closely fit data points of interest, such as for py(φ). o ‘Correctly’ plotting the curve where it is necessary to interpolate across wide spans requires an iterative, trial-and-error procedure, in which modelling such as presented here would have to be conducted for each material in the region of interest. The interpolation would be adjusted until the model prediction was concordant with the laboratory response. o The sensitivity seen here is greater than that implied by DE KRETSER, SCALES & USHER [606]. The sensitivity here would be magnified because the validation attempted to replicate low-pressure filtration, which means that the accurately known high pressure data is not used at all, which may explain the difference.

906



• Amending the dewatering parameter curves to permit accurate quantitative predictions to be made is a tedious process. For the purpose of making qualitative comparisons of dewatering behaviour, it is generally acceptable to simply use the py(φ) and R(φ) curves optimised within B-SAMS. There is currently also some variation in the predictions depending upon the detailed algorithm settings, such as iteration step sizes.

S13▪8

Conclusions

Throughput modelling generally confirms the conclusions reached previously regarding the effect of coagulant dose and coagulation pH upon dewatering. The results presented are best interpreted as qualitative, and additional fine-tuning of the curve fits used as inputs to the computation would be required to obtain more quantitative results. However the trends are not expected to change. The results indicate that the kinetic parameters — hindered settling function (especially at high solidosities) and membrane resistance — will dominate throughput industrially. It is important to recognise that the throughput graphs are presented in terms of volumetric s o l i d s flux, φ0 Q. Thus, for a given φ0 Q: • a lower input solidosity implies greater sludge inflow volume (larger Q), requiring larger equipment (or longer time) to process; • a lower output solidosity implies a greater volume of filter cake, according to the balance φ0 Q = CφfD Qcake, affecting the scale of the disposal operation.


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D. I. VERRELLI

S14. POLYMER CONDITIONER MIXING RECOMMENDATION OF WRc A critical aspect of polymer conditioning is the shear field experienced by the fluid, and the duration of exposure, as this governs the initial dispersal of the chemical, and then the growth of the flocs through (gentle) collisions. The WRc [315] recommends that the mixing be carried out by turbulence induced by an orifice plate (or possibly a proprietary static in-line mixer, or in the body of a pump), in which case the head loss should be about 1m (alum sludge) to 4 to 5m (ferric sludge). It is not clear why such different energy inputs might be needed. It is also not obvious how this specification might translate to an equivalent energy input for mechanical mixers, as in stirred tanks. This depends implicitly on the absolute pipe diameter and pipe flowrate, the relative orifice diameter, and the volume of the mixing zone. With regard to the former two parameters, a relation is implied by DILLON [315] through his recommendation that the (downstream) pipeline G not exceed 300s–1, with an accompanying table listing pipe diameters from 25 to 300mm. The relative orifice dimensions are then determined by suggested orifice velocities of 5m/s (alum sludge) and 11m/s (ferric sludge) [315], increasing from D/3 to D/2 with D. (The pipe and orifice velocities and areas are related by mass balance [cf. 315].) The most problematic aspect is the mixing volume, which implicitly requires a mixing length, L. The fundamental flow dynamics and mixing properties of free, turbulent orifice jets are not well understood [741]; confinement of the jet in a pipe introduces further complications, namely recirculation of the bulk fluid [cf. 549]. The velocity profile exiting the orifice is unlike that for other geometries, with a maxima away from the centreline, towards the e d g e s o f t h e j e t , where turbulence is also greatest [415, 741]. The mixing efficiency and peak local velocity gradients appear to be higher for an orifice plate than for smoother comparable nozzles or exits [741]. Some rough limits on the mixing length may be considered, given orifice diameters between D/4.4 and D/1.6 (see Table S14-1): • The downstream pressure should be almost stabilised following the vena contracta by about 4 D [186, cf. 1043]. BOYCE [186] also recommends spacing downstream fittings at least a distance of 3 D from such an orifice used for metering. Likewise the data of MI, NATHAN & NOBES [741] for warm air, when converted to cool water using the correlation of RUSHTON [see 1043], indicates mixing is almost complete within a distance 3 D to 3.5 D. However the most intense effects would occur at much shorter distances from the orifice. • Determine the mixing length from the distance at which the expanding free, turbulent jet impinges on the pipe wall. According to TILTON [1043], the jet angle is typically 14° for water systems. This gives a limit value of L → 2 D for small orifices. For the orifices in question here, L drops to 1.5 D to 0.75 D.

908

Appendix S14 : Polymer Conditioner Mixing Recommendation of WRc


(Data in MI, NATHAN & NOBES [741] suggests the angle could be somewhat smaller [1043], implying a somewhat larger L. Also GOULD [415] gave an angle of 8.3° for free circular water jets, for which the limit in the confined case would be L → 3.4 D.) • GOULD [415] criticised the preceding approach as “very artificial”. He [415] focussed on the “initial zone” of a jet in which a core of uniform velocity persists — beyond this zone (in the “main zone”) the entire cross-section of a free water jet would become turbulent. This zone extends to a distance of approximately four times the orifice diameter for (free) jets [415]. For the orifice diameters presently under consideration, this would yield L between 0.9 D and 2.5 D. GOULD [415] assumed that the energy was dissipated across the cross-section of the (free) jet, even though he recognised that the intense turbulence is primarily located in a thin region at the perimeter of the jet, acting on only a small proportion of the total flow. No integrated form was given [see 415]. • A correlation has also been developed between the centreline velocity and the downstream distance [1043]. By setting the centreline velocity equal to the mean pipeline velocity (assuming plug flow), one obtains:  D  0.135    D . L = 1.41 Reorifice   Dorifice  For the scenarios described by DILLON [315] this implies L > 10 D, which seems excessive. • As the pressure drop measured immediately after the orifice is practically equal to that measured a distance D/2 downstream [186, 847], even shorter mixing lengths might be relevant. Considering that the orifice thickness itself should not be less than 0.02 D [847] or 0.03 D [186], the smallest length can be inferred as being of order 0.1 D.

The characteristic velocity gradients, G, for the specified flowrates were validated from equation S26-1 using the HAALAND correlation for the FANNING friction factor (see §S26▪1▪1) and an absolute roughness of 0.1mm [cf. 1043]. The resulting values fell in the range ~300±60 s–1 (Table S14-1(a)) when a viscosity of 1mPa.s was supposed, roughly in line with DILLON’s [315] recommendation. It should be noted, however, that the true viscosity of settled sludge may be closer to 6mPa.s (results in the present work, §7▪4▪1▪3), which rather yields ~140±35 s–1. While DILLON [315] indicated both orifice velocities and head losses, these are related by well-known empirical correlations, as in [847]: v2 Hloss = K , [S14-1] 2g in which Hloss represents head losses, and the factor K is a multiple of the ‘velocity head’ for a given fitting. For the orifices in question, with large diameter ratios and REYNOLDS numbers, K is estimated from [847, cf. 1043]: 2

 A  − 0.6  . K = 2.78  [S14-2]  Aorifice  It turns out that the quoted orifice velocities and head losses are not compatible with this correlation. Hence each is taken in turn as a basis below, in Table S14-1(b–e). G is then estimated by multiplying Hloss by the mass flowrate to obtain power dissipation, P [W], and dividing by the mixing volume and viscosity in accordance with equation R1-5b. In


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D. I. VERRELLI

the tables the mixing volume was taken as the full pipe area multiplied by the wall impingement distance for a jet angle of 14°. The residence time, t, has been simplistically computed for plug flow, and no flow weightings have been applied [cf. 427]. Table S14-1: Mixing of polymer conditioner into settled sludge using an orifice plate according to the specifications of DILLON [315] (shown in bold).

(a) System properties, either sludge with two alternatives for viscosity.

SYSTEM V

PIPE D

v

G

3

[m /h]

[mm]

[m/s]

1 5 12.5 25 64 125 210 322

25 50 75 100 150 200 250 300

0.57 0.71 0.79 0.88 1.01 1.11 1.19 1.27

[s–1] (1mPa.s) (6mPa.s) 352 175 310 150 280 133 277 130 260 121 250 115 242 111 237 108

(b) Mixing of alum sludge with two alternatives for viscosity. Basis is orif ice v elocity .

SYSTEM V

v

D

Hloss

P

[m3/h]

[m/s]

[mm]

[m]

[W]

[s]

1 5 12.5 25 64 125 210 322

5 5 5 5 5 5 5 5

8.4 19 30 42 67 94 122 151

3.1 3.0 2.9 2.8 2.7 2.7 2.6 2.6

8 40 99 193 478 908 1490 2236

0.06 0.09 0.12 0.13 0.16 0.19 0.22 0.24

910

ORIFICE t

Ga

G.t b

[s–1] [–] (1mPa.s) 22700 1330 18100 1600 15700 1810 14500 1910 12800 2100 11700 2240 10900 2350 10300 2430


Ga

G.t b

[s–1] [–] (6mPa.s) 9300 540 7400 650 6400 740 5900 780 5200 860 4800 920 4400 960 4200 990


(c) Mixing of alu m sludge with two alternatives for viscosity. Basis is h ead loss.

SYSTEM V

ORIFICE t

Hloss

v

D

P

[m3/h]

[m]

[m/s]

[mm]

[W]

[s]

1 5 12.5 25 64 125 210 322

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

3.0 3.1 3.1 3.2 3.3 3.3 3.4 3.4

11 24 38 53 83 115 148 183

3 14 34 68 174 340 572 877

0.05 0.07 0.10 0.11 0.13 0.15 0.17 0.19

Ga

G.t b

[s–1] [–] (1mPa.s) 14000 700 11500 850 10100 970 9600 1030 8600 1140 8000 1230 7600 1300 7300 1350

Ga

G.t b

[s–1] [–] (6mPa.s) 5700 290 4700 350 4100 390 3900 420 3500 470 3300 500 3100 530 3000 550

(d) Mixing of ferric sludge with two alternatives for viscosity. Basis is orifice v elocity .

SYSTEM V

ORIFICE t

v

D

Hloss

P

[m3/h]

[m/s]

[mm]

[m]

[W]

[s]

1 5 12.5 25 64 125 210 322

11 11 11 11 11 11 11 11

5.7 13 20 28 45 63 82 102

16.1 15.9 15.7 15.5 15.3 15.2 15.0 14.9

44 216 535 1058 2671 5157 8580 13039

0.07 0.11 0.14 0.16 0.21 0.25 0.28 0.31

Ga

G.t b

[s–1] [–] (1mPa.s) 48000 3290 38300 4060 33100 4650 30600 4980 26800 5600 24500 6070 22800 6450 21500 6770

Ga

G.t b

[s–1] [–] (6mPa.s) 19600 1340 15600 1660 13500 1900 12500 2030 11000 2290 10000 2480 9300 2630 8800 2760

(e) Mixing of ferric sludge with two alternatives for viscosity. Basis is h ead los s.

SYSTEM V

Hloss

[m3/h]

1 5 12.5 25 64 125 210 322

c

ORIFICE t

v

D

P

[m]

[m/s]

[mm]

[W]

[s]

4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5

6.0 6.1 6.1 6.2 6.2 6.3 6.3 6.4

7.7 17 27 38 60 84 108 133

12 61 153 306 784 1531 2573 3945

0.06 0.09 0.12 0.14 0.18 0.21 0.24 0.26

Ga

G.t b

[s–1] [–] (1mPa.s) 26800 1640 21700 2030 19000 2330 17700 2490 15700 2810 14500 3050 13600 3250 12900 3410

Ga

G.t b

[s–1] [–] (6mPa.s) 10900 670 8900 830 7700 950 7200 1020 6400 1150 5900 1240 5500 1330 5300 1390

Notes a Volume taken as full pipe up to impingement for a jet angle of 14°; values rounded to nearest 100s–1. b Values rounded to nearest 10. c Specified as 4 to 5m.

Unfortunately the specifications do not appear to provide for a characteristic velocity gradient, G, that is independent of system size. The other key operational parameters t and G.t also vary. Appendix S14 : Polymer Conditioner Mixing Recommendation of WRc

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D. I. VERRELLI

Neither is there consistency between the two bases for computation: relying on orifice velocities tends to yield estimates of G about 60% greater than those relying on the head loss. The estimates of G tend to be about twice as high for the ferric sludge, and the indicative exposure time is also slightly larger for the ferric sludge based on the smaller orifice diameters required to generate the larger shear. There is a significant reduction in the mixing intensity predicted if the viscosity is raised from that of water (1mPa.s) to 6mPa.s, dropping by a factor of 2.45 following the square-root proportionality. All of these variations notwithstanding, the estimated mixing parameters can be expressed to order of magnitude as: G = O(104) s–1; t = O(10–1) s; and G.t = O(103). This is much shorter and more intense mixing than that proposed for the laboratory (p. 400).

912



S15. BOOTSTRAP AND JACKKNIFE STATISTICS S15▪1

Motivation

In §7▪4▪4▪2(b) the bootstrap method of evaluating confidence intervals on estimates arising from the computation of D (φ∞) — namely D (φ∞) itself, along with φ∞, and assorted quantifications (as R2) of the goodness of fit. As alluded to in that sub-section, key advantages of the bootstrap method are that it enables computation of confidence intervals: • on any parameter(s) (θ, say) for which evaluation(s) from multiple observations are available [cf. 230]; • without assuming any distribution *; • incorporating all sources of variation. The assessment of only one V (t) filtration profile was presented in §7▪4▪4▪2(b) — for a given period of constant pressure — leading to a single evaluation of D (φ∞) and the associated parameters of interest. However, the underlying data comprises multiple observations, namely the time series of pairs of (t, V ), so the method can be applied. Most of the ‘traditional’ statistical analyses are rooted in the assumption of ‘normality’: i.e. that the parameter of interest follows a GAUSSian distribution. This assumption can have a huge effect on statistical inferences, such as in the evaluation of confidence intervals. As an example, the coefficient of determination, R2, is known to deviate strongly from GAUSSian behaviour [464], and it should be obvious that assuming otherwise would lead to unrealistic predictions, such as symmetrical confidence intervals of the form R2 = 0.999±0.005 [cf. 336]. The most common method of mitigating against this problem is to use a ‘normalising’ (or ‘variance stabilising’) transform, so that the transformed data d o e s follow a GAUSSian distribution, for which inferences can be made and then ‘inverted’ back into the original number space. The problem with this technique is that the assumption of a distribution is still implicit in the choice of a normalising transform. While simple transforms (e.g. taking logarithms) are popular choices, the proper transformation can be considerably more complicated (e.g. FISHER’s Z-transformation for R2 [109, 336, 464]) and cannot, in general, be ascertained by any simple technique. Bootstrapping (or jackknifing) does away with this problem by using the empirical distribution to estimate the population distribution [109, 336]. (Jackknifing is avoided for estimation of confidence intervals in the present work due to the discomforting fact that the very process of correcting bias in jackknife estimates can cause the

*

In a limited number of exceptional cases, such as for non-smooth statistics or inferences on the extreme tails of the distribution, it is advantageous to smooth the empirical distribution function, with one procedure for doing so being to fit it using a well-behaved ‘model’ distribution function [109, 336]. Appendix S15 : Bootstrap and Jackknife Statistics

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D. I. VERRELLI

‘corrected’ estimate to diverge outside the appropriate domain * [see 833]. Furthermore, MILLER demonstrated that the jackknife gives strictly correct results only when the parameter of interest is asymptotically locally linear, which confers asymptotically normal properties onto the problem [336, 833] — the parameters of interest in the present work are expected to be quite non-linear.) In terms of including all sources of variation, it is known that excluding some of the fitting parameters from the uncertainty analysis will tend to underestimate the margins for error in all of the fitting parameters (see e.g. §7▪4▪4▪2(b)) — and any derived quantities. In the present application there are three fitting parameters (E1, E2, E3), but the concept is neatly illustrated for the case of two parameters. Consider a data set to be fit by the straight line y = m x + c. If the intercept, c, is fixed, then the slope, m, will be more constrained, and the range of feasible values it could take would be reduced, and vice versa, as in Figure S15-1.

y

y

A

x

y

B

x

C

x

Figure S15-1: Illustration of the effect of assuming a fitting parameter to be constant when evaluating uncertainties of the fit. A — Limits on intercept (c) when holding slope (m) constant. B — Limits on slope (m) when holding intercept (c) constant. C — Two possible fits when both fitting parameters are allowed to vary.

S15▪2

Application

Although nowadays a standard tool of statisticians, the bootstrap — and its companion or alternative, the jackknife — remain less well known outside of that arena [226, cf. 464]. Nevertheless, recognition is growing [464]. The methods can be implemented in a “bewildering array” of subtly different ways, and have the potential to “lead to disastrous results” if applied “blindly” [109, also 230], so it is appropriate to outline the version adopted in the present work.

*

914

For example, the uniformly minimum variance unbiased estimator (UMVUE) obtained by the biascorrected jackknife for the s q u a r e of the population mean c a n be n e g a t i v e [833]. Appendix S15 : Bootstrap and Jackknife Statistics


S15▪2▪1 S15▪2▪1▪1

Bootstrap procedure Constructing bootstrap data sets

As mentioned, the essence of the bootstrap method is the estimation of the population distribution of a given parameter of interest, θ, by means of the corresponding empirical distribution, i.e. the distribution of the bootstrap estimates, Bθ, given the original data [109, 336]. Let us denote the empirical distribution of θ as H (with inverse H‒1), so that we may write Bθ ~ H. What this means in practice is that the empirical distribution of N observations * is randomly sampled, with replacement, N times to obtain one ‘bootstrap sample’; this yields a data set of the same size as the original, from which the parameter(s) of interest can be (re-)evaluated [226, 336, 464]. In principle this can be done by bootstrapping (i.e. sampling) the residuals or by bootstrapping the data points; however only the latter makes sense for timeseries data (or other ordered s e r i e s ), because variance (and so the expected magnitude of the residuals) may well be a function of time and moreover a functional form for V (t) would otherwise need to be assumed a priori [see 109, 336]. (Autocorrelation of residuals should also be less problematic when bootstrapping the data points [cf. 109]: in general, “bootstrapping [data] pairs is less sensitive to assumptions than bootstrapping residuals” [336].) Naturally the elements of the bootstrap sample are arranged in physically-meaningful order (e.g. chronologically) here. The above sequence is repeated, say M times, to obtain the desired number (M) of bootstrap samples. Each bootstrap sample permits an evaluation of the parameter(s) of interest ( B θm , say), and so collectively these estimates are useful for estimating the distribution(s) of those parameter(s). (It is hence trivial to extend the technique to obtain accurate estimates of j o i n t distributions, if desired, unlike the case for other techniques [e.g. 226].) This procedure can be recognised as just an instance of Monte Carlo estimation [109]. (In principle the scope of the bootstrap method extends to other techniques — not described here — that do not involve Monte Carlo estimation, but they are seldom applied in practice [see 109].)

S15▪2▪1▪2

Correcting bias

In terms of confidence intervals, two important aspects are compensation for bias in the estimates and reduction in the amount of computer processing required. The latter has an obvious practical implication in terms of the computation time, but is also interrelated with the accuracy through the dependence on random number generation (see §S15▪2▪3, following). Methods that either do not account for bias, or account for it simplistically, have been curtly dismissed as “not satisfactory” [109, see also 336, 464]. The two (relatively) well-known techniques of bias compensation that typically produce estimates accurate to second order are ‘percentile-t’ † and ‘accelerated bias-correction’ ‡ [109, 230, 336, 464].

*

A set of c o r r e s p o n d i n g data is here considered a single observation, as in a single pair of (t, V ) data.

†

Also known as ‘bootstrap-t’ [336] and ‘studentised pivotal method’ or ‘variance-stabilised bootstrap-t’ [230].

‡

Also known as ‘BCa’ or ‘bias-corrected and accelerated’ [230, 336] and ‘accelerated bias-corrected’ [109]. Appendix S15 : Bootstrap and Jackknife Statistics

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D. I. VERRELLI

The p e r c e n t i l e - t technique ‘studentises’ [755] the estimates obtained from the bootstrap samples (i.e. ‘normalises’ according to the empirical mean and standard deviation), so that inferences are instead made on approximately pivotal parameter(s) [109]. In theory this method can perform better than the accelerated bias-correction technique, but that depends strongly upon correct specification of the (true) population standard deviation, which is used to transform the inferences back to the original number space [109, 230]. The population standard deviation is typically estimated by jackknifing [109]. An iterative or double-bootstrap procedure has also been suggested as a more accurate alternative, but is computationally-prohibitive [109, 336], and may exceed the limits of the random number generator (see §S15▪2▪3▪4). It appears that a c c e l e r a t e d b i a s - c o r r e c t i o n is the more robust technique, and it was recommended by EFRON & TIBSHIRANI [336] *, so it has been adopted here. It is most neatly described as a sequence of two adjustments to the simple percentile calculation. It is also worth noting a rule of thumb proposed by EFRON & TIBSHIRANI [336] which states that the bias need not be corrected if it is estimated to be small compared to the standard error. The recommended threshold for the ratio of estimated bias to standard error is |±0.25|, for which the root-mean-square error is underestimated by only +3.1% (less for smaller-magnitude ratios) [336, 464]. The bias is estimated as the sample mean of the bootstrap parameter estimates less the parameter estimate based on the original data [336] †, i.e. mean{ B θ} – θˆ . The standard error is estimated with the standard deviation of the bootstrap estimates treated as a population [336] ‡. Before proceeding to confidence interval applications, it is useful to reflect on the ‘direction’ of bias correction. It can be confidently assumed that our original estimate, θˆ , will be different from the corresponding naïve bootstrap estimate mean{ B θ} . There is a common misconception that mean{ B θ} is, itself, the bias-corrected estimator of θ [336]. In fact  mean{ B θ} is more biased than θˆ . The bias-corrected estimator of θ, θ , can be estimated by approximating the general formula  θ = θˆ − bias

[S15-1]

using the bootstrap data [336]:

*

HENDERSON [464] also recommended this option, or alternatively a more-complicated ‘tilting’ (i.e. weighted) version introduced by EFRON (1981). (The latter did not perform as well in HENDERSON’s [464] test analysis.) CARPENTER & BITHELL [230] critically examined the most common approaches, and outlined the d i s a d v a n t a g e s of accelerated bias-correction.

†

An “improved” estimate of the bias is available, which converges faster and more robustly (oscillates less) to the asymptotic bootstrap bias estimate as M is increased [336], but which is more cumbersome to implement.

‡

The standard error is more robustly estimated with (H‒1(α/2) – H‒1(1 – α/2)) / 2zα/2, in which H‒1 is the inverse of the empirical distribution function (H) and zα/2 is the α/2 critical point of the standard normal distribution, Φ [336]; typically α = 0.05 is used.

916

Appendix S15 : Bootstrap and Jackknife Statistics


B

 θ ≡ θˆ − B bias

(

= θˆ − mean{ Bθ} − θˆ

)

[S15-2]

= 2θˆ − mean{ θ}  ≈θ. B

The rationale for this can be quickly demonstrated through the example of bootstrapping a numerical integration, in which the parameter of interest is the area, A. Consider the diagramme in Figure S15-2. Here the curvature of the true curve means that the original estimate is biased downward, but the bootstrap samples are universally biased even further downward. (In fact, for this scenario strictly BAm ≤ Â for all i; if M is not large, then for all computations BAm / Â may even result!) By comparing mean{ B A} and Â it can be inferred that the true value of the area, A, can be expected to be greater than Â, and the bias correction of equation S15-2 does increase the estimate.  Unfortunately, in this artificial scenario the bias-corrected estimate, B A , is actually somewhat further from the true value, A, than was the original estimate, Â. This is an example of why “bias correction can be dangerous in practice” [336]. Even if the biascorrected estimator is less biased than the original estimate, it may have substantially greater standard error, which in turn results in a larger root-mean-squared error [336, 464]. B

Â = 0.380

A1 = 0.309

Selected thrice

1

B

A2 = 0.361

Selected twice

A = π/8 ≈ 0.393

0 true bias = –0.013

1

After several more bootstrap samples... ... mean{ B A} = 0.334 estimated bias = –0.046   B A = 0.426

Figure S15-2: Illustration of the bias arising as parameters are bootstrapped. Estimation of area by numerical integration of observed data points. It is assumed the intercepts are fixed. Values are indicative only.

It has already been noted that where the (estimated) bias is small relative to the standard error, it can be neglected, and indeed it may be safer to do so [336]. On the other hand, if the (estimated) bias is large relative to the standard error *, then it may be an indication that the method of computing the parameter θˆ (and Bθm) “may not be an appropriate estimate of the parameter θ”. For the artificial scenario discussed here, the standard error is presumably quite large too; it is reasonable to concur that the simple

*

HENDERSON [464] at one point in his discussion interprets the threshold value of |±0.25| as the limit beyond which bootstrap estimates are no longer “allowable”; the statement is not supported elsewhere. Appendix S15 : Bootstrap and Jackknife Statistics

917

D. I. VERRELLI

integration method illustrated in Figure S15-2 is particularly unsuitable for estimating A, given that it is inherently biased downwards for the true curve as sketched. Moderate biases tended to be estimated in the present application, and so these were corrected in the manner described below. The following method is not subject to the same overcorrection as above: rather, the confidence intervals come exclusively from the bootstrap sample evaluations, and it is easy to identify excessive bias.

S15▪2▪1▪3

Accelerated bias-correction

Given M bootstrap samples have been produced, M evaluations of each parameter of interest should have been generated, so that an empirical distribution can be constructed for each. Supposing that a specific parameter of interest, θ, has the empirical distribution H (with inverse H‒1) — we may write this as θ ~ H — then the most basic estimate of the two-sided, symmetrical 100(1 – α)% confidence interval is given by [cf. 109, 336]: [S15-3] [H‒1(α/2), H‒1(1 – α/2)] ; in other words, the α/2 and 1 – α/2 p e r c e n t i l e s of H. It is common to take α as 0.05, so that 95% confidence intervals are estimated. The ‘bias-corrected’ method adjusts this for bias in the median by comparing the median of the M bootstrap evaluations ( median{ B θ} ) with the parameter estimate obtained by evaluating the original data, θˆ [336]. Mathematically this is written as [109, 336] [H‒1( Φ(2 zˆ 0 + zα/2) ), H‒1( Φ(2 zˆ 0 + z1 – α/2) )] ,

[S15-4]

in which zα is the 100αth percentile point of the standard normal distribution, Φ (i.e. cumulative density function, whose inverse is Φ‒1), and zˆ 0 is the percentile point of Φ corresponding to H( θˆ ). That is, zα = Φ‒1(α), and zˆ = Φ‒1(H( θˆ )) [109, 336] *. 0

A slight variation has been employed in the present work, to improve robustness. In this variation, presented by EFRON & TIBSHIRANI [336], zˆ 0 is instead estimated by finding:  count{ Bθm < θˆ }  . zˆ 0 = Φ −1  [S15-5]   M   This is unbounded for ratios of either zero or unity; hence a novel enhancement is instituted whereby the former is replaced with 1 / 2M and the latter with (2M – 1) / 2M. (The reasoning is based on the assumption that a single more-extreme value would be returned at the relevant end if M were doubled.) In either case, if median{ B θ} = θˆ , then H( θˆ ) = 0.5, so that zˆ = 0, and the interval in S15-4 0

reduces to the simple percentiles of S15-3. It is important to appreciate the direction of bias correction. Namely, if the bootstrap estimates are characterised by much l a r g e r estimates than the original estimate ( median{ B θ} [ θˆ ; count{ Bθ < θˆ } / M), then zˆ / 0 and the confidence interval endm

0

points are chosen as smaller percentiles of H, so the interval covers values of s m a l l e r magnitude than the uncorrected case. The logic behind this is the same as was outlined in the previous sub-section.

*

918

By symmetry of the standard normal distribution, –zα/2 = Φ‒1(1 – α/2). Appendix S15 : Bootstrap and Jackknife Statistics


Lastly, the accelerated bias-correction approach stabilises the variance in addition to correcting any bias [109]. (The method assumes the e x i s t e n c e of a normalising transform, such as referred to in §S15▪1, but k n o w l e d g e of the transform is n o t required [109].) This is achieved by adjusting the effective critical values according to an ‘acceleration constant’, â [109, 336]: [H‒1( Φ( zˆ α / 2 ) ), H‒1( Φ( zˆ 1 − α / 2 ) )] , [S15-6a] where zˆ α / 2 ≡ zˆ 0 +

zˆ 0 + zα / 2 . 1 − aˆ ( zˆ 0 + z α / 2 )

[S15-6b]

The acceleration is so called because it is a measure of the rate of change of the standard error of θˆ — i.e. the predictor of the standard deviation — with respect to the true value, θ [336]; this permits the correction for heteroscedasticity. If â = 0 then the interval in S15-6 reduces to that of S15-4. There are a number of ways to compute â [336]. â is typically approximated by the skewness of the score function [see 336] evaluated at θˆ [109]. The simplest computation uses the jackknife to obtain [230, 336]:

 (mean{ aˆ = 6   (mean{  N

J

n=1

N

n=1

J

θ } − J θn

θ } − θn J

) )  3

2

3/ 2

.

[S15-7a]

The jackknife and its notation are described in the following section (§S15▪2▪2). As mentioned, â can be interpreted in terms of the skewness of J θ , G1 { J θ } , as per aˆ = −

G1 { J θ } ( N − 2) . 6 N N −1

[S15-7b]

There are a few “pathological” scenarios under which the recommended bootstrap procedures will ‘fail’, but these are unlikely to arise in practice [230] (and under such scenarios the more commonplace methods would surely ‘fail’ also).

S15▪2▪2

Jackknife procedure

The jackknife yields an approximation to the bootstrap [336]. The parameter(s) of interest must be evaluated for N different jackknife samples, and so the jackknife may be attractive where N is rather small (i.e. less than the intended M), but will involve more work otherwise [336]. Whereas the bootstrap typically involves parameter evaluation based on randomly constructed data sets, the jackknife is more systematic. The parameter(s) of interest are evaluated ( J θn , say), for each of the N sets of (N – 1) data points for which the nth data point of the original series has been deleted, with n incremented from 1 to N [226, 336].


919

D. I. VERRELLI

The jackknife estimator of θ * is intended to be less biased than θˆ and is given by [833]:  J θ ≡ θˆ − J bias

(

= θˆ − ( N − 1) mean{ J θ} − θˆ = N θˆ − ( N − 1) mean{ J θ}  ≈θ

).

The mean of the jackknife evaluations is just [336, 833]: 1 N J θn . mean{ J θ } = N n =1



[S15-8]

[S15-9]

Notice that the deviation of mean{ J θ } from θˆ is much less than that of mean{ Bθ } ; for the jackknife an ‘inflation factor’ of (N – 1) is required — compare equations S15-2 and S15-8. The reason is that in the jackknife only a single data point is deleted for each evaluation of the parameter of interest, so that the N jackknife data series are much more similar to the original data series than the bootstrap samples are. As a point of interest, it is possible to approximate mean{ J θ } a posteriori by a selective analysis of the Bθm data referred to as “jackknife-after-bootstrap” [336, cf. 464]. Although this avoids the N parameter estimations needed for the standard jackknife, it does require additional processing to select the relevant elements of Bθ and furthermore introduces additional errors which can be significant [336]. Given that in the present work N ≤ M always, and usually N / M, this option was not implemented. A further use of this idea is to assess the sensitivity of the (bootstrap) estimates to particular data points, or to identify high-leverage data points [230]. Numerous alternatives to the standard jackknife have been proposed, most with the objective of increasing robustness and reducing error; a number are described by PEDDADA [833]. The “butcher knife” procedure of HESTERBERG has also been suggested for nonsmooth statistics [464]. These were not used in the present work, given that here the jackknife has been used only for estimating â (see equation S15-7), which generally has been close to zero.

S15▪2▪3 S15▪2▪3▪1

Optimising the accuracy of the estimate Censoring bootstrap sample results

In rare instances a given bootstrap sample might not be evaluable. For example, in a scenario s i m i l a r to that of Figure S15-2 where it was desired to estimate 1 / A, rather than A, the situation might arise where BAm = 0, so that B(1 / A)m → ∞. Such a situation could arise if one of the data points lay exactly on the horizontal axis, and by chance it was repeatedly chosen as the only element in the bootstrap sample. Obviously such a situation is far more likely to occur if N is small and M is large. Specifically, the expected number of occurrences among the M bootstrap samples is equal to M / NN. Taking a typical M of 2000, then the likelihood of an occurrence is rather low even for

*

920

Strictly it is the jackknife estimator of θˆ [833]. Appendix S15 : Bootstrap and Jackknife Statistics


small data series sizes: e.g. an expected value of 2000 / 1010 = 0.0000002 for N = 10. (Alternatively, the probability of at least one occurrence is given by 1 – (1 – 1 / NN)M; for the previous example this is negligibly smaller than 0.0000002, as also obtained using M / NN *.) Other scenarios may be still more sensitive to ‘degenerate’ bootstrap samples. In that case it is proposed that the degenerate results be censored from the analysis [226, 230]. Of course, this action is undesirable, and a preferable course would be to ensure a sufficiently large number of data points (N). The issue did not arise in the present work.

S15▪2▪3▪2

Number of data points

The experimenter does not always have control over the number of data points (N). Nevertheless, there are a couple of issues to be aware of. With regard to significance testing, “simulation studies show that the bootstrap procedure is never reliable for [N ≤ 20]” [109]. However, this conclusion is not necessarily applicable to the computation of confidence intervals, where in fact interest often arises b e c a u s e of a small number of data points giving rise to significant uncertainty. Often the estimated confidence intervals are slightly wider than the specified α would dictate; this is referred to as ‘coverage error’ [230]. For the accelerated bias-correction method this increases (surprisingly) as â → 0, and decreases with N–1 [230]. In the present work N is expected to be large enough in most cases that this is not a significant problem (compared to the true modelling error). Where N is indeed small enough for coverage error to be a significant concern, then other approaches such as the percentile-t (see §S15▪2▪1▪2) m i g h t be preferable [230, cf. 336].

S15▪2▪3▪3

Number of bootstrap samples

As a point of interest, there is clearly no benefit in constructing an ‘excessive’ number of bootstrap datasets: increasing M enhances the precision with which the empirical cumulative density function, H, is known, but at large values of M the significant additional computational effort yields negligible benefit. A simple indicator of the magnitude of this value is given by considering a bootstrap analogue of the jackknife, in which every possible combination of the N data points (or residuals) is evaluated exactly once. Then the number of distinct bootstrap datasets is equal to 2N – 1CN = (2N – 1)! / ( N! (N – 1)! ) [336, 464]; for N = 10 this is already 92378. Hence it is only for the case of N ( 6 that it is worthwhile considering a reduction in M below the conventional guideline values presented below. Although a few such cases were evaluated in the present work, M was not reduced per se, to avoid writing of additional code. In the above discussion the number of bootstrap samples was left open as the variable M. A number of practical guidelines have been proposed by various researchers.

*

With N T 10 the two formulæ yield practically the same results for any practically-conceivable M. Appendix S15 : Bootstrap and Jackknife Statistics

921

D. I. VERRELLI

BABU & SINGH reported that second-order accuracy of bootstrap estimates was maintained provided that M ≥ N ln(N) [109]. In the present case the maximum sub-set size is limited to 1000, i.e. N ≤ 1000, so that the infimum condition (greatest lower bound) on M is ~6900. In practice it was not found necessary to consider sub-set sizes greater than N = 500, and so M T 3100 is a conservative criterion for the range of all sub-sets computed. HALL argued that 95% coverage probability could be maintained with merely M = 19, however the resulting confidence intervals would tend to be rather conservative [109]. As a more practical rule of thumb EFRON & TIBSHIRANI [336] recommended M = 1000 for general use of the accelerated bias-correction technique in order to reduced Monte Carlo sampling error [cf. 109]. YAFUNE & ISHIGURO [1136] indicated M ~ 2000 to be a suitable value. CHERNICK suggests ~10000 on the basis that the incremental ‘cost’ is small so a (perhaps wildly) conservative M is best [464]: that assessment may be true for relatively simple parameter function evaluations on modern computers, but is not valid as a general guideline. CARPENTER & BITHELL [230] suggest specification of M = 999 or 1999 (et cetera), to avoid interpolation of percentiles. In the present work a reasonable compromise was achieved by setting a standard minimum M of 1000. The estimates arising from these computations were assessed to ensure appropriate coverage at the tails of the distribution (at least five points of the empirical distribution to be beyond the estimated confidence interval at each end for D ). When this condition was not satisfied for a given run with M = 1000, then M was doubled (once only) to 2000. This echoes a methodology suggested by LUNNEBORG (2000), except that there the criterion is the standard error of the estimate(s) [464]. Setting M < 1000 is probably a ‘false economy’ for confidence intervals [464].

S15▪2▪3▪4

Random numbers

An easily-overlooked issue is the randomness of the computer algorithm that is used to select the data to be included in the bootstrap sample at each iteration; such algorithms are almost always based on a ‘random number generator’ implemented in software code and evaluated ‘on the fly’ by the computer. Although it is comforting to imagine that the outputs of such generators are indeed truly random, in fact they are strictly p s e u d o - r a n d o m numbers [174, 464], because the generators rely on rules, making both the process and results strictly deterministic [74, 906, 1127]. One useful quantification of the ‘randomness’ of generator output is the p e r i o d of the algorithm, i.e. the number of iterations until it repeats itself [464]. This varies significantly between algorithms [e.g. 464, 1127]. Certain ‘tricks’ have been found to enhance randomness, including the use of cellular automata [74, 1127] and the combination of multiple sources of randomness such as multiple algorithms [1117] or incorporation of noise

922



from ‘external sources’ * [702]. The digits of transcendental numbers such as π hold further promise [906]. Standard statistical packages are presumed to have ‘large’ periods (>1018 [719, 1117] †), while non-specialised software packages often implement generators with smaller periods [464]. The following periods have been reported (target uses in parentheses): ~7×1012 for Excel 2003 ‡ (Microsoft, ‘office’ spreadsheet) [719]; ~5×1018 for S-PLUS (Insightful, statistical analysis) [464]; up to ~1×101535 for the default § generator in Mathematica 6.0 (Wolfram Research, mathematical analysis) [74, 937, cf. 1127]; and ~2×106001 for Gnumeric 2003 (GNOME, ‘office’ spreadsheet) [719]. The most straightforward means of justifying the use of a given random number generator is to s o m e h o w (see below) compare its period with the total number of evaluations required to obtain the bootstrap estimate. The number of evaluations can be very large indeed. Consider that a typical confidence interval will require M T 1000 bootstrap samples to be taken to yield a statistically sound estimate. Each bootstrap sample will be comprised of N data points, each of which has been chosen through execution of the random number generator. (The jackknife requires N further computations of the parameter(s) of interest, but does not require random number generation.) Thus the number of calls, И, to the random number generator is M N; in the present work this may be as large as 106. Although the number of calls (И ( 106) appears comfortably less than the likely period of the random number generator, this comparison may not be meaningful. RIPLEY suggested that the period should be greater than 200 И2 [464, 718, 1117]! For the present work this may be as large as 2×1014. (This is the most conservative suggestion. KNUTH and RIPLEY had earlier suggested minimum periods of 1000 И and O(101 И2), respectively [718]: up to 109 or 1013 for the present work.) It is evident that Excel 2003 does not satisfy RIPLEY’s suggestion for И ~ 106 calls. However, for many of the analyses И was considerably smaller (due to smaller N), and so for the purposes of the present work Excel 2003 is deemed ‘adequate’. Furthermore, Excel’s non-

*

The external sources can include suitably processed physical device output, digital recordings of rap music, or digital (bitmap) images of naked ladies [702]. (Regardless of the arguably playful tone, this comes from a reference that was generally acknowledged as the standard on the topic for around a decade [e.g. 1117] — the current benchmark is the TestU01 suite of L’ECUYER & SIMARD [see 719].)

†

Standards continue to rise as theoretical understanding improves, experience increases, and computing capabilities rise (so that greater demands are made) [e.g. 719, 1117]. A sensible approach is to consider the maximum demand that could possibly be made : e.g. allowing a v e r y f a s t O(109) i t e r a t i o n s per second for one solid year (O(107) seconds) would result in O(1016) calls to the generator, so any period greater than O(1034) should suffice for any practical application in the foreseeable future [cf. 1117] (for comparison one of the largest simulations run prior to 1998 made O(1011) calls [718]).

‡

Severe problems in Excel’s random number generation have been ameliorated (when using the command “=RAND()”; but u n f i x e d in the ‘Analysis Toolpak’!), although it is still not recommended for high-end use, as some bugs reportedly remain in the implementation of the current algorithm [719].

§

The precise period depends upon the seed, but an upper limit is defined by the Size parameter of the cellular automaton ‘grid’ and the number of values skipped (to avoid near correlations) [74, 696, 937]. Using the default parameter settings [74], the upper bound on the period is estimated as ~25120 / (4 × 5120 × 64) [937]. Potentially much larger periods could be obtained by increasing the Size parameter [74, 696]; Appendix S15 : Bootstrap and Jackknife Statistics

923

D. I. VERRELLI

linear solver * was also called in the present work, and so it was useful to perform bootstrap analysis on the model including the software’s built-in regression algorithm. Other software packages do offer superior statistical algorithms, and could be considered for future work of a similar nature in order to further improve accuracy. Further alternatives would be to import random numbers from an archive, or to generate them using custom code [e.g. 702].

*

924

As stated, the initial objective is to maximise R2 (called using “=RSQ(·, ·)”) for the linear fit between t and ln(E3 – V ) by adjusting the predicted φ∞. The Solver command from the Analysis Toolpak was trialled with various configurations: ultimately the only settings changed were MaxTime (10000s) and Iterations (10000); it was not found advantageous to change the default Convergence (0.0001) or Precision (0.000001) values or other settings. Note that φ∞ was adjusted rather than E3 for convenience in ensuring the critical constraint φf < φ∞ ≤ 1 was observed in all attempted solutions (φf is the largest φ in the data sub-set input, i.e. the final φ). Despite reasonable criticisms of the Excel Solver routine(s) [e.g. 719], they appeared to perform acceptably in the present work; it may be noted that care was taken to always start with a valid initial guess of φ∞, being either the result of the immediately preceding optimisation or else unity (if the former was invalid). Appendix S15 : Bootstrap and Jackknife Statistics


S16. SILANISATION Glassware surfaces may be rendered more hydrophobic by a process of silanisation (or silylation), in which a chlorosilane is reacted at the surface, where the glass is assumed to consist largely of SiO2. The most commonly chosen chlorosilanes for this process are: dichlorodimethylsilane (“DCDMS”), chlorotrimethylsilane (“CTMS”), (CH3)3SiCl; (CH3)2SiCl2; and trichlorooctadecylsilane (“TCOS”), (C18H37)SiCl3 [492, 987]. Chlorodimethyloctadecylsilane, (C18H37)(CH3)2SiCl, is also sometimes used [492]. The hydrophobicity does not generally depend greatly on the chlorosilane chosen [492]. Silanisation with CTMS has been identified as a more ‘robust’ treatment, in that results are more reproducible, perhaps due to the ability of di- and trichlorosilanes to form dimers or polymers, especially in the event of contamination of the reagents by water * [987]. Polymerisation of trichlorosilanes can lead to the formation of lumps and aggregates on the sample surface (or, indeed, in solution [392]), which is avoided by silanisation using a vapour deposition method [843]. It is suggested that available CTMS contains inevitably some small amounts of higher chloro derivatives, such as trichloromethylsilane (“TCMS”) [150]. When the reaction is carried out in solution, these contaminants may react faster than the CTMS or may preferentially polymerise at the surface due to a lower solubility of the hydrolysis products [150]. When the reaction is carried out in the vapour phase, the contaminants do not cause a thick layer to form because CTMS [being more volatile] will be more abundant at the surface and reaction of this species will dominate [150]. For successful grafting using anhydrous solvent, there must still be some water present at the surface for the hydrolysis to proceed [150, 392]. Silanisation of glassware with CTMS can be expected to produce surfaces with contact angles in the range 70° to 76° under neutral to slightly acidic conditions † [637, 987]. The contact angle decreases significantly as pH rises above about 8, but it can be restored almost to its previous high value (i.e. hydrophobicity regained) by decreasing the pH to 6 (or lower) or heating at 110°C [637]. Numerous techniques that are more or less sophisticated exist for silanisation with CTMS [e.g. 150, 492, 637, 987] and other silanes [392]. The procedure adopted here is:

*

Interestingly, HORR, RALSTON & SMART [492] argue that the presence of cross-linking in the case of trichlorosilanes is favourable, as it permits closer packing by removing some of the steric hindrance between methyl groups.

†

Coverage of the surface by methyl groups estimated to be on the order of 54% [637]. Contact angle would increase with increasing coverage. Appendix S16 : Silanisation

925

D. I. VERRELLI

1.

2. 3.

4.

5.

Fill and wash measuring cylinder with hot (>70°C) water at or slightly above pH of solution to be investigated (here approximately 0.01M NaOH was used for >10 minutes). Some researchers [392, 825] recommend heating (covered) in deionised water in the oven, so as to maximise the number of Si–O–Si groups at the surface of the glass hydrolysed (or ‘hydroxylised’) according to bSi–O–Sib + H2O # bSiOH + bSiOH, where b signifies a surface group *. Note that this reaction denotes a reversible shift from a hydrophobic surface at left to a (potentially) hydrophilic surface at right. The cylinder was then rinsed with deionised water, then again with ethanol, and air-dried. Dry cylinder at ambient temperature either using ethanol or isopropyl alcohol, or simply by standing. Pour about 30mL of (dry †) hexane ‡ into cylinder and add about 3mL CTMS § to make a 10%V mixture, and swirl around. This is done in a fumehood wearing rubber gloves and a face shield or goggles (CTMS is flammable, corrosive and a strong irritant — avoid all contact). The cylinder may be inverted by covering the top with a suitable rubber closure (e.g. a new rubber glove). Let stand for about 10 minutes, swirling or inverting again every minute to recoat sides. Originally the reaction was thought to proceed at the hydrolysed surface groups (silanols): bSi–OH + (CH)3 SiCl # bSi–O–Si(CH)3 + HCl More recent evidence indicates the chlorosilane first hydrolyses with available water (in the atmosphere, in solution, or adsorbed to the silica surface), (CH)3 SiCl + H2O # (CH)3 Si–OH + HCl bSi–OH + (CH)3 Si–OH # bSi–OH/HO–Si(CH)3 forming hydrogen bonds with the surface (or rather, surface-adsorbed water), and may then undergo condensation reaction (producing further water to ‘catalyse’ additional hydrolysis) to form a polymer [150]. As noted, contaminantinduced condensation polymerisation may commonly occur prior to bonding of the silanes to the surface [150]. Pyridine may be used to capture HCl, but was not considered necessary here. Pour mixture off and rinse out with (dry) hexane then/or ethanol, followed by deionised water. Slowly add excess (waste) mixture to water to induce exothermal reaction consuming remaining CTMS before disposal. Dry cylinder in oven at 100°C, if desired. This will temporarily increase the hydrophobicity, but the benefit of this step may be relatively short-lived as the surface is exposed to the sample for a long period and therefore re-hydrolyses.

*

It may be expected that the hydroxyls can be singly, doubly, triply, or geminately co-ordinated with surface Si atoms [280, 825].

†

Ideally the solvent should be dried before use, to remove residual water content. However, as the reaction was not carried out in a water-free glove-box atmosphere, such a step seemed omissible, and the hexane was used as received.

‡

95% pure (BDH).

§

99+% pure, redistilled (Aldrich).

926

Appendix S16 : Silanisation


The observed decrease of the contact angle with increasing pH is simply due to the equilibrium in the reaction bSi–O–Sib + OH– # bSiOH + bSiO– (where b signifies a surface group) shifting to the right, and noting that the kinetics are more rapid at higher pH [825].

Appendix S16 : Silanisation

927

D. I. VERRELLI

S17. BULK VISCOSITY POTANIN & RUSSELL [845] considered the parallel resistances to dewatering separately due to the compressive yield stress and the l o w - c o m p r e s s i o n b u l k v i s c o s i t y of the “weak” fractal aggregates produced from colloidal dispersions. In their model a high bulk viscosity implied that the material would dewater purely by ‘yielding’ [845]. However, low bulk viscosities, relative to the compressive yield stress, would allow viscous (i.e. NEWTONian) flow deformation [845]. Hence, this model allows the possibility of dewatering when pS < py. POTANIN & RUSSELL [845] concluded that viscous flow would persist (even if very slowly) as the system approached an asymptote of φcp. The model bulk viscosity is given by  − z U min  ( 3 + 2 Dl ) / ( 3 − Df ) d0 φ exp ,  2δ  kB T  and the compressive yield stress * by − 4 U min 3 / ( 3 − Df ) σy ~ k0 n1 φ , d0 2 δ

ηbulk ~ ηL n1 k0

[S17-1]

[S17-2]

[845], in which δ is the interparticle separation, ‒Umin is the depth and k0 the curvature [defined in 844, 872] of the (primary) minimum in the interparticle pair potential, z is a coordination number †, n1 is the number of active chains per junction, and Dl is the fractal dimension of the (load-bearing) chains [cf. 681] [see 551, 872]. A typical value of ~k0 is 100 [845], although this parameter is not well characterised, with uncertainty of one or even two orders of magnitude [cf. 844, 872]. n1 is likely to be of order unity for low to moderate solidosities (estimated from the correlation n1 ~ (1 ‒ φ / φm)‒г, with φm ~ φcp ≈ 0.64, and г ~ 1) [845]. The ‘flow’ is described by a characteristic relaxation time, trelax, which is a statistical measure of the likelihood that a given (load-bearing) chain in the network will fail [241, 845]:  − z U min  Dl / ( 3 − Df ) 3 φ π ηL d0 2 exp . [S17-3]  − U min k0 2  kB T  (Such models have a long pedigree, being first applied to polymer networks [see e.g. 636].) That is, trelax is a measure of the timescale at which dynamic breakage and reformation of interparticle bonds is significant. The formula for trelax was derived by combining the physical consideration of the characteristic diffusion time of an isolated particle with the chemical consideration of reaction rate theory (as by EYRING (1936) [127, 636]) [844]. Following from the latter consideration, the above equations assume that elasticity of chain

trelax ~

δ

*

A rather different form was suggested by BARNES [127] for the s h e a r yield stress of a system of fractal aggregates.

†

More accurately, z represents the “minimum number of bonds” that must be broken for a given particle to restructure [844]. It is implied that such bonds break fully, whereas it may be possible for particles to restructure while maintaining a weakened bond [see e.g. 175, 546].

928

Appendix S17 : Bulk Viscosity


deformation (elongation, say) is due to enthalpic, rather than entropic, contributions — which is not true for e.g. polymer systems [872]. A more direct experimental indication of the relaxation time of a gel might be gained by monitoring the ‘speckle’ fluctuation rate in SALS [840, 841, 1107] [see also 262, 263] — despite their characterisation as an artefact [969]. The above three parameters — σy, ηbulk, and trelax — are strictly properties of the solid phase network only, different to the usually-measured rheological properties [347]. Note that if the compressive yield stress were defined strictly as the threshold applied stress to cause an increase in solidosity, as in the LANDMAN–WHITE analysis, then allowance for a bulk viscosity would formally imply zero yield stress for all solidosities below close packing and infinite yield stress at close packing. (The gel point, however, would be unchanged.) A l i t e r a l interpretation of this would then deduce that, according to equation 2-57, the dynamic compressibility must be small and strongly decrease with φ. That is, the mechanism by which Dφ / Dt decreases would not be the increase of py, but rather the decrease of κ. However, the literal interpretation does not account for the apparent change in network collapse mode that occurs at py = σy. Hence σy is better interpreted as a ‘practical’ yield stress, below which consolidation may only proceed very slowly — by ‘creep’. POTANIN and co-workers’ [844, 845] theory contains some simplifications: • exclusive action of the yield stress and bulk viscosity resistances is assumed, but physically a transition regime should exist in which both mechanisms are important; • modelling of chain elasticity is suitable only in the limit of long lengths between junctions, so that the dominant deformation mode is bending — in real systems the chain length between junctions may be relatively short, so that chain stretching (through the bond axes) is more important [347]; • centrosymmetric particle interactions are assumed, which is reasonable for electrostatic interaction, but not for surface binding [see 81, 175, 386, 813]. The issue of non-central interactions is not significant, as the key feature of such interactions, namely their ability to resist bending, is captured by considering instead multiply-connected particles in thick chains [844], the analogue of a truss structure. EVANS & STARRS [347] derived alternative relations for σy, ηbulk, and trelax, and argued that ηbulk is isotropic. Very similar power-law behaviour with respect to φ to that in equation S17-2 has been proposed by a number of researchers in the e l a s t i c deformation regime [175].

S17▪1

Estimation from physical properties

CHANNELL, MILLER & ZUKOSKI [241] used the above formulation of the relaxation time to estimate trelax T 1012 years for their aggregated alumina system, implying that bulk viscosity effects would be imperceptible. However this large value is primarily attributable to the large interaction energy specified, namely (50 to 100) kB T, calculated based on the VAN DER


929

D. I. VERRELLI

WAALS * attraction [241, 242]. Their arguments are adapted for the present system in the following. The VAN DER WAALS attraction between two identical s p h e r i c a l particles is given by [241, 437, 517] A d − U vdW ≈ H 0 , [S17-4a] 24 δ with AH the ‘effective’ HAMAKER constant, which is valid for δ / d0 / 1 [924]. Where δ and d0 are of similar magnitude (δ / d0 T 10–2), the equation derived by HAMAKER (1937) [437] † should be used ‡ [517], viz. [538, 636, 804, 924]:  x ( x + 2)   A  1 1  , [S17-4b] − U vdW = H  + + 2 ln 2 2  12  x ( x + 2) ( x + 1)  ( x + 1)  in which x ≡ δ / d0. Equation S17-4b relies on the assumption that p a i r w i s e interactions between volume elements § of the particles are a d d i t i v e [517, 750, 756], implying that there is no long-range correlation between polarisation of the volume elements of either particle [cf. 511, 751] (presuming the particle comprises a single material [cf. 826]) — this may be violated in condensed phases [81] and has been judged: “valid for dielectrics though probably not for metals” [516]; “probably [does] not hold for long chain molecules” [750]; “fundamentally unsound”, and “unlikely to hold [in] water” (due to water’s high lowfrequency polarisability), except at either very high dilutions or very small separations [826]. ** Despite being ‘embedded’ in water, the particulates studied in the present work are expected to be either quite dilute (as primary particles) or closely spaced (in aggregates); hence the chief residual source of potential discrepancy stems from suggestions of ‘cluster polarisability’ raised for WTP aggregates [184, 542, 1008]. Additionally, when δ T 10nm †† a retardation effect reduces the value of ‒UvdW [538, 688, 924], although that is not germane to the present work in the context of the foregoing model. A further source of inaccuracy is the assumption that the particles are spherical [437]. Real particles may not be spherical, and the potential may be enhanced by interaction between flat surfaces — e.g. crystal faces or surfaces deformed under the attractive force — or reduced (or enhanced) by the presence of significant asperities [81, 167, 220, 438, 813]. It is just as reasonable to suppose that the primary particles are acicular or have another elongated morphology [280, 306, 573, 584, 616, 768, 870, 940, 986, 1118, 1130, 1131, 1150], with

*

It is implicitly assumed that the LONDON attractive energy controls the 437], which is reasonable for all but highly-polar materials [924].

†

The same result was apparently derived earlier (1933) by J. M. RUBIN, but never published [438].

‡

For example, with δ / d0 = 10–1, the difference is a factor of 2.4.

§

Integration of volume elements is based on a continuum representation of the solids [438]. Such an approach is valid provided that the particle separation is considerably g r e a t e r than the interatomic spacing of the solid phase(s) [167] (HAMAKER [438] apparently misread this). At very small separations summation over individual atoms is required (at least near the contacting surface(s)) [167].

**

The more rigorous LIFSHITZ theory avoids these limitations [517], but is less convenient to work with and requires accurate dielectric data for all materials involved [877].

††

Alternative suggestions for the practical non-retarded threshold are ≤5nm [517], 10 to 15nm [81] and 50nm [cf. 510, 511]. Such distances are beyond the practical reach of the VAN DER WAALS forces for small particles (d ( 10nm) [1074] as discussed here.

930


VAN DER

WAALS forces [see also


aspect ratios up to about 10 [cf. 573, 910, 1118, 1130, 1131, 1150]. Interaction between such particles would be better approximated by treating them as either rods or ellipsoids (or spheroids with low sphericity). The shape of the particles is most important when their separation is small [438], as is expected in the present case. The interaction of such elongated shapes tends to favour the parallel alignment of their major axes [see 343, 516, 1114] [cf. 81, 1131]. This is consistent with the view that acicular primary particles may initially form ‘rafts’ (e.g. goethite at elevated ionic strength (I ~ 0.2M) in acid media [280, 767, 1130, 1131], akaganéite [388, 767, 768], et cetera [325]). Unfortunately the interaction between particles of these (rod-like) geometries has not been a n a l y t i c a l l y derived except for special (limiting) cases [cf. 81, 348, 756], especially for particles that are very long [343, 348, 516, 517, 826, 1131] and that are either very thin with a moderate separation [516, 750, 751, 826] or very closely spaced with a moderate thickness [81, 301, 348, 1114] *. There is no derivation for thinnish, closely-spaced rods of moderate length. Even incorporating a moderate length is intractable except for special cases [see 751]. There is, moreover, little consideration of retardation effects, which are more likely to affect extended geometries [see 751]. (Simplifying assumptions regarding the relative thickness of the double layer are probably also invalid in the present application, as the DEBYE length, κ‒1 ≈ 0.304 / I [517, 636, 752], is predicted to be of order 2 to 8nm in the present work [cf. 505] given the bulk conductivities noted in §3▪4▪6.) Nevertheless, to the same order of accuracy as equation S17-4a, we may take for two l o n g , c l o s e , a l i g n e d identical r o d s [511, 517] 12 32 A L  d /2 A Γ  d0  [S17-5] − U vdW ≈ H  0  = H   , 24 δ  δ  24 2  δ  in which Γ ≡ L / d0 is the aspect ratio. This also assumes pairwise additivity of interactions [cf. 516]. (See EVERAERS & EJTEHADI [348] for approximate formulæ for interacting e l l i p s o i d s .) In order to obtain a meaningful comparison between the sphere and rod geometries, the two cases in which the particles have equal volume are considered. The relation between the diameters is then: dsphere = ( 23 Γ )

13

drod .

[S17-6]

For Γ = 10 this gives dsphere ≈ 2.5 drod. The ratio of interaction energies can be found as equal volume

13

 Γ 2   d 1 2 [S17-7] =    rod  .  12   δ  To illustrate the magnitude of this ratio, taking Γ = 10 and drod / δ = 5nm / 1nm (so that dsphere ≈ 12.3nm) yields a ratio of approximately 4.5, assuming also equality of AH and δ for the − Urod Γ drod 3 2 ≈ − U sphere 2 dsphere δ1 2

*

It may be noted that the DERJAGUIN approximation [generalised from 301] applied in some of the derivations cited is — for nanoparticles — less accurate for the attractive (VAN DER WAALS) forces of interest here than for repulsive (electrostatic) forces [382]. Appendix S17 : Bulk Viscosity

931

D. I. VERRELLI

two cases *. As equation S17-5 is derived based on infinite length, the ratio ‒Urod / ‒Usphere may be significantly overestimated by equation S17-7 for Γ ( 10. For the small particles considered here, often Umin ~ UvdW (see below) †. A major correction may be required under the action of an external applied stress [243, 262, 411, 412, 567, 582, 1052]. Such a load would seem to be necessary [cf. 327, 551] to shift the equilibrium of the dynamic restructuring process to favour the progressive formation of a more consolidated structure — based on the argument that the postulated creep must have a ‘driving force’ causing it to progressively adjust towards a more-consolidated equilibrium state, as in EYRING rate theory [127, cf. 636]. When the external stress is above the yield stress, the material is assumed to restructure almost instantaneously, and the ‘corrected’ trelax would be very small. The importance of bulk viscosity arises, however, when the applied stress is significantly below the yield stress, in which case the correction is smaller, and trelax can then be taken as a conservative estimate. From the same thermodynamic perspective, an external stress must also modify the nett particle interaction energy [327], just as externally applied stress will act to shift the equilibrium, and favour consolidation. BOTET & CABANE [175] developed a particle interaction model for which stored bond energy, E0, could be estimated from the formula E0 ~ π l0 d02 p0 / 8, in which l0 is the length of the ‘unstressed’ bond, d0 is the primary particle diameter, and p0 is the applied pressure. A pressure of p0 = 100kPa then equates to an energy of 2 kB T in the affected particle bonds at room temperature for l0 = 1.5nm and d0 = 12nm [cf. 175]. Evidently the value will vary depending upon l0 and d0, but can be seen in any case to be of comparable magnitude to the anticipated particle interaction energy, ‒Umin. Despite the foregoing, it is entirely possible for creep to proceed in the a b s e n c e of any e x t e r n a l ‘driving force’, provided that i n t e r p a r t i c l e a t t r a c t i o n is significant. In that case the thermodynamically favoured (i.e. minimum energy) state will be that with the lowest attainable interparticle spacing — expected to be random close packing. A good way to understand this is to consider a particle (A) with a single bond to a second particle (B) but no bond to a third particle (C): the system could be represented by ‘C A-B’. If — rather, when — the bond ruptures by thermal fluctuations (or local variations in network stress) [140, 551, 969], A may reform a bond with B (giving C A-B), or with C (C-A B), and statistically the bond would flip-flop between the two pairs shown. However, if the particles are able to move so that A forms t w o unstrained bonds (C-A-B), then a new configuration is attained that is m o r e c o m p a c t and also m o r e s t a b l e , as the transition

*

Even this assumption is not entirely accurate. In terms of δ, repulsive forces will scale differently, so that the separation of minimum energy need not be the same in both cases; furthermore, larger particles are less able to access the minimum energy state if there is an energy ‘barrier’ (or activation energy) to overcome, as they have a smaller BROWNian velocity [438, 517]. In terms of AH, the effective HAMAKER constant defined above is i n d e p e n d e n t of geometry, yet formulæ describing interaction potentials between non-spherical particles [e.g. 516] suggest that the equivalent ‘material constant’ is geometryd e p e n d e n t [cf. 517]. AH could even be a (weak) function of particle separation, given fluid ‘structuring’ effects may not scale in the same way as in vacuo particle interactions (all due to VAN DER WAALS forces) [cf. 437].

†

Cf. discussion on pp. 938f..

932



from doubly-bonded to singly-bonded is statistically less likely than the converse * [cf. 303, 681]. Hence, high co-ordination numbers are ‘thermodynamically’ favoured in attractive particle systems, so the proportion of multiply-bonded particles will tend to increase over time. This is essentially a description of s y n æ r e s i s (see §R2▪1, especially §R2▪1▪2▪2). When the applied load is low, this description of thermodynamic creep implies that the dewatering rate will be controlled by diffusion processes, in contrast to the dominance of hydrodynamic resistance on the rate at higher stresses [140]. For systems with lower interaction energies, as originally envisaged, the relaxation time would be very much smaller, suggesting that creep effects could be explained by this mechanism. It is not clear what the precise form of the long-time h(t) creep settling profile would be, as it must depend upon the variation of the hindered settling rate and the bulk viscosity with solidosity [although these should be material properties!], and the governing partial differential equation is solved numerically [845]. With respect to the published formulation [845], bulk viscosity effects would be expected to dominate compressive yield effects if the magnitude of the interaction potential is decreased, if the particle size is decreased, and if the solidosity is decreased. These reductions are all expected to be true for the present WTP sludge system relative to that of CHANNELL, MILLER & ZUKOSKI [241]. For example, the interparticle spacing could be expected to be larger, presuming the primary particles to have rough surfaces and their interaction to be ‘impeded’ by sorbed NOM. (It is reasonable to suppose that the NOM has an effect on surfaces at the primary particle scale, given that it is able to influence metal (oxy)hydroxide formation and transformation [e.g. 584, 707, 940] — i.e. the molecular level.) The HAMAKER constants for the amorphous precipitates generated in WTP sludges are not well known. It is known that the ‘true’ HAMAKER constant for pure (condensed) phases interacting across a vacuum is usually of order 10–20 to 10–19J [see also 343, 437] — or ~(2.5 to 25) kB T for T ~ 300K — and the ‘effective’ value (to account for the suspending fluid, water), AH, is generally somewhat lower [517, 750, 924]. HUNTER [511] indicates AH ~ (1 to 3)×10–20J for oxides in water. FU & DEMPSEY [382] quote AH = 4.12×10–20J for (hydrous) metal oxides (in water), and describe this as “relatively large” [cf. 538]. Values of AH for the well-characterised crystalline (oxy)hydroxides of iron and aluminium have been reported. For corundum (α-Al2O3) AH ≈ 5×10–20J [e.g. 446, 517] and for goethite (αFeOOH) AH ≈ 5×10–20J too [162, 817, cf. 1131]. The value for the amorphous or poorly-crystalline phases should be less than this, based on their lower densities [cf. 372, 437, 517, 898]. Pseudoböhmite could be estimated at ~ 3×10–20J (density ratio ~ 2500 / 3980); while ferrihydrite would not differ greatly from goethite, at ~ 5×10–20J (density ratio ~ 4000 / 4260). If NOM were adsorbed in significant amounts on the surfaces, AH would be depressed still further (by the VOLD effect [924]), although this seems unlikely to be a major effect at the primary particle scale. KWON & MESSING [616] used a rather high value of AH = 10–19J for their nanocrystalline aggregates of pseudoböhmite, which was presumably an order-of-magnitude estimate. Likewise, MOSLEY, HUNTER & DUCKER [762] estimated AH ~ 1.3×10–19J for a presumed

*

Consider: it is unlikely that one or both bonds would break and the particles separate so that the doublebonding was not re-established. Appendix S17 : Bulk Viscosity

933

D. I. VERRELLI

ferrihydrite *, although DUCKER [327] has recently indicated that this is likely to be an overestimate. HARBOUR, DIXON & SCALES [446] reported δ lay in the range ~2±0.5nm for 300nm alumina particles, with the larger separations corresponding to (unfractionated) NOM adsorption. In general, separations down to ~0.5nm [81, 472] (or lower [see 380]) can be contemplated. Based on XRD measurements in the present work (see §4▪2▪3) and various published observations (see §R1▪5▪7▪4), it seems reasonable to take d0 ( 20nm. Parameter values or ranges were specified based on three key considerations: • comparison with known or estimated magnitudes (guided especially by the data of POTANIN and co-workers [844, 845, 872], EVANS & STARRS [347], and CHANNELL and co-workers [241, 242]); • sensitivity of outputs to the variable; • generation of plausible values of trelax, ηbulk and σy in light of results and observations from the present work. To allow for uncertainty in the parameters, a range of plausible d0 values are plotted for various combinations of values for the other parameters. Of initial concern are z, AH, δ, d0, and T, which affect the argument of the exponentials in equations S17-1 and S17-3 (see equation S17-4), and thus dominate the uncertainty in ηbulk and trelax. It is believed that AH is sufficiently well estimated, but sensitivity to this parameter is presented for completeness; it also serves as a vicarious indication of the influence of particle shape (cf. equation S17-7). T will be taken as 298K, with deviations of (say) 15K being relatively insignificant. Df and φ do not appear in the exponential, but are nevertheless of fundamental importance because of the physical insight they provide, their effect on the predicted properties, and their common estimation in the literature. Solidosity values are chosen representative of typical equilibrium values in gravity settling (0.005) and filtration (0.05) for WTP sludges. From equation S17-2 the compressive yield stress should vary according to  φ 3 / ( 3 − Df ) , σy ∝ [S17-8] provided n1 (and the other parameters) are not strong functions of φ. Df is then estimated using real py(φ) data for alum and ferric WTP sludges. The relevant correlation is shown in Figure S17-1. The various curves, which span the range of observed behaviour, roughly converge to a nearly constant power-law exponent of approximately 2.75 at the ‘moderate’ solidosities of interest. This exponent corresponds to Df ≈ 1.9, which neatly fits in the domain between the theoretical DLCA and RLCA limits — and is also plausible for many deviations from those regimes, such as orthokinetic coagulation. Nonetheless, very low estimates of Df have been published by some researchers, and this will also be explored.

*

934

Strictly this was a silica surface covered with a layer of an iron oxide with an a v e r a g e thickness of 0.3nm [762]. Appendix S17 : Bulk Viscosity


100


1.E+2 1.E+1 1.E+0 Poor lab. alum — 80 , 8.6 Poor lab. ferric — 80 , 5.6 Good lab. ferric — 5.0 , 5.6 Good lab. alum — 1.5 , 6.0 Plant alum — 1.9 , 6.1 Plant ferric — 2.2 , 8.7 Plant ferric — 1.5 , 9.0

1.E-1 1.E-2 1.E-3 1.E-4 1.E-5 1.E-3

1.E-2

1.E-1

1.E+0

Exponent, d[ln(p y)] / d[ln(φ )]


1.E+3

10

1 0.001

0.01

0.1

1



Figure S17-1: Compressive yield stress as a function of solidosity (left) as per Figure 5-18, and the corresponding local power-law exponent (right). The yield stresses at φ = 0.005 and φ = 0.05 are highlighted. Numbers in the legend refer to coagulant dose and pH.

The parameters are taken as in Table S17-1. Table S17-1: Values of parameters used to estimate ηbulk, σy, and trelax. Baseline values are presented, along with values used in the alternative scenarios (where relevant).

d0 δ AH z Df φ

5 to 50nm 1nm 4×10–20J 3.5 1.9 0.005

(or 2nm — scenario B) (or 1.3×10–19J — scenario C) (or 2.5 — scenario D) (or 1.1 — scenario E) (or 0.05 — scenario F)

T k0 ηL г Dl φm

298K 100 1mPa.s 1 1.1 0.5

Aside from d0, only one parameter is adjusted in each alternative scenario. Of course, some parameters would be correlated to a significant extent in at least some real systems, such as Df and z *, but exploration at such detail is beyond the scope of the present work.

*

This argument is based on the premise that the fractal structure persists down to the level of the primary particles; i.e. the aggregate is not composed of fractally-arranged clusters with internal fractal dimensions different to that of the aggregate. It is known that real aggregates do often have a multilevel fractal structure (see §R1▪5▪1▪1, §R1▪5▪7▪4). The practically measured fractal dimension is often dominated by the long-to-medium-range structure [546], whereas the mean co-ordination number is linked purely to the shortest-range structure. Restructuring can affect large and small lengthscales differently [e.g. 733]. Although z and Df are not uniquely associated [cf. 217, 733], low (or high) values of either are more likely to be associated with low (or high) values of the other. The strength of the association will vary in different systems, and may only apply for limiting values of z or Df in some. Appendix S17 : Bulk Viscosity

935

D. I. VERRELLI

Scenario A: baseline

1E+15

Scenario B: δ = 2nm

45

1E+15

40

1E+12

35

1E+9

30

1E+6

1E+3

25

1E+3

25

1E+0

20

1E+0

20

1E-3

15

1E-3

15

1E-6

10

1E-6

10

1E-9

5

1E-9

5

0

1E-12

t_relax [s] η_bulk [Pa.s] σ_y [Pa] /(kBT) [–] –Umin / (kB.T)

1E+12 1E+9 1E+6

1E-12 0

10

20

30

40

50

Scenario C: A H = 1.3×10–19J

1E+15

45

t_relax [s] η_bulk [Pa.s] σ_y [Pa] /(kBT) [–] –U min / (kB.T)

40 35 30

0

0

10

20

30

40

50

Scenario D: z = 2.5

45

1E+15

1E+12

40

1E+12

1E+9

35

1E+9

1E+6

30

1E+6

1E+3

25

1E+3

25

1E+0

20

1E+0

20

15

1E-3

15

10

1E-6

10

5

1E-9

5

0

1E-12

1E-3

t_relax [s] η_bulk [Pa.s] σ_y [Pa] –Umin /(kBT) [–] / (kB.T)

1E-6 1E-9 1E-12 0

10

20

30

40

50

Scenario E: D f = 1.1

1E+15

45

t_relax [s] η_bulk [Pa.s] σ_y [Pa] –Umin / /(k (kB.T) BT) [–] [–]

40 35 30

0

0

10

20

30

40

50

Scenario F: φ = 0.05

45

1E+15

40

1E+12

35

1E+9

30

1E+6

1E+3

25

1E+3

25

1E+0

20

1E+0

20

1E-3

15

1E-3

15

1E-6

10

1E-6

10

1E-9

5

1E-9

5

0

1E-12

t_relax [s] η_bulk [Pa.s] σ_y [Pa] –Umin /(kBT) [–] / (kB.T) [–]

1E+12 1E+9 1E+6

1E-12 0

10

20

30

40

50

45

t_relax [s] η_bulk [Pa.s] σ_y [Pa] /(kBT) [–] –Umin / (kB.T)

40 35 30

0

0

d 0 [nm]

10

20

30

40

50

d 0 [nm]

Figure S17-2: Estimates of the characteristic relaxation time (trelax), bulk viscosity (ηbulk), and compressive yield stress (σy), based on the interaction potential (–Umin) as a function of particle size (d0) for several scenarios. The baseline values are given in Table S17-1. The particle separation (δ), HAMAKER constant (AH), mean co-ordination number (z), characteristic network 1y ≈ 3.2×107s. fractal dimension (Df), and solidosity (φ) were varied as shown. −20 kBT ≈ 0.41×10 J.

936



Interaction potentials of kB T < ‒Umin ( 20 kB T were anticipated, corresponding to ‘weak aggregation’ [636, 844], for which structure can be readily disrupted by macroscopic shearing [872]. Interactions of ‒Umin ( kB T would be too weak to hold together *, and thus must be underestimates. The estimates of ‒Umin are below those of CHANNELL and colleagues [241], which can be attributed to their large particles. They are also less than the largest ‒Umin of MOSLEY and colleagues [762], which can be attributed to their large HAMAKER constant and low pH. (Silica tends to have a somewhat lower value of AH than metal (oxy)hydroxides, but the particle size in natural waters is considerably larger than the proposed d0 for the precipitate [e.g. 214], so silica interactions would give a large ‒Umin.) The predicted compressive yield stress, σy, is seen to lie at about 100Pa for the baseline case (φ = 0.005), which is compatible with the py data in Figure S17-1. It shows only a weak increase with decreasing d0. In scenario F the predicted σy (~103Pa) is lower than experimental py data (~104 to 105Pa) from the present study at φ = 0.05. By comparing with scenario E, this could indicate that Df has been slightly overestimated. It can also be seen that the separation is unlikely to be as large as 2nm (scenario B) if the model is correct (see discussions pp. 929 and 938), and given that the HAMAKER constant has not been greatly underestimated (cf. scenario C). Estimates of the bulk viscosity, ηbulk, and characteristic relaxation time, trelax, are seen to vary over more than twenty orders of magnitude! This is because of the uncertainty-amplifying effect of the exponential in equations S17-1 and S17-3. By way of comparison, small molecules have relaxation times of order 10–13s (or 10–11s [243]), a polymer melt had trelax ~ 103s, while SCHERER and co-workers [902] estimated trelax ~ 105s (T 1d) from measurements on a gelled silica system that had a low-shear-rate viscosity of ~1012Pa.s [636]. Table S17-2: Indicative viscosities (in the zero-shear-rate limit) of several materials usually classed as ‘solids’, “mostly at room temperature” [127].

Material Gelatine gel Ice cream Cheddar cheese Solid soap Tin Cement Mortar Glass

*

Indicative viscosity, η [Pa.s] 106 108 1010 1012 1014 1016 1018 1020

HAMAKER in 1938 [438] justified the comparison of ‒U with kB T for colloidal particles as a comparison between the interaction energy and the kinetic energy due to BROWNian motion [cf. 969]. Appendix S17 : Bulk Viscosity

937

D. I. VERRELLI

Many of the estimates of ηbulk appear to represent significant underestimates, seen in comparison with the viscosity of pure water, ηL ≈ 10–3Pa.s. Nevertheless, an acceptable proportion of physically plausible values are generated at the higher values of d0 — published viscosities of several ‘solids’ are presented in Table S17-2. When AH is increased (scenario C), some massive predictions of ηbulk and trelax are generated, but these may be excluded based on the improbably large values of ‒Umin. It is striking that so many combinations of the parameters result in relatively low predictions for trelax: the majority are significantly less than one year. While a number of assumptions have been made, and the uncertainty in the actual value of trelax is huge, the data support the p o s s i b i l i t y that WTP aggregates d o r e s t r u c t u r e on a practically-meaningful timescale. It can be seen that trelax increases strongly with increasing d0, implying that aggregates composed of small primary particles are less stable under the influence of ‘thermal’ fluctuations (cf. BROWNian motion). This is consistent with the predictions of KANTOR & WITTEN [551]. However these researchers also noted that decreasing d0 yields a lower susceptibility to gravitational collapse *, indicating that an optimum size (or size range) should exist from which aggregates may be constructed [551]. (An equivalent finding was sketched by HAMAKER in 1938 [438].) The existence of aggregates many times larger than the predicted maximum stable sizes (based on d0) may provide a rationalisation for the observation of different structures at different lengthscales (i.e. multilevel structure, see §R1▪5▪7▪4) in some natural aggregates — or the kinetics of rupture could be very slow. Uncertainties in several parameters were neglected, however the effects are obvious from the equations. The most important neglected uncertainty is that of k0, for which insufficient information was available: if this was greatly under- or over-estimated, then the values of σy, ηbulk, and trelax could change by up to a factor of ~10. A number of additional interactions have been proposed for aggregate particle networks such as WTP sludges: • NOM could form adhesive bridges between particles (on a lengthscale of order 5nm) [762]; however, such bridges would be unlikely to affect many of the interactions between primary particles. • Double-layer interactions can modify the attraction, but these also tend to be minor compared to VAN DER WAALS forces at small separations (i.e. in the ‘primary minimum’ of potential energy) [304, 517, 538]; they would yield a r e p u l s i v e contribution for like-charged particle surfaces. • Forces due to structured solvation layers and other types of steric barriers can dominate both VAN DER WAALS and electrostatic forces at short range (“below 1 to 3nm”) [517, 538] [cf. 804]. Relaxation of these, and of STERN layer counterions (cf. §R1▪5▪6▪1(b)), could increase bond ‘strength’ [cf. 380]. • Differently-charged crystal faces were proposed as a mechanism for enhanced attractive forces between ~1μm-sized goethite particles (analogous to surface charges

*

938

This conclusion was reached under the assumption that the aggregate has a branched structure with no loops (except on the smallest lengthscales) [551]. Such an assumption is not true of natural aggregates, especially in consideration of aggregate restructuring. Nonetheless, the general result is expected to hold true, and is consistent with the trend predicted for σy by the model of POTANIN & RUSSELL [845] (see text). Appendix S17 : Bulk Viscosity


on clay particles) [162]. The nominally amorphous precipitation products of water treatment possess only short-range crystalline ordering, and crystallites do not necessarily align within a given particle. It is not clear whether this would tend to invalidate the above mechanism on the basis that different charges could not be sustained over large enough areas, or whether it extends the mechanism through consideration of a ‘charge patch’-like interaction [426, 813] (see §R1▪3▪2▪1). Certainly magnetic dipolar interactions have been suggested in aluminium and iron (oxy)hydroxides [184, 542, 1008]. • After the initial contact, the bonds may strengthen in a s e c o n d s t a g e resulting from “the formation of covalent or metallic bonds, sintering, silicate bridge formation, etc.” [734] [see also 550, 571, 690, 1141] [cf. 81, 100, 379, 380, 804]. In this model significant restructuring would only take place in the initial phases of aggregation [546, 734]. o Solid bridging, where solid necks form between particles, could occur by a dissolution–re-precipitation mechanism (as OSTWALD ripening) [cf. 367, 616, 768, 977], by surface diffusion, or by other sintering mechanisms [550, 571, 800] (cf. §9▪1▪1▪1(b)); however, the presence of NOM would tend to stabilise particles against this *. MURPHY, POSNER & QUIRK [768] reported the formation of rafts of nanorods that were in turn comprised of essentially spherical polycation particles; however in some cases these spheres “ c o a l e s c e d ” . This implies that the spheres within a rod are more strongly bound to each other than the bonds between rods or rafts, and so breakage of the aggregated structure would be much more likely between rafts or between rods than between those primary spheres. This suggests an alternative view of WTP sludges, where circa 3nm particles or crystallites bind strongly at very short separations into what effectively become primary particles, which are larger but more separated from each other, so that their interaction energy is smaller in magnitude. The analysis of multiple batch settling experiments presented in §S10▪2 and §S10▪3 further supports the existence of creep at long times.

S17▪2

Estimation from phenomenological observation

Another way of thinking about the applicability of the bulk viscosity concept to the present work is to take o b s e r v e d long-time gravity settling r a t e s (i.e. creep data) and use that to estimate ηbulk. This can then be compared to the estimated compressive yield stress. (No simple means of applying this approach to filtration data is apparent.) The model for one-dimensional, gravitational settling is [845]:  1 ∂σ min  u = udrag only 1 + [S17-9] , φ Δ ρ g ∂z  

*

Sintering by ‘viscous flow’ [347, 800] or by transport along the “grain boundary” [cf. 571] might still proceed, as they do not rely on surface lability [550]. Appendix S17 : Bulk Viscosity

939

D. I. VERRELLI

which is similar to that presented by HOWELLS et alia [495] and others. The difference is that consolidation can occur by two modes, either in s h e a r or c o m p r e s s i o n . Thus viscous (shear) stresses and compressive stresses are compared to determine the weakest resistance, which is then taken as the failure mode [845]: ∂u  σ min = min  p y , −ηbulk [S17-10]  . ∂z   Note that σmin is positive and increases with decreasing z (i.e. towards the base). The variable udrag only represents the settling velocity obtained with the particle pressure equal to zero: Δρ g (1 − φ) 2 − udrag only = . [S17-11] R Inverting equation S17-9 to yield parameter estimates that would provide accurate predictions of observed settling data (including long-time behaviour) would demonstrate the importance or otherwise of creep processes. Unfortunately an analytical solution is not available, so iteration of a numerical procedure [see 845] would be required — along with a great deal of effort. σmin can be very roughly estimated by approximating the local partial derivatives with secants over the entire column and setting u equal to the interface fall rate, h :  Δρ g (1 − φ) 2  1 1  h   − h ~ min  p y , −ηbulk [S17-12] 1 +  . R φ Δ ρ g Δ z  Δ z     At 100 days h was shown to be about ‒0.86mm/d ≈ ‒1.0×10–9m/s for the 160mg(Fe)/L, pH 5.1 laboratory WTP sludge in Figure 9-10. Other relevant values are: Δz ~ h∞ = 0.056m; h0 = 0.246m; φ0 = 0.00075; φg ≈ 0.0028; Δρ ≈ 3000kg/m3; and pbase = 5.4Pa — corresponding to which φ∞,base ≈ 0.0035 and Rbase ≈ 1.3×1013Pa.s/m2. This yields an estimate of udrag only at the equilibrium base * conditions of 2.2×10–9m/s. Then σmin is estimated to be ~3Pa, which is a little less than pbase. Further, if the dewatering is occurring in a bulk shear mode, then ηbulk ~ 2×108Pa.s. The primary outcomes of this second analysis approach are: • affirming the difficulty in evaluating parameters in this model both easily and accurately; • bulk viscosity effects can be important even for values of ηbulk many orders of magnitude above viscosities commonly encountered elsewhere (e.g. η ~ 10‒3Pa.s for water and dilute WTP sludge); and • confirming that long-time dewatering behaviour could be caused by bulk viscosity effects. Final points of interest are that a reduction in Δz proportionally decreases σmin in the above approximation, and decreasing the estimate of |u| has little effect on σmin, which asymptotes to a maximum of ~6Pa (although ηbulk does increase).

*

940

Although not entirely clear, modelling of gravity settling in the absence of bulk viscosity effects indicates that long-time consolidation behaviour is related to dewatering at the base of the column [495], where the liquid phase ‘drainage path’ is longest and resistance is greatest. The drag force should reduce with elevation in the settling bed, because the permeability of the structure increases as the liquid rises. Appendix S17 : Bulk Viscosity


S18. BARRIER HOPPING THEORY GOPALAKRISHNAN, SCHWEIZER & ZUKOSKI [411] [see also 412] have recently investigated the application of naïve (i.e. single-particle) mode coupling theory, NMCT, to describe thermally-activated (‘barrier hopping’) particle rearrangement resulting in network coarsening and — ultimately — catastrophic failure. Experimental systems investigated involved delayed settling [411] [cf. 248] and delayed flow [412] [cf. 582]. The approach could also be applied to more general creep modelling [cf. 582]. [See also 243.] GOPALAKRISHNAN et alii [411, 412] also employed a characteristic time parameter, thop. In contrast to trelax (defined in equation S17-3), which describes the likelihood of c h a i n failure [241, 845], thop is more fundamental, describing the average time for a single p a r t i c l e to escape from a potential well [411]. Two realisations have been presented. The first extends KRAMERS’ [601] result for viscous disaggregation * to give [248, 411, 582]  Δ U barrier  g (d0) ηL d0 3 , thop ∝ [S18-1] exp  Kw Kb  kB T  in which ΔUbarrier represents the barrier in potential energy (relative to the aggregated state) †, Kw and Kb are curvature parameters respectively for the interparticle potential curve well ‡ and barrier, and g(d0) = g(φ) is a factor that increases monotonically with φ and represents a friction-factor correction due either to binary particle collisions § or to solvent-mediated highfrequency lubrication [see 908]. This is broadly similar to the dependence of trelax — as expected [582] [cf. 908] — though with some significant differences. (Note that empirically Kw ∝ U barrier ∝ 1 / δ [908] [cf. 248, 582], where δ is the aggregated interparticle separation. ΔUbarrier is also linearly correlated with the inverse isothermal compressibility [582, 908] (B∗ of equation 9-12).) See also §R2▪2▪3▪3. Although the formulæ contain only parameters with precise physical definitions, and “no [arbitrarily] adjustable parameters or postulated underlying dynamic or thermodynamic divergences” [908], in practice significant uncertainty is associated with the value of the ‘physical parameters’, and numerous assumptions must be made for the theory to be used **; furthermore, predicted values of thop *

Practically accordant with earlier reaction rate theory of EYRING and others, and specifically ‘transition state’ theory [see 601]. Note that KRAMERS’ derivation [601] assumes ΔUbarrier [ kB T ideally, or ΔUbarrier T 5 kB T in practice [cf. 248, 908].

†

For RLCA ΔUbarrier > ‒Umin. Yet although ΔUbarrier ≈ ‒Umin for DLCA, so that either will predict the correct ‘escape’ probability, the re-aggregation rate may not be well modelled (cf. R1▪5▪6▪1(b) and e f f e c t i v e stability ratio [379, 538] [see also 804, 1074]).

‡

“The well curvature controls the vibrational amplitude and oscillation frequency in the (quasi)localized state” [582], and thus influences the likelihood of ‘escape’ from the well.

§

In which case it is equal to the value of the hard-sphere radial density distribution function (or ‘pair correlation function’) [see 517] at contact [248, 411, 908].

**

That is, apart from those used in its development: for example, the original theory was developed for systems near to close-packing [908]. (For the present systems this might seem acceptable on a l o c a l level [cf. 248], but it is “well known” that mode coupling theory is invalid at very short times and lengthscales [582].) The theory “has not been rigorously derived” [248] [582, 908]. Appendix S18 : Barrier Hopping Theory

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D. I. VERRELLI

span many (~7) orders of magnitude [see 411] [cf. 248] — as with the analysis in §S17▪1. These issues motivate the second realisation, in which thop is approximated based on a series of ad hoc empirical correlations of uncertain generality [412] [cf. 248, 411] to give: β

 − U min  − γ  σ , thop ∝ ηL d0 φ  [S18-2]   kB T  where α, β and γ are adjustable parameters and σ represents the (externally) imposed stress [see also 567, 1052]. The time to “break a bond”, tbreak, is assumed to be proportional to thop after suitable adjustment for the proportion of the stress borne by every bond (assumed equal) [412]. (Experimental data supports this [212].) thop was then used as an input to evaluate the dynamic balance between bond breakage and reformation; the balance is hypothesised to shift at a critical value of the stress (cf. yield stress), σy [412]. (It is assumed that macroscale τ is a surrogate for microscale σ [412] [cf. 582].) In general 3

α

1/ γ

β   α  − U min    , [S18-3] σy = Ξ φ     k B T   where Ξ = Ξ(γ, Umin, φ) ~ Ξ(γ, Umin) * [cf. 412]. While specification of γ = 2 is expedient, empirically γ ~ 7 was reported [412]. (For comparison, TRAPPE et alia [1052] proposed a functional form arising in the study of equilibrium critical phenomena, viz. σy = Ξ′ (φ ‒ φcrit)α′ (‒Umin ‒ Ucrit)β′, where φcrit = φcrit(‒Umin) and Ucrit = Ucrit(φ), with α′ ~ 3 and β′ ~ 2 for a carbon black system.) Imposition of a stress greater than σy eventually results in a large — “catastrophic” — increase in the strain rate (cf. §R2▪3▪3) at time tfail (cf. §R2▪2▪3▪3) [412]. tfail is different from tbreak, and does not scale in the same way with thop, because only tfail is supposed to depend upon bond reformation as well as rupture [412]. tfail decreases as σ increases above σy [412]. Even for σ < σy quite large strains can be attained [see 412]. A moderate rate of bond breakage (and reformation) occurs below σy, permitting slow ‘creep’ deformation with the strain rate diminishing to zero over time; when σ > σy slow creep also occurs for t < tfail, but with steadily increasing strain rate [412]. As with the fibre bundle models (§R2▪3▪3), the system manifests strain-softening behaviour, because the stress acting on each bond increases as more bonds fail and the particle co-ordination number decreases [412].

Numerous other thermally-activated, particle-hopping models have been developed by different groups, such as those of BAXTER-DRAYTON & BRADY (1996) and SOLLICH (1998) adopted by CHANNELL [243] for shear relaxation.

*

942

There appears to be an experimental uncertainty of a factor of 10 in this parameter [see Figure 8 in 412]. Appendix S18 : Barrier Hopping Theory


S19. FILTRATION RIG FRAME EXPANSION It can be seen in Figure 9-23(b) that the height appears initially to spike to a lower value, before increasing as the elastic recovery proceeds. The downward spike is an artefact due to imperfection in a correction made for frame expansion, as explained below. However, the artefact is smaller in magnitude than the measured recovery, and in the opposite direction, and so does not detract from the results and discussion of §9▪4. Filtration experiments have been carried out on a rig in which a piston is forced into a stationary sample cell by a pneumatic cylinder. Both the pneumatic cylinder and sample cell are mounted on a metal frame, which can undergo expansion in response to the forces applied by the pneumatic cylinder. Such expansion (or ‘compliance’ [745]) is a function, then, of the cylinder pressure, as shown in Figure S19-1. The correlation is seen to be essentially linear. 350

Frame expansion, ΔH [μm]

300 250 200 150 100 ΔH = 0.5776p - 63.379 R2 = 0.9988

50 0 0

100

200

300

400

500

600

700

Cylinder pressure, p [kPa(abs)]

Figure S19-1: Correlation for frame expansion correction.

Figure 9-23(b) shows that the cylinder pressure drops sharply as the set pressure decreases to 200kPa and to 100kPa. In response, a small spike downwards in the height is recorded. It seems highly improbable that a cake that has been compressed to essentially equilibrium would compress further in response to a pressure d e c r e a s e , and therefore this downwards spike in height is interpreted as an artefact arising from a discrepancy between the true and the predicted frame contractions (the prediction being slightly greater than the true contraction).

Appendix S19 : Filtration Rig Frame Expansion

943

D. I. VERRELLI

The possibility remains that the frame may continue to slowly contract over a period of about 5min, during which time the piston shaft would be forced back into the pneumatic cylinder, which would be recorded as an increase in height (as seen). This would not be corrected for, as the data used to obtain the correlation in Figure S19-1 were each taken after a pause of only ~10s following pressure stabilisation.

944

Appendix S19 : Filtration Rig Frame Expansion


S20. ESTIMATION OF THE BULK MODULUS OF COMPRESSIBILITY, BS, THROUGH CENTRIFUGATION Estimation of the bulk modulus of compressibility, BS, by centrifugation experiment may have advantages of speed and equipment availability, and the load can be rapidly altered simply by changing the rotation rate. When estimating BS it is necessary to be able to estimate the solidosity and the change in (axial) stress e x p e r i e n c e d by the particles. Centrifugation relies on (enhanced) selfweight, and so naturally these quantities vary axially for the sample in the centrifuge tube, even at equilibrium. The solidosity will thus need to be obtained either directly by simultaneously running a dissection experiment or indirectly from equilibrium predictions based on prior evaluation of py(φ). Provided the elastic component of the strain is small, the solidosity at the beginning and end of unloading will be practically the same. The axial network stress follows from the known solidosity profile, through simple selfweight calculations. Ideally the system will be run to equilibrium, so that no correction for residual hydrodynamic drag is required — although such a computation is theoretically possible. A systematic approach for associating a given bulk modulus with a given solidosity is illustrated below using the hypothetical data shown in Figure S20-1.

0.15m CφD = 0.1 pS = 50kPa → 25kPa 0.10m CφD = 0.2 pS = 100kPa → 50kPa

0.05m CφD = 0.1 pS = 50kPa → 25kPa 0.15m CφD = 0.2 pS = 100kPa → 50kPa

Δh = +0.002m

Δh = +0.001m

Figure S20-1: Hypothetical centrifugation unloading results.

Using the expedient definition of equation 9-11 the first system suggests BS :φ=0.1 = 25kPa / (Δh :φ=0.1  / 0.15) , BS :φ=0.2 = 50kPa / (Δh :φ=0.2  / 0.10) , Δh :φ=0.1  + Δh :φ=0.2  = 0.002m . The second system suggests BS :φ=0.1 = 25kPa / (Δh :φ=0.1  / 0.05) ,

BS, Through Centrifugation Appendix S20 : Estimation of the Bulk Modulus of Compressibility, BS,

[S20-1] [S20-2] [S20-3] [S20-4]

945

D. I. VERRELLI

BS :φ=0.2 = 50kPa / (Δh :φ=0.2  / 0.15) , [S20-5] [S20-6] Δh :φ=0.1  + Δh :φ=0.2  = 0.001m . There are six equations in six unknowns, so a unique solution should exist. For the hypothetical data specified above, the solution is: Δh :φ=0.1  ≈ 0.00171m, Δh :φ=0.1  ≈ 0.00057m, Δh :φ=0.2  ≈ 0.00043m; BS :φ=0.1 = 2187.5kPa, Δh :φ=0.2  ≈ 0.00029m, BS :φ=0.2 = 17500kPa. Obviously for greater resolution more experimental data must be collected. The assumption implicit in the foregoing is that BS = BS(φ), and is independent of the axial stress. The estimates in Table 9-3 suggest that this may not be reliable.

946

BS, Through Centrifugation Appendix S20 : Estimation of the Bulk Modulus of Compressibility, BS,


S21. METAL COMPLEXATION BY ‘FOREIGN’ ANIONS HENRY, JOLIVET & LIVAGE [466] derived a formula relating the ‘critical’ pH of a system to the mean electronegativity of q-protonated anions, with 0 ≤ q ≤ n where n is the (bare) anion valence. The scheme depicting relevant reactions was given in Figure R1-5. The formula is [466] *: ( Δ + 5.732 m α + 2.064 m q) χ q − 4.071 ( 3.507 m α + 2.064 m q) , [S21-1a] χw = Δ + (1.408 m α + 0.507 m q) χ q − ( 3.507 m α + 2.064 m q) in which χq is the mean electronegativity of the species HqX(n–q)–, Δ is defined 0 4.071 − χ M Δ ≡ z − 2.225 N − , 0 1.36 χ M

[S21-1b]

0 the electronegativity of the isolated metal atom, and the mean electronegativity of with χ M

the aqueous solution, χw, is related to the ‘critical’ pH by 2.621 − 0.01866 pH∗q ∀ pH∗q ≤ 7 . [S21-1c] χw ≈  ∗ ∗ 2.647 − 0.02235 pH q ∀ pH q ≥ 7 This corresponds to reference species of [H9O4]+, H2O, and [H7O4]‒ at pH 0, 7 and 14 respectively † [cf. 538]. In all cases the ALLRED–ROCHOW electronegativity scale is used [466, 538]. The meanings of the remaining variables were explained in the discussion around Figure R1-5, and are summarised below. A single plot illustrating the implications of the above relations was presented for complexation of octahedral Al3+ by a single ‘foreign’ bidentate ion in Figure R1-6. Additional plots are provided here for a selection of conditions of interest. These explore the 0 and z, its valence), the co-ordination number (N), the influence of the cation (through χ M denticity (α), and the number of ‘foreign’ ions complexed per metal (m). It should be noted that calculations for fluoride and chloride ions assume aqueous solvation [see 466, 538]. The meaning of a denticity of zero is not obvious: HENRY, JOLIVET & LIVAGE [466] interpret it as o u t e r - s p h e r e c o m p l e x a t i o n . Trends for aluminium are presented first, in Figure S21-1. These illustrate the influence of α and N. The corresponding plots for iron(III) using the s a m e b a s i s look almost identical to Figure S21-1, so they are n o t presented here.

*

A more elegant formulation was given by JOLIVET [538].

†

Earlier formulations used just two reference species, yielding a single line for the entire pH domain: originally [H5O2]+ and H2O [466], and later revised to [H9O4]+ and H2O [see 538] — both at pH 0 and 7 respectively. The latter is fortuitously in good agreement at pH 14 with the presently adopted reference set [see 538], which is agreed [535] to be a more generally accurate approach. Appendix S21 : Metal Complexation by ‘Foreign’ Anions

947

D. I. VERRELLI

Instead alternative predictions for aluminium using an older basis, viz. using [H5O2]+ as the pH 0 reference species [see 466, 538], are presented in Figure S21-2 — this indicates the potential level of systematic bias in the predictions. 0 Plots for magnesium are given in Figure S21-3, illustrating the effect of χ M and z in comparison to Figure S21-1. Figure S21-4 illustrates trends for zirconium with increasing m. The results should be interpreted with caution, as JOLIVET [538] has warned that the model precludes precise 0 0 = χ Mg [466, 538], so the data with N = 6, α = 2 and m = 1 analysis for m ≠ 1. Note that χ Zr differs from the corresponding plot of Figure S21-3 only through the influence of z. As alluded to above, comparison of the plots shows that there is little influence of the cation 0 (through χ M and z) on predicted complexation behaviour. Despite JOLIVET’s [538] claim that “similar results” are obtained when using [H9O4]+ and [H5O2]+ as pH 0 reference species, comparison of Figure S21-1 and Figure S21-2 indicates that this is not the case. Although the trends are generally the same, some critical pH values are quite different. As a case in point, the three-species basis predicts ‘hydrolysis’ of bidentate chlorido complexes of Al or Fe(III) for pH < 2.3 or pH < 2.2 (N = 6) and ionic dissociation for pH > 8.7 or pH > 8.6 (N = 4), whereas in the original basis the respective critical values were 4.4 and 8.1 or 8.0. Smaller co-ordination numbers (N) tend to encourage ionic dissociation, except for highly electronegative ions of low protonation (e.g. NO3–); most of the ‘foreign’ ions cause a decrease in the mean electronegativity of the complexed precursor, and (for equal m) the contribution is more significant at lower N (for a given pH). Correspondingly ‘hydrolysis’ is discouraged in most cases; the exceptions are highly electronegative neutral salts (e.g. HNO3 and HF (aq)) at denticities above zero. However p h y s i c a l l y - a t t a i n a b l e ‘hydrolysis’ is predicted only for species like HCl (aq) with critical pH values above 0, according to the simple model: increasingly n e g a t i v e pH values might be interpreted approximately as decreasing thermodynamic favourability, or as a greater degree of certainty that ‘hydrolysis’ will n o t occur. It might be anticipated that the (inner-sphere) co-ordination number should not affect outersphere complexation: in fact the model predicts that this is only the case for f u l l y deprotonated anions. Lower denticity (α) generally leads to reduced likelihood of ionic dissociation or ‘hydrolysis’ — i.e. an increased likelihood of complexation. Exceptions are HCl (aq) and NO3–. For PO43– α is likely to be 3 or 4, while SO42– “generally” has α = 2, and smaller, simpler anions such as Cl– most probably have α = 1 [535, 538] [cf. 677, 831].

948

Appendix S21 : Metal Complexation by ‘Foreign’ Anions


Complexation

0 H2PO4

-7

2.50

HCl HC2O4– –

HSO4

–

NO3–

2.70

H2C2O4 H3PO4

-14

HF

H2SO4

HNO3

2.90

-21 -28

'Hydrolysis' 1.6

1.8

2.0

PO43–

14

2.4

2.6

2.8

3.0

SO4 C2O4–2– F Cl–

7 0 -7

Critical pH [–]

HPO42–

HCl

H2PO4–

HC2O4– HSO4

-14

H3PO4

–

NO3

2.70

–

H2C2O4 H2SO4

-21 -28

2.30

2.50

0 -7

q=0 q=1 q=2 q=3

F–

Complexation

2.90

HF HNO3

'Hydrolysis' 1.6

1.8

2.0

1.8

2.4

2.6

2.8

3.0

21

C2O42–

Critical pH [–]

Cl–

2.30

7

2.50

0 H2PO4–

-7

HCl HC2O4–

H3PO4

-21 -28

2.70

HSO4– NO3–

-14

2.90

H2C2O4 H2SO4

1.6

1.8

2.0

HF HNO3

'Hydrolysis' 2.2

2.4

2.6

2.8

3.0

Electronegativity of q -protonated anion [–]

3.2

2.10

q=0 q=1 q=2 q=3

0

Complexation

-7

2.30

2.50

H2PO4

HCl HC2O4– HSO4

–

NO3–

2.70

–

H2C2O4

2.90

HF

H2SO4 HNO3

-21 'Hydrolysis' 1.6

1.8

2.0

3.10

2.2

2.4

2.6

2.8

3.0

3.2

Al(III), N =4, α =0, m =1

28 PO43–

F–

Complexation

3.0

F–

H3PO4

3.10

3.2

21 SO42–


HPO4

14

2.8


q=0 q=1 q=2 q=3

Ionic

Cl–

HPO42–

-14

2.10

SO42– dissociation 2–

2.6

SO42– C2O42–

7

-28


21

2.4

Ionic dissociation

14

3.2

Al(III), N =6, α =0, m =1 PO43–

2.2

PO43–

Electronegativity of q -protonated anion [–] 28

2.0

3.10

Al(III), N =4, α =1, m =1

28

3.10

2.2

2.90

H2SO4


C2O42– Cl–

7

H2C2O4 HF HNO3

'Hydrolysis' 1.6

2.10

Ionic dissociation

2.70

-21

Critical pH [–]

SO4

14

2–

–

HSO4–

H2PO4–

-28


21

NO3

HCl HC2O4–

Complexation

H3PO4

3.2

Al(III), N =6, α =1, m =1 PO43–

2.50

HPO42–


28

2.30

2–

-14

3.10

2.2

Ionic dissociation

21


HPO42–

7

2.10

q=0 q=1 q=2 q=3

HPO42–

2.10

q=0 q=1 q=2 q=3

Ionic dissociation C2O42– Cl–

2.30

F–

7

2.50

0

Complexation

-7

H2PO4–

HCl 2.70

HC2O4– HSO4

–

NO3–

-14

2.90

H2C2O4

-21 -28

H3PO4

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

2.6

HF

H2SO4

2.8

HNO3

3.0


SO42– C2O42– F– Cl–

14

2.30

Critical pH [–]

Ionic dissociation

21

Critical pH [–]

q=0 q=1 q=2 q=3


PO4

Al(III), N =4, α =2, m =1

28

2.10

3–


Al(III), N =6, α =2, m =1

28

3.10

3.2


Figure S21-1: pH–electronegativity diagrammes for complexation of Al3+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively.


949

D. I. VERRELLI

2.3

SO42– HPO42–

7.0

C2O42– Cl–

2.4

F– 2.5

Complexation HCl

3.5

2.6

HC2O4–

H2PO4–

HSO4–

0.0

NO3–

2.7 2.8

H2C2O4

-3.5

H3PO4

H2SO4

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

HF

2.6

2.8

14.0

PO43–

10.5 7.0

3.2

Critical pH [–]

SO42–

10.5

HPO42–

7.0

q=0 q=1 q=2 q=3 q=4

2.1 2.2 2.3

C2O42– Cl–

2.4

F–

Complexation

3.5

2.5 HCl

2.6

HC2O4–

H2PO4–

2.7

– HSO4– NO3

0.0

2.8

-3.5 -7.0

H2C2O4

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

H3PO4 H2SO4

HNO3 HF

2.6

3.0

2.8

'Hydrolysis'

SO42–

Critical pH [–]

HPO42–

10.5 7.0 3.5

H2PO4–

0.0

q=0 q=1 q=2 q=3 q=4

2.2 2.3 2.4 2.5

HCl

2.6

HC2O4–

2.7

HSO4– NO3–

H3PO4

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

2.6

H2C2O4

2.8 HNO3

2.8

3.0

3.0

2.9

3.2

Al(III), N =4, α =1, m =1

2.0 q=0 q=1 q=2 q=3 q=4

Ionic dissociation

2.1 2.2 2.3

SO42– C2 O 4 HPO42–

7.0

Cl–

2–

2.4

F– 2.5

Complexation

3.5

2.6

HCl HC2O4–

NO3

–

2.7

HSO4–

H2PO4–

'Hydrolysis' 1.6

1.8

2.8

2.0

H3PO4

2.2

2.4

H2C2O4

HNO3 HF

H2SO4

2.6

2.8

3.0

2.9

3.2

2.9

3.2

Al(III), N =4, α =0, m =1

21.0

14.0

2.0 q=0 q=1 q=2 q=3 q=4

Ionic dissociation

17.5

SO42–

2.1 2.2 2.3

C2O42–

10.5

HPO4

7.0

2–

Cl–

2.4

F–

2.5

Complexation

3.5

2.6

HCl

2.7

HC2O4–

0.0

H2PO4–

HSO4

-3.5 -7.0


2.8

PO43–

10.5

-7.0

2.1

-3.5 -7.0

2.6

-3.5

2.0

F–

Complexation

2.4

2.8


C2O42– Cl–

2.2

0.0

Critical pH [–]

14.0

2.0

14.0

2.9


Ionic dissociation

1.8

H2SO4

H3PO4

17.5

3.2

Al(III), N =6, α =0, m =1

17.5

HF HNO3

H2C2O4

Electronegativity of q -protonated anion [–] 21.0

2.7

HSO4–

H2PO4–

21.0

2.0

Critical pH [–]

14.0

2.6

NO3–

HCl HC2O4–

1.6


Ionic dissociation

2.5


Al(III), N =6, α =1, m =1

17.5

2.4

HPO42–

Electronegativity of q -protonated anion [–] 21.0

2.3

Complexation

3.5

-7.0

2.2

SO4 C2O42– F– Cl–

-3.5

2.9

2.1

2–

0.0

HNO3

3.0

Ionic dissociation

17.5


10.5

-7.0

2.2

2.0 q=0 q=1 q=2 q=3 q=4

'Hydrolysis' 1.6

1.8

2.0

H3PO4

2.2

2.4

2.6

–

NO3–

2.8

H2SO4 H2C2O4 HF HNO3

2.8

3.0


Critical pH [–]

14.0

2.1

Critical pH [–]

Ionic dissociation


PO4

17.5

q=0 q=1 q=2 q=3 q=4

3–

Al(III), N =4, α =2, m =1

21.0

2.0


Al(III), N =6, α =2, m =1

21.0

2.9

3.2


Figure S21-2: pH–electronegativity diagrammes for complexation of Al3+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H5O2]+ and H2O at pH 0 and 7 respectively.

950



0

2.50

HCl HC2O4–

H2PO4–

HSO4

-7

H3PO4

-14

–

NO3–

2.70

H2C2O4 H2SO4

HF

2.90

HNO3

-21 -28

'Hydrolysis' 1.6

1.8

2.0

14

2.4

2.6

2.8

3.0

7

HPO42–

H2C2O4

-28

Critical pH [–]

Cl–

7

2.30

2.50

HCl HC2O4–

H2PO4–

HSO4– NO3

-7 -14

H3PO4

2.70

–

H2C2O4 H2SO4

-21

2.90

HF HNO3

'Hydrolysis' 1.6

1.8

2.0

2.4

2.6

2.8

3.0

HPO42–

7

Critical pH [–]

Cl–

2.30

F– 2.50

HCl

0

H2PO4–

HC2O4–

-14

2.90

H3PO4 H2C2O4 H2SO4

-21 -28

2.70

HSO4– NO – 3

-7

1.6

1.8

2.0

HF HNO3

'Hydrolysis' 2.2

2.4

2.6

2.8

3.0


Cl–

2.10

2.30

F–

HCl

Complexation

HC2O4–

H2PO4–

HSO4–

-7

NO3–

2.70

H2C2O4 H3PO4

2.90

HF

H2SO4

HNO3

'Hydrolysis' 1.6

1.8

2.0

3.10

2.2

2.4

2.6

2.8

3.0

3.2

Mg(II), N =4, α =0, m =1

28 PO43–

Complexation

7

3.2

q=0 q=1 q=2 q=3

SO42– C2O42–

-21

3.10

3.2

21 SO42–


C2O42–

3.0

2.50

0

-28


HPO4

14

2.8


q=0 q=1 q=2 q=3

SO42– dissociation

2–

2.6

-14

2.10

Ionic

21

2.4

Ionic dissociation

14

3.2

Mg(II), N =6, α =0, m =1 PO43–

2.2

21


2.0

Mg(II), N =4, α =1, m =1

28

3.10

2.2

1.8

3.10

PO43–

F–

Complexation

0

-28

q=0 q=1 q=2 q=3

SO42– C2O42–

2.90


Critical pH [–]

HPO42–

HNO3

'Hydrolysis' 1.6


14

HF

H2SO4

H3PO4

-21

2.10

Ionic dissociation

21

2.70

HSO4–

H2PO4–

-7

3.2

Mg(II), N =6, α =1, m =1 PO43–

NO3–

– Complexation HC2O4


2.50

HCl

0

2.30

SO42– C2O42– F– Cl–

-14

3.10

2.2

Ionic dissociation

PO43–


Complexation

2.10

q=0 q=1 q=2 q=3

HPO4

2.10

q=0 q=1 q=2 q=3

Ionic dissociation

2–

C2O42–

Cl–

2.30

F–

7

2.50

HCl

0

Complexation H2PO4–

-7

HC2O4–

2.70

HSO4–

NO3–

-14

2.90

H3PO4 H2C2O4 HF

-21 -28

H2SO4

'Hydrolysis' 1.6

1.8

2.0

HNO3

2.2

2.4

2.6

2.8

3.0


HPO42–

7

SO42– C2O42– F– Cl–

21

Critical pH [–]

14

2.30


Ionic dissociation

21

Critical pH [–]

q=0 q=1 q=2 q=3

Mg(II), N =4, α =2, m =1

28

2.10

PO43–


Mg(II), N =6, α =2, m =1

28

3.10

3.2


Figure S21-3: pH–electronegativity diagrammes for complexation of Mg2+ (co-ordination number = 6 or 4) by single ‘foreign’ anions of various types (denticity = 2, 1, or 0). The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively.


951

D. I. VERRELLI

F– 2.50

0

HCl HC2O4–

H2PO4–

– HSO4– NO3

-7

H3PO4

-14

2.70

H2C2O4 H2SO4

2.90

HNO3

-21 -28

HF

'Hydrolysis' 1.6

1.8

2.0

14

2.4

2.6

2.8

3.0

HPO42–

7

HC2O4– H2PO4–

-7

-28

HPO42–

0

Complexation

-7

H2PO4–

2.30

2.50

HCl HC2O4–

NO3– 2.70

HSO4– H2C2O4

-14

H2SO4

H3PO4

HF HNO3

2.90

-21 -28

'Hydrolysis' 1.6

1.8

2.0

'Hydrolysis'

2.4

2.6

2.8

3.0

14

0

HPO42–

C2O42– F– Cl– HCl

Complexation

-7

2.50

HC2O4– HF

2.70

HNO3

H2C2O4

H2PO4–

-14

H2SO4

-21 -28

2.30

NO3–

HSO4–

2.90

H3PO4

'Hydrolysis' 1.6

1.8

2.0

3.10

2.2

2.4

2.6

2.8

3.0


2.8

3.0

3.2

2.10

q=0 q=1 q=2 q=3

PO4

3–

2.30

Cl– SO42– F– C2O42–

2.50

NO3–

0

HPO42–

-7

HCl HC O – 2 4

2.70

HSO4–

Complexation

HFHNO 3 H2PO4–

H2C2O4

2.90

H2SO4

H3PO4

-21

'Hydrolysis' 1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.10

3.2

3.2

Zr(IV), N =6, α =2, m =3

28 q=0 q=1 q=2 q=3

21 14 Critical pH [–]

Critical pH [–]

SO4

2–

2.6

-28


PO43–

7

2.4


q=0 q=1 q=2 q=3

14

2.2

-14

2.10

Ionic dissociation

2.0

7

3.2

Zr(IV), N =8, α =2, m =3

21

1.8

Ionic dissociation


2.90

3.10

Zr(IV), N =6, α =2, m =2

21

3.10

2.2

HF

H2SO4 HNO 3

28

Critical pH [–]

Critical pH [–]

7

2.70


q=0 q=1 q=2 q=3

SO42– C2O42– F– Cl–

NO3–

H2C2O4

H3PO4

1.6


14

HSO4–

-21

2.10

Ionic dissociation

PO43–

2.50

HCl

0

3.2

Zr(IV), N =8, α =2, m =2

21

2.30

F–

Cl–

Complexation


SO42– C2O42–

-14

3.10

2.2

Ionic dissociation


Complexation

PO43–

2.10

q=0 q=1 q=2 q=3

Ionic dissociation

7

SO4

2–

Cl– F–

2.30

NO3– 2.50

C2O42–

PO43–

0 -7

HNO3

HPO4

-14

2.10

2–

HCl

Complexation

HSO4–

HF

2.70

HC2O4– H2C2O4

H2SO4

2.90

H2PO4–

-21

H3PO4 'Hydrolysis'

-28 1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0


Cl–

7

Critical pH [–]

SO42– C2O42–

HPO42–

2.30

21

Critical pH [–]

Ionic dissociation

21 14

q=0 q=1 q=2 q=3


PO43–

Zr(IV), N =6, α =2, m =1

28

2.10


Zr(IV), N =8, α =2, m =1

28

3.10

3.2


Figure S21-4: pH–electronegativity diagrammes for complexation of Zr4+ (co-ordination number = 8 or 6) by multiple ‘foreign’ bidentate anions of various types. The reference species are [H9O4]+, H2O, and [H7O4]− at pH 0, 7, and 14 respectively.

952



Increasing the number of ‘foreign’ ions complexed per metal (m) results in changes similar to increasing N: most of the critical pH values decrease, so there is an increased tendency toward ionic dissociation, and a decreased tendency toward ‘hydrolysis’, with the exceptions of HF (aq), NO3– and HNO3. Given the critical pH values for hydrolysis are often negative (except e.g. HCl (aq)), however, this tends to result in a reduced probability of complexation. This suggests a simple way of estimating the number of ‘foreign’ ligands at equilibrium. Thus, for Zr(IV) with N = 8 and α = 2 complexation by sulfate is predicted for ‒14 ( pH ( 13 when m = 1, ‒15 ( pH ( 11 when m = 2, ‒15 ( pH ( 8 when m = 3, ‒16 ( pH ( 6 when m = 4, and so on. If the system pH were neutral, then it would be predicted as a first estimate that each zirconium ion would be complexed by 3 sulfate ions, replacing 6 water molecules; only 4 water molecules are likely to be present at pH 6 (cf. Figure R1-3), though, and so each zirconium might rather by complexed by just two sulfates each [cf. 466].


Having seen the importance of the pH 0 reference species, it is worth including here also the older version of Figure R1-3. Figure S21-5 shows that the predicted hydrolysis ratio is moderately sensitive to the presumed “molecular entity” at pH 0 [cf. 538], with the greatest discordance at extremes of pH. (Negative values of h are taken as h = 0 [538].)

7

Al(III), N=6 Al(III), N=4 Fe(III), N=6 Fe(III), N=4 Mg(II), N=6 Mg(II), N=4 Zr(IV), N=8 Zr(IV), N=6

6 5 4 3 2 1 0 0.0

3.5

7.0

10.5

14.0

pH [–]

Figure S21-5: Prediction of the theoretical extent of hydrolysis (or deprotonation), h, for four different metals as a function of pH according to the partial charge model referenced to [H5O2]+ and H2O at pH 0 and 7 respectively [466, 675].


953

D. I. VERRELLI

S22. PSEUDOBÖHMITE STRUCTURE AND COMPOSITION BAKER & PEARSON [121] proposed that: [...] pseudoboehmite can be considered to be ultramicrocrystalline boehmite where all of the excess water is simply terminal water on the crystallite surfaces.

So pseudoböhmite is an aggregate of böhmite-like crystallites [121]. They elaborate [121]: [We] assume that the term, pseudoboehmite, includes every polymeric aggregate from Al2(H2O)4(OH)24+ to some relatively well crystallized boehmite with the exception of those aggregates having a bayerite or gibbsite like ordering of AlO6 octahedra. In practice the term [...] would include only those aggregates [...] large enough to precipitate from solution [...].

They [121] proposed a mechanism for formation of pseudoböhmite whereby Al(OH)x(H2O)y species undergo rapid condensation polymerisation to form dimers and trimers and ultimately moderately-long linear chains (similar to böhmite) that can also condense together; upon ageing the chains may convert to an annular structure (similar to gibbsite), which may also form if the original polymerisation occurs slowly. The molecular formula of the chains is (H2O)2–(AlO(OH))n–Al–(H2O)2, where n is not too large, so that the ‘extra’ Al and the terminal water groups have a significant effect on the overall ratio of water to aluminium [121]. An equivalent set of formulæ can be written down for the sheets comprised of a few of these chains [121, cf. 500]. The result is a ratio ranging from very hydrous values at low n to that of böhmite as n → ∞. For example, condensing 7 chains of four Al atoms each yields Al28(H2O)22(OH)28O28, or AlOOH·0.785H2O [121]. BAKER & PEARSON [121] found a range of water contents in the pseudoböhmite samples they studied, with a clear dependency on crystallite size (see Figure S22-1) and good agreement with theoretical predictions. Smaller crystallites imply larger ratios of external surface area to amount of crystallite, permitting greater proportions of physically-bound water to adsorb and increasing the importance of terminal chemically-bound water [121]. WANG et alii [1099] argued that the above results are strongly dependent upon the water vapour partial pressure during the drying operation: they found that the water content may vary continuously from about 42%m down to 15%m, or slightly less, as p(H2O) is decreased from its saturation value at 22°C. As shown, the pure chemical AlOOH contains 15.0%m water (referenced to corundum, Al2O3). WANG et alii [1099] found evidence for the capillary condensation [cf. 349] of water in “slitlike” mesopores of 2 to 50nm between platy particles of poorly crystalline böhmite (or pseudoböhmite).

954

Appendix S22 : Pseudoböhmite Structure and Composition


45 41% — Al(OH)3·0.5H2O

40

35% — Al(OH)3

Water content [%m ]

35 30

26% — AlOOH·0.5H2O

25 20

Chemical / Total Outlier Physical / Total Outlier Chemical / (Total – Physical) Outlier

15 10

15% — AlOOH 8.1% — Al2O3·0.5H2O

5 0 0

5

10

15

0.0% — Al2O3 20

Crystallite size [nm] Figure S22-1: Variation in physically- and chemically-bound water with pseudoböhmite crystallite size. (Data of BAKER & PEARSON [121].)

BAKER & PEARSON [121] discount the likelihood of two alterative models for the association of water in pseudoböhmite: • The average lattice expansion of 40 to 60pm, does not allow sufficient space for interlayer water molecules, which would require about 300pm [cf. 674, see also 677]; if interlayer water were sparsely distributed so as to achieve the same average spacing [cf. 312], then such trends of uniformly increasing hydration with the small crystallites observed would not be expected *. In fact, the observed lattice expansion correlates almost linearly with the ratio of peripheral water (repulsive) to OH (attractive). Furthermore, drying at 100°C under vacuum yielded a dry product that was still more hydrous than böhmite. • If pseudoböhmite had a defect structure involving cation (Al3+) vacancies, balanced by partial OH and O group protonation, the number of vacancies would be excessive. It is now accepted that pseudoböhmite is indeed made up of AlOOH double chains, along with some molecular water [504].

*

This does not preclude the existence of small amounts of locally-distributed interlayer water altogether. Appendix S22 : Pseudoböhmite Structure and Composition

955

D. I. VERRELLI

S23. OCCURRENCE OF IRON(II) In solid state or aqueous suspension ferrous species are “very sensitive” to oxidation [118, 536], and the +2 oxidation state of iron can generally be ignored in aqueous systems in equilibrium with the atmosphere [307] [cf. 462, 1095]. This matches the conditions typically found in a water treatment plant, where dissolved oxygen levels are raised due to increased turnover of the liquid surface. (Solids that have accumulated at the bottom of a clarifier, thickener, lagoon, et cetera can become anaerobic (or anoxic [668]) due to a combination of biological activity * and a lack of vertical mixing [480, 797]. Yet anaerobic or anoxic conditions do not guarantee reduction [see 633] [cf. 677].) In the present work the observation of ferrihydrite formation (§4▪2) supports the contention that — at least initially — iron is (practically) all present in the +3 oxidation state [466, 674] [cf. 538, 1053]. Nevertheless, reducing conditions may be relevant to sludge storage and analysis in the laboratory. MENG et alii [740] found that dissolved oxygen (DO) levels in ferric sludge samples stored in closed containers with minimal headspace very quickly dropped to around 0.5mg/L after 2 days. The anoxic conditions they found in their samples and in sludge dewatering ponds on site were such that at equilibrium all precipitated Fe(III) species would have been converted to Fe(II) species [740]. However, the transformation was very slow, so that after 80 days less than 25% of the iron in ‘fresh’ sludge had undergone the reduction, and the proportion in sludge after about 1 year of ponding was about 50% [740]. Preliminary experiments were carried out to measure the electrochemical potential, E, of a ferric sludge sample to determine the likelihood of Fe(III) being reduced to Fe(II). The sample chosen was of low pH (5.1) and had been stored (settling) for 2½ months in a glass cylinder sealed with Parafilm M (Pechiney Plastic Packaging, Wisconsin, U.S.A.), which was expected to represent the most reducing conditions [cf. 147, 775, 848] — albeit that the dose was high (160mg(Fe)/L), and it would have been biologically inactive. This yielded values of E from +400 to 450±10mV with respect to the standard hydrogen electrode. Partially neutralising the mixture to pH 6.4 gave E = 370±10mV. These conditions appear to approach reduction at equilibrium [cf. 480], but remain in the stable crystalline Fe(III) region [147, 848]. Organic species present can form complexes, altering the equilibria, and here the solid phase is unlikely to be crystalline; kinetic effects are likewise unaccounted for [775, 848]. As there is no observed or published evidence of WTP ferric sludge being reduced under ambient conditions, it can be concluded that only Fe(III) species are important in the present work. The exception to this is where biological activity causes reduction [394]: this produces an obvious change in appearance [480] beyond that encountered in the present work.

*

956

Prompted by either greater amounts or greater biodegradability of organic matter in the raw water (and hence sludge) [480]. Appendix S23 : Occurrence of Iron(II)


S24. RELATIVE STABILITY OF HÆMATITE AND GOETHITE The relative stability of hæmatite and goethite has been a considerably controversial topic, and there are certain conditions under which hæmatite formation may be favoured * [280, 633, 634]; nevertheless, goethite is expected to be the most stable species in conditions relevant to the present work. DIAKONOV et alia [307] claimed that, although hæmatite is not stable with respect to goethite below 100°C, “no cases of hæmatite to goethite transformation have ever been reported in the literature” [see also 306]. One interesting correlation of the relative stability of goethite and hæmatite (in terms of the GIBBS energy) is in terms of particle size. LANGMUIR [633, 634] derived a relationship which suggested that [280]: • Goethite particles are generally more stable than hæmatite particles if the goethite particles are larger. • When the particles are the same size, goethite particles are more stable above 0.08μm. • If (initially) the goethite particles are < 1μm and the hæmatite particles are [ 1μm, then the goethite particles are more stable for (goethite) particle sizes greater than about 0.15μm. The above results, which were charted by LANGMUIR (1971), can be closely reproduced by using the proposed apparent thermodynamic values of DIAKONOV et alia (1994), as in the graph below [280]. Note that the conclusions to be drawn are highly sensitive to the chosen values of s o m e of the parameters — for example, specifying ΔfG°298 = ‒490 instead of ΔfG°298 = ‒492.1kJ/mol for goethite leads to an asymptotic (i.e. bulk crystal) value of ΔG°298 = ‒2.2kJ/mol for the reaction, rather than +2kJ/mol. The above figures were based on the surface enthalpies of goethite and hæmatite being 1.55 and 1.1J/m2 [280], while the surface entropies were estimated (by analogy to similar metal oxides) to be of order 0.5mJ/m2.K [306]. Using the larger surface enthalpies of FERRIER (1966) — 1.25 and 0.77J/m2 , respectively [306] — leads to no significant change in the curves in Figure S24-1 (i.e. relative stabilities) for particle sizes down to about 0.1μm. Even at such very small particle sizes where the quantitative results change, qualitatively there is no significant change, and in any case the uncertainty due to surface morphology becomes more important in that range, rendering any of these results only of qualitative value [306]. In theory the computations should include the GIBBS energy of mixing [see 977]. However in the present case this appears to be a negligible effect.

*

A statement of GARRELS is helpful [280]: If one assemblage of phases differs from another by a free energy change of ca. 8 kJ mol‒1 or less, either assemblage may form or exist.

Of course, the GIBBS energies generally reported refer to standard conditions, which may be quite different to the prevailing sample conditions. Appendix S24 : Relative Stability of Hæmatite and Goethite

957

D. I. VERRELLI

Gibbs energy change, ΔG °298 [kJ/mol]

20 15 10 5 0 -5 -10 -15 -20 Gt >> 1μm Gt = Hm Hm >> 1μm

-25 -30 0.01

0.1

1

Particle size (side of cube) [μm]

Figure S24-1: Influence of particle size on the relative stability of hæmatite (Hm) and goethite (Gt) in the (hypothetical [280]) reaction 2Gt → Hm + H2O at 298K [cf. 633, 634]. Negative values imply the presence of hæmatite is favoured. Thermodynamic data used: GIBBS energies: Gt: ‒492.1kJ/mol (bulk), 1.4J/m2 (surface); Hm: –744kJ/mol (bulk), 0.95J/m2 (surface); H2O: ‒238.2kJ/mol. (Data of DIAKONOV et alia [306] and others [280]*.)

In the foregoing the particles were modelled as smooth cubes. Of course, this is a simplification of the true state. For a start, the particles typically have aspect ratios markedly different from unity [280, 306]. For another thing, the size of the particles can change with time, and evidence suggests that goethite, for example, initially forms as “badly shaped microporous crystals with serrated edges and other surface defects” (implying a high surface area) and over time the specific surface area can decrease by a factor of 3 or more [306]. The specific surface area also decreases with the temperature at which the ageing occurs [306]. (Note: no evidence of such dependencies for hæmatite was observed [306].) Furthermore, the simple geometrical estimates of surface area can still underpredict the true surface area of even the aged material by a factor of up to 3 [306]. An additional complication is the possible variation in properties among crystallographic faces [633], not to mention defects and complexation, [370, 537, 538] which are not treated here. It should be noted that direct experimental evidence for the dependence of solubility upon particle size is not available for goethite or hæmatite [280, 633].

*

958

The GIBBS energy for water is ostensibly taken from WAGMAN et alia (1982) [1094], but actually differs slightly in value: the original source suggests a slightly greater stability of goethite over hæmatite. Appendix S24 : Relative Stability of Hæmatite and Goethite


According to CORNELL & SCHWERTMANN (2003) [280] neither the transformation from goethite to hæmatite under ambient conditions nor the reverse transformation has been experimentally observed, regardless of crystal size [see also 633]. Yet WEIMARN & HAGIWARA (1926) [1109] reported rudimentary evidence for transformation from goethite to hæmatite following intensive grinding; while the sample temperature may have been elevated above the nominal room temperature, it seems unlikely to have risen to levels over 100°C (unless on a local nanoscale), as usually required for the transformation. The same type of analysis has been applied to predict the influence of particle size upon the solubility product of goethite and of hæmatite [280]. The influence is significant, as the surface GIBBS energies of these two materials are relatively high [280]. This also lays a foundation for ‘OSTWALD ripening’ (§R1▪2▪4▪5), where the lower stability of smaller particles leads to their transformation into larger particles (via solution) [280, 538]. In practice, specific adsorption can modify the surface energies, and so change the position of equilibrium in OSTWALD ripening or other ‘ageing’ processes [538].

Appendix S24 : Relative Stability of Hæmatite and Goethite

959

D. I. VERRELLI

S25. CORRELATIONS OF dmax The empirical correlation dmax = м G–ш was introduced in §R1▪4▪4▪2 as equation R1-9.

[S25-1]

While consideration of м is important, comparisons are difficult due to variability between experimental conditions and means of characterising aggregate size [523] and shear field. Also, values may vary wildly if ш changes only moderately [e.g. the data of 960]. The analysis of PARKER, KAUFMAN & JENKINS [819] suggested ш = 1 for dagg / dKolmogorov, and ш = 2 for dagg [ dKolmogorov for colloidal aggregates, but ш ( 0.5 for filamentous flocs. (In experimental analysis they [819] substituted dKolmogorov directly for dKolmogorov.) TAMBO & HOZUMI [996] derived theoretical expressions of ш for colloidal aggregates as follows (adapted using the definitions of Df [see also 997] and G): • for dagg ( dKolmogorov , ш = 3 / (6 – Df), so that ш ≈ 0.67 to 0.75 for their suggested Df from ~1.5 to 2.0 for WTP flocs; • for dagg [ dKolmogorov , ш = 2 / (4 – Df), so that ш ≈ 0.8 to 1.0 for their suggested Df. BACHE et alia [116] derived a theoretical expression of ш for colloidal aggregates as follows (adapted using the definition of G and their approximate equality for Df):  d0 − Df / ( 3 − Df ) G −1 / ( 3 − Df ) , dmax ∝ [S25-2] which incorporates a s m o o t h dependence upon dKolmogorov (as this can be written as a function of G). For their suggested Df ≈ 1.0 to 1.2 for aggregates generated by alum coagulation of low-turbidity, coloured water [116] this implies ш ≈ 0.50 to 0.56. Experimentally they estimated ш = 0.44 in the range 50s–1 ≤ G ≤ 230s–1 [116]. BACHE & RASOOL [114] obtained ш = 0.44 to 0.64 for flocs from six WTP’s running DAF (dissolved air floatation) processes, and 0.81 for another plant with high-alkalinity raw water. Under laminar flow conditions reported values of ш include 0.2 and 0.5 [763]. Experimental values in turbulent flow range from 0.30 to 1.7, but more commonly fall in the range 0.4 to 0.8 [763, 776]. NEEßE et alii [776] stated that predominantly laminar flow, including the dissipation range of turbulent flow, theoretically yields ш = 1.0, while in the inertial subrange ш = 2.0 is obtained [cf. 819]. MÜHLE and colleagues [763, 776] derived the correlations in Table S25-1.

960

dmax Appendix S25 : Correlations of dmax


Table S25-1: Floc breakage correlations of MÜHLE and colleagues [763, 776].

Lengthscale Name

Mechanism

Correlation a

Range

Laminar flow

 d0 −1 G −1 Particle erosion dmax ∝ N/A

N/A Cluster erosion

 dmax ∝

 2 − Df   4−D d0 f

   

 −1   4−D G f

   

Turbulent flow  d0 −1 G −1 Particle erosion dmax ∝

“Viscous subrange”

dagg / dKolmogorov ( 3 Cluster erosion

Laminar subrange of “transition range”

3 ( dagg / dKolmogorov ( 7 Floc splitting

Turbulent subrange 7 ( dagg / dKolmogorov ( 58 Floc splitting of “transition range” “Inertial subrange”

dagg / dKolmogorov T 58

Floc splitting

 dmax ∝

 2 − Df   4−D d0 f

   

 −1   4−D G f

 dmax ∝

 −2   5−D d0 f

   

 7 − Df   −  2 ( 5 − Df )  G 

 dmax ∝

 −2   4−D d0 f

   

 6 − Df   −  2 ( 4 − Df )  G 

 dmax ∝

 −6   11 − 3 D f d0

   

   

b

b

 17 − 3 Df   −  2 ( 11 − 3 Df )  G 

b

Note a The correlations displayed here assume no variation of bond strength with either d0 or G — see text. b The correlations have been r e - d e r i v e d from NEEßE et alii [776], but equating their exponent, k, to approximately 3 – Df, given their result (for d / dagg) that φagg ≈ (d/dagg)k – (d/dagg)2k [see also 763].

In Table S25-1 the derived dependence upon the strength of individual bonds has been omitted, although — based on the theoretical work of DERJAGUIN [301] — it was presumed that this adhesive strength would vary in direct proportion to d0 [776] *. Such presumption cannot be accepted uncritically [see 116]; the derivation of DERJAGUIN [301] is, itself, only strictly valid in a limited range of cases, including the occurrence of failure in a purely tensile mode (i.e. with the applied forces acting collinear with the symmetry axis through each doublet) [1084]. Note that the correlations for turbulent flow in Table S25-1 reduce to those of the laminar case at the smallest lengthscales [776] [see also 613, 763] [cf. 469]. For aggregates larger than dKolmogorov the derivation follows BABENKOV (1981) in setting the constituent ‘cluster’ size equal to dKolmogorov [776]. It may be mentioned that the erosion processes can be expressed in terms of a hypothetical ‘surface tension’ of the aggregate [763, 776]. It is unclear which conditions favour erosion and which favour breakup [776].

*

The same proportionality is obtained by supposing that the bond strength is proportional to the surface area between two spheres in which the local separation is less than a critical distance; the area of a spherical cap then varies directly with radius. dmax Appendix S25 : Correlations of dmax

961

D. I. VERRELLI

MÜHLE [763] claimed — indirectly — that Df ranges from 2.00 (for cluster–cluster aggregation) to 2.33 (for particle–cluster aggregation) or even higher (in case of “mechanical floc densification”) *. These data are outdated: one is based on a 1963 paper [see 763]. Rather than the tabulated data inspiring confidence for thoroughness, they elicit scepticism due to the suspiciously precise specifications of turbulence ranges — or lengthscales — and the corresponding variation of the “constant” exponents. The derivation also curiously blends assumptions of homogenous and (implicitly) fractal arrangement of primary particle within aggregates [see 763, 776]. Experimental support is also incomplete [469, 776] [cf. 763]. TOMI & BAGSTER (1978) derived a theoretical formula describing “the ratio of pressure fluctuations over a floc due to [inertia] effects and those due to viscous effects” (cf. Re), equal to 2.7 (d/dKolmogorov)2/3 [368]. FRANÇOIS [368] suggested that viscous effects (ratio values ( 1.2) would tend to promote floc erosion, while inertia would tend to promote fragmentation — although “in many cases” the two mechanisms occur simultaneously [see also 110, 523]. Physically the erosion has been attributed to tangentially-acting shear stresses occurring on lengthscales smaller than dKolmogorov (perhaps predominating for dagg < dKolmogorov), whereas fragmentation has been attributed to normally-acting tensile stresses occurring on lengthscales larger than dKolmogorov (perhaps predominating for dagg > dKolmogorov) [see 110, 523] — although even ‘shear’ stresses may translate to tensile forces on the microscale of interparticle bonds. (JARVIS et alia [523] note that conclusions such as these are “open to debate”.) KOBAYASHI, ADACHI & OOI [581] considered floc breakup ensuing from viscous shear for dagg ( dKolmogorov, and from dynamic pressure fluctuation for dagg [ dKolmogorov. Nevertheless, their [581] simple model of aggregate strength, which emphasised the average co-ordination number for clusters, predicted ш = 1/2 for b o t h cases; this was supported by experimental results. VAN DE VEN & HUNTER [1069] suggested that ш ≈ 1.0 when aggregate size is controlled by capture efficiency limitation on growth, and ш ≈ 0.3 when a dynamic balance between aggregation and rupture exists. For a wider range of materials OLES [799] cited values of ш from 1 to 2.7, while he fitted his own data † on aggregated polystyrene spheres to a straight line — although forcing power fits yields negative exponents of about 0.6 to 0.7. This is reasonably consistent with the hypothesis that the KOLMOGOROV turbulence microscale controls aggregate break-up, as dKolmogorov varies according to G–0.5 (see equation R1-11) [114]. SPICER & PRATSINIS [960] claimed consistency with the foregoing work [799], although in fact forcing power-law fits yielded estimates of ш increasing from ~0.2 to 1.0 as G increased from 63 to 129s–1. Nonetheless, all quoted “average steady state floc length” observations were smaller than dKolmogorov [960]. In a separate paper SPICER & PRATSINIS (1996) reported ш = 1.6 [1018].

*

The earlier publication with NEEßE and IVANAUSKAS [776] implied reported Df values from 1.5 to 2.84.

†

The median size was presented, rather than the maximum, as the median is a more “robust” parameter [799].

962

dmax Appendix S25 : Correlations of dmax


Fitting the turbulent flow data * of SERRA, COLOMER & CASAMITJANA [921] to equation R1-9 yielded values of ш from 0.7 to 1.1; an exponent of –ш = –1 was associated with a surface erosion mechanism of breakup. Primary particle size had no significant effect on the stable aggregate size [921]. The data of GORCZYCA & GANCZARCZYK [413] imply ш = 0.32 for alum coagulation flocs. SONNTAG & RUSSEL [953] effectively found ш = 0.35 for aggregates of polystyrene particles in their ‘spiked shear’ experiments. FRANÇOIS [367] claimed that different ш values could be distinguished for the large aggregates and the component clusters, with the latter, smaller elements allegedly more susceptible (higher ш) to shear. Further, ш was reported to universally decrease upon ageing for the large aggregates, from ~0.5 to ~0, but to generally increase (after an initial decrease, from ~0.8), from ~0.4 to >0.7, for the constituent clusters for alum flocs [367]. The dubious statement was also made that the large aggregates would reform larger than their initial size following the application of shear [367] — not consistent with the other literature. Several of the foregoing results used models to predict floc strength as a function of size. In the real world, “it is most unlikely that there is a unique correlation between strength and floc size” [115]. Through an “idealised” force balance BACHE et alia [116] derived a relationship between aggregate size, d, and “average strength per unit area at the plane of rupture”, σ: ρ 5 / 4 ε3 / 4 d σ = L 1/ 4 [S25-3] μ — of course, the area must vary with d2. Although the decrease in aggregate size with increasing G is regularly linked to the idea of small aggregates being ‘stronger’, as they are able to ‘withstand the greater stresses’, the above equation posits a c o n t r a r y relationship where strength i n c r e a s e s with increasing aggregate size [see 111]. While there may be flaws in the derivation, the departure from the common conception that ‘small aggregates persisting at large G must be strong’ [cf. e.g. 523, 524] is eminently defensible, as the small particles are exposed to significantly lower stresses. Furthermore, the statement is supported by the argument of GREGORY [429], who stated that higher bond densities imply stronger structures, and a stronger aggregate will grow to a larger size, which may ultimately be quite porous due to the inverse relationship between size and concentration of solids for fractal objects. In an earlier paper BACHE & HOSSAIN [111] concluded that 2 log (ε2 / ε1 ) ‒0.24 ( ( ‒0.07. [S25-4] 3 log (d2 / d1 ) so that larger aggregates rupture at lower rates of energy dissipation per unit volume, ε ρ [111]. (Note that by converting from an intensive property to an extensive property, E ∝ ε ρ d3, it can be shown that for rupture the a m o u n t of energy dissipation per unit time would be l a r g e r for a larger floc size.)

*

The median size was presented, rather than the maximum. dmax Appendix S25 : Correlations of dmax

963

D. I. VERRELLI

S26. ESTIMATION OF G FOR INDUSTRIAL SCENARIOS §R1▪4▪4▪1 presents formulæ for computation of G in the general case, with emphasis on stirred tanks. Here formulæ and representative calculations are presented for a range of other scenarios encountered on WTP’s.

S26▪1

Mixing in pipes

Static mixers are passive elements that achieve mixing of fluid ‘packets’ by promoting turbulence and the formation of eddies. These usually comprise highly structured elements through which the fluid must take a tortuous path. However the simplest mixer of all consists of turbulent flow in an unrestricted pipe (laminar flow may also be used, in the laboratory) [518]. A disadvantage is that G cannot be controlled independently of the flowrate. Furthermore, at practical industrial flowrates G is often rather high (e.g. 80s–1) and a long pipe (of order 102m) would be required to obtain conventional detention times [518].

S26▪1▪1

Theory

Substitution of the power * and volume into equation R1-5b yields an expression for G in terms of known parameters [415, 518]: 3 2 ρL f v ρLV ⋅ g Hloss P/V = = G= , [S26-1] η η (π D 2 L / 4) ηD where V is the volumetric flow rate, Hloss is the frictional head loss, D is the pipe diameter, and f is the FANNING friction factor defined by f ≡ Hloss g D / 2 v 2 L, with v the time- and area-averaged fluid velocity [154, 518]. The FANNING friction factor can be obtained from charts (MOODY diagrammes) or correlations as a function of the REYNOLDS number and the relative roughness (the ratio of ‘average’ surface roughness to diameter), e ≡ e / D. Although flexible plastic or polymer tubing is often assumed to be perfectly smooth, it is likely to have a non-zero roughness of order e = 10–2 to 10–3mm (say 0.003mm) [357]. Tubes used in this work had diameters of order D = 100 to 101mm, so this level of roughness can still be significant, depending on the REYNOLDS number. A suitable correlation for f in the turbulent regime with rough pipes is that of HAALAND (1983) [154]:

*

DELICHATSIOS & PROBSTEIN [299] used an alternative expression for the rate of energy dissipation, intending to better capture the properties of the turbulent core; this yields: G=

964

2 ρL f

3/2

ηD

v

3

.

Appendix S26 : Estimation of G for Industrial Scenarios


 6.9  e  10 / 9  1 = − 3.6 log 10  +  , Re 3 . 7 f    

[S26-2]

accurate to ±1.5% for 4×103 < Re < 108 and 0 < e < 0.05. Using the indicative values above suggests e is of order 10–3, so the effect on f will be significant for Re > 104. In the present work equation S26-2 was used for Re > 2100, and the laminar regime limit of f = 16/Re for lower REYNOLDS numbers. The HAALAND correlation is appropriate for NEWTONian fluids. The fluids studied in this work are non-NEWTONian: the sludge is composed of fractal aggregates that may rupture under shear, affecting (lowering) the viscosity, and it has a yield stress at sufficiently high solidosity (i.e. above φg); flocculants added comprise polymers that may have viscoelastic rheology and may contribute to drag reduction. E l a s t i c characteristics can increase the (METZNER & REED) threshold Re value for transition to turbulent flow by a factor of up to ~5 [1043], but the deviation is likely to be negligible in the present systems. The existence of a y i e l d s t r e s s tends to decrease f, but the effect is small provided the prevailing shear yield stress is small compared to the shear stress at the wall — which is a good assumption for the present materials, especially in turbulent flow [see 1043]. S h e a r t h i n n i n g behaviour, as encountered with solutions of high-molecular-mass polymers, likewise leads to a decrease in f (according to power-law models) [see 1043]. D r a g r e d u c t i o n is associated with the addition of “extremely low” concentrations * of (‘elongatable’) high-molecular-mass polymers to a NEWTONian fluid [1043] (such as water), or the presence of other “rod-like” objects such as surfactants or fibres [1046]. Again this can lead to significant decreases in f, but neat alignment in flow for the present system seems unlikely [cf. 345, 491, 1043, 1046].

S26▪1▪2

Laminar flow

GREGORY [427] discussed the mean shear rate applicable to laminar flow in pipes — i.e. POISEUILLE flow — based on the work of ROBINSON, SAATCI & OULMAN. Derivations by standard methods [cf. 154, 847] lead to the following ‘local’ results [427]: 2

 v   r    = 1 −   ,  vmax   rmax   rmax   r    , γ  =  2v  max   rmax  1 1  v max  t = = ,  2  L  (v / v max ) 1 − (r / rmax )  rmax  (r / rmax )     2 L  ( γ t ) = 1 − (r / r )2 , max   in which the terms in parentheses are dimensionless.

*

[S26-3] [S26-4] [S26-5] [S26-6]

For ~6×106g/mol poly(1-carbamoylethylene) observations of drag reduction span at least 20mg/L [1046] to 2g/L [345]. Appendix S26 : Estimation of G for Industrial Scenarios

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A useful summary of these equations is presented in Figure S26-1. The ‘importance’ of fluid at a given radial location increases with local velocity, because this increases the amount of this material exiting the pipe over a given run time [cf. 228], and as r/rmax increases, because elements are summed azimuthally [cf. 427].

r /r max

1

0

1 Velocity (v) Time (t) v.r/́V (Importance)

Shear strain rate (́γ) ́γ.t ́γ.t × v.r/́V (Contribution) Mean{ ́γ.t }

Figure S26-1: Representative profiles for key variables (taken as dimensionless in the plot) related to the shear imposed on fluid elements in lamin ar pipe flow. The ‘importance’ and ‘contribution’ have been weighted by azimuthal summation, and have been shifted rightward for clarity. The indicated ‘mean’ takes this weighting into account too.

When assessing turbulent pipeline flow the integral energy dissipation is calculated to find G (see equation S26-1), and then the (mean) residence time, t, is found by assuming plug flow. A more rigorous analysis including the variation of the local time-averaged velocity, v , with r could be carried out for turbulent flow in a similar fashion [cf. 228]. For laminar flow G can be exactly derived using standard techniques [cf. 154, 847] as [cf. 427]: v v G = 2 max ≈ 1.414 max , [S26-7] rmax rmax where the use of the parameter G implicitly indicates an integral (i.e. mean) quantity. In comparison the average shear strain rate for the exiting fluid is: v 4 vmax γ = ≈ 1.333 max , [S26-8] 3 rmax rmax which is approximately 6% less than G [cf. 427]. Note that the m e a n velocity is CvD = vmax / 2; the volumetric flowrate is just V = π (r ) 2 v /2. max

max

The mean residence time is: 2L t = . vmax It can also be demonstrated that [427]: 8 L . γ . t = γ . t = 3 rmax

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[S26-9]

[S26-10]


Hence the foregoing equation S26-1 can be applied to both laminar and turbulent pipe flow, provided it is recognised that this computes a characteristic velocity gradient, mathematically distinct from the integral shear strain rate.

S26▪2

Fluidised bed (floc blanket clarifiers)

For a fluidised bed the drag force on the particles is equal to their buoyant weight, and the power may be obtained by multiplying this by the superficial fluid velocity, v, [518], viz.: φ Δ ρS g v P/V . [S26-11] G= = η η IVES [518] gives indicative values for the variables in equation S26-11, except making the substitution φ ΔρS = φ Δρagg, where φ ≡ (φ/φagg) is the ‘apparent’ solidosity: G ~ [(0.15) × (5kg/m3) × (9.8m/s2) × (0.55×10–3m/s) / (0.001Pa.s)]0.5 ~ 2s–1 . This exemplifies the much lower shear in this type of unit (typically less than 5s–1) compared to conventional paddle mixers, [518]. A mean residence time of 20 to 30min gives G.t ~ 3×103, which seems low, however the apparent solidosity leads to φ.G.t ~ 450 which is in the recommended range [518]. The performance can be further enhanced by dosing ‘ballast’ material (see §8▪3▪5) into the system to increase the particle concentration [518].

S26▪2▪1

Settling

One could also use equation S26-11 to estimate the shear rate experienced by the sample in typical batch s e t t l i n g tests carried out in the present work. For alum sludges the settled bed mean solidosities were generally of order 0.0025, and the cylinders were loaded at solidosities around 0.0010. Typical initial (hindered) settling rates in the present work ranged from 5×10–7 to 5×10–6m/s, so 1×10–6m/s is a representative value. This gives: G ~ [(0.001) × (1500kg/m3) × (9.8m/s2) × (1×10–6m/s) / (0.001Pa.s)]0.5 ~ 0.1s–1 , which is exceedingly low. Of course, the time and solidosity are considerably higher here than in typical aggregation scenarios, say t ~ 2×104s or more, so that G.t ~ 2×103, and φ.G.t ~ 3 (accounting for changing φ). These values are also below those encountered in conventional coagulation and flocculation operations [518].

S26▪3

Flow through deep bed filters

It is possible to use the shear arising as a fluid stream passes through a deep bed filter to facilitate particle aggregation [518]. In this case a formula such as the KOZENY–CARMAN equation [518] or ERGUN equation may be used to estimate the head loss per unit depth, which can be substituted into equation S26-1. For example, using the KOZENY–CARMAN equation yields [518]: V ρL g Hloss 180 v 2 φ 2 13.4 v φ P/V . [S26-12] G= = = ≈ 2 2 4 (1 − φ) D (1 − φ )2 D η η (1 − φ )(π D L / 4) in which v is the superficial fluid velocity.


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For conventional rapid sand filtration we may expect v = 5m/h ≈ 0.0014m/s, φ = 0.6 and D = 0.5mm, giving G = 140s–1 [518].

S26▪4

Filtration

G was estimated by NOVAK & LYNCH to be as large as 500s–1 for vacuum filtration [576] (typically Δp ≈ 50 to 70kPa). G.t has been estimated at ~30000 for a “pilot filter press” and ~10000 for a belt press at a WWTP [789]. For flocs a better estimate might be obtained using φ rather than φ.

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